The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of CH 4 is 0 .175 atm and O 2 is 0 .250 atm . Concept introduction: Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone. Partial pressure of a gas in terms of its mole fraction and total pressure is, ` P A = χ A × P TOTAL A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture. The number of moles of molecule can be find out by using its mole fraction, numbers of moles of molecule A (n A ) = molecule fraction of A, ( χ A ) × total number of moles Number of grams of a substance from its number of moles is, Number of moles × Molecular mass in grams = Number of grams Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation. According to ideal gas equation, Total number of moles = Total pressure × Volume R × Temperature To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

Question

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Answer 1

Question

Chapter 5, Problem 89E

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

a)

Expert Solution

Answer to Problem 89E

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

Explanation of Solution

To find: the mole fractions of $CH4$ and $O2$ in the given mixture if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

The partial pressure of $CH4$ is given as $0.175 atm$

The partial pressure of $O2$ is given as $0.250 atm$ .

Therefore, the total pressure of the mixture is,

$0.175 atm + 0.250 atm = 0.425 atm$

Equation for finding mole fraction from partial pressure and total pressure is,

$χA = PAPTOTAL$

Therefore,

The mole fraction of $CH4$ is,

$χCH4 = 0.175 atm0.425 atm = 0.412$

The mole fraction of $O2$ is,

$χO2 = 0.250atm0.425 atm = 0.588$

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

b)

Expert Solution

Answer to Problem 89E

Total number of moles of gas in the mixture is $0.161 mol$ .

Explanation of Solution

To find: the total number of moles of gases in the given mixture.

The total number of moles of gases in the given mixture is $0.161 mol$ .

The total pressure of gases presented in the mixture is given as $0.425 atm$ .

The volume of flask is given as $10.5 L$ .

The temperature of flask is given as $65oC = (273+65) K = 338 K$ .

The total number of moles of gas in the mixture is determined by using ideal gas equation According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

Therefore,

The total number of moles of gas in the mixture is,

$Total number of moles = 0.425 atm × 10.5 L 0.08206 L atm/ K mol × 338 K = 0.161 mol$

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

c)

Expert Solution

Answer to Problem 89E

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

Explanation of Solution

To find: the number of grams of $CH4$ and $O2$ in the given mixture.

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

The mole fraction of $CH4$ is calculated as $0.412$ .

The mole fraction of $O2$ is calculated as $0.588$ .

The total number of moles of gases in the given mixture is calculated as $0.161 mol$ .

The number of moles of molecule can be find out by using its mole fraction,
Equation for finding number of moles,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Therefore,

-The number of moles of $CH4$ is,

$nCH4 = 0.412 × 0.161 mol = 6.63 × 10-2 mol$

-The number of moles of $O2$ is,

$nCH4 = 0.588 × 0.161 mol = 9.47 × 10-2 mol$

The number of grams of a substance is determined from its number of moles is,
Equation for finding number of grams is,

$Number of moles × Molecular mass in grams = Number of grams$

-The number of grams of $CH4$ is,

$6.63 × 10-2 mol × 16 g = 1.06 g$

-The number of grams of $O2$ is,

$9.47 × 10-2 mol × 32 g = 3.03 g$

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Answer 2

Question

Chapter 5, Problem 89E

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

a)

Expert Solution

Answer to Problem 89E

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

Explanation of Solution

To find: the mole fractions of $CH4$ and $O2$ in the given mixture if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

The partial pressure of $CH4$ is given as $0.175 atm$

The partial pressure of $O2$ is given as $0.250 atm$ .

Therefore, the total pressure of the mixture is,

$0.175 atm + 0.250 atm = 0.425 atm$

Equation for finding mole fraction from partial pressure and total pressure is,

$χA = PAPTOTAL$

Therefore,

The mole fraction of $CH4$ is,

$χCH4 = 0.175 atm0.425 atm = 0.412$

The mole fraction of $O2$ is,

$χO2 = 0.250atm0.425 atm = 0.588$

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

b)

Expert Solution

Answer to Problem 89E

Total number of moles of gas in the mixture is $0.161 mol$ .

Explanation of Solution

To find: the total number of moles of gases in the given mixture.

The total number of moles of gases in the given mixture is $0.161 mol$ .

The total pressure of gases presented in the mixture is given as $0.425 atm$ .

The volume of flask is given as $10.5 L$ .

The temperature of flask is given as $65oC = (273+65) K = 338 K$ .

The total number of moles of gas in the mixture is determined by using ideal gas equation According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

Therefore,

The total number of moles of gas in the mixture is,

$Total number of moles = 0.425 atm × 10.5 L 0.08206 L atm/ K mol × 338 K = 0.161 mol$

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

c)

Expert Solution

Answer to Problem 89E

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

Explanation of Solution

To find: the number of grams of $CH4$ and $O2$ in the given mixture.

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

The mole fraction of $CH4$ is calculated as $0.412$ .

The mole fraction of $O2$ is calculated as $0.588$ .

The total number of moles of gases in the given mixture is calculated as $0.161 mol$ .

The number of moles of molecule can be find out by using its mole fraction,
Equation for finding number of moles,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Therefore,

-The number of moles of $CH4$ is,

$nCH4 = 0.412 × 0.161 mol = 6.63 × 10-2 mol$

-The number of moles of $O2$ is,

$nCH4 = 0.588 × 0.161 mol = 9.47 × 10-2 mol$

The number of grams of a substance is determined from its number of moles is,
Equation for finding number of grams is,

$Number of moles × Molecular mass in grams = Number of grams$

-The number of grams of $CH4$ is,

$6.63 × 10-2 mol × 16 g = 1.06 g$

-The number of grams of $O2$ is,

$9.47 × 10-2 mol × 32 g = 3.03 g$

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Answer 3

Question

Chapter 5, Problem 89E

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

a)

Expert Solution

Answer to Problem 89E

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

Explanation of Solution

To find: the mole fractions of $CH4$ and $O2$ in the given mixture if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

The partial pressure of $CH4$ is given as $0.175 atm$

The partial pressure of $O2$ is given as $0.250 atm$ .

Therefore, the total pressure of the mixture is,

$0.175 atm + 0.250 atm = 0.425 atm$

Equation for finding mole fraction from partial pressure and total pressure is,

$χA = PAPTOTAL$

Therefore,

The mole fraction of $CH4$ is,

$χCH4 = 0.175 atm0.425 atm = 0.412$

The mole fraction of $O2$ is,

$χO2 = 0.250atm0.425 atm = 0.588$

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

b)

Expert Solution

Answer to Problem 89E

Total number of moles of gas in the mixture is $0.161 mol$ .

Explanation of Solution

To find: the total number of moles of gases in the given mixture.

The total number of moles of gases in the given mixture is $0.161 mol$ .

The total pressure of gases presented in the mixture is given as $0.425 atm$ .

The volume of flask is given as $10.5 L$ .

The temperature of flask is given as $65oC = (273+65) K = 338 K$ .

The total number of moles of gas in the mixture is determined by using ideal gas equation According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

Therefore,

The total number of moles of gas in the mixture is,

$Total number of moles = 0.425 atm × 10.5 L 0.08206 L atm/ K mol × 338 K = 0.161 mol$

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

c)

Expert Solution

Answer to Problem 89E

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

Explanation of Solution

To find: the number of grams of $CH4$ and $O2$ in the given mixture.

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

The mole fraction of $CH4$ is calculated as $0.412$ .

The mole fraction of $O2$ is calculated as $0.588$ .

The total number of moles of gases in the given mixture is calculated as $0.161 mol$ .

The number of moles of molecule can be find out by using its mole fraction,
Equation for finding number of moles,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Therefore,

-The number of moles of $CH4$ is,

$nCH4 = 0.412 × 0.161 mol = 6.63 × 10-2 mol$

-The number of moles of $O2$ is,

$nCH4 = 0.588 × 0.161 mol = 9.47 × 10-2 mol$

The number of grams of a substance is determined from its number of moles is,
Equation for finding number of grams is,

$Number of moles × Molecular mass in grams = Number of grams$

-The number of grams of $CH4$ is,

$6.63 × 10-2 mol × 16 g = 1.06 g$

-The number of grams of $O2$ is,

$9.47 × 10-2 mol × 32 g = 3.03 g$

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Answer 4

Question

Chapter 5, Problem 89E

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

a)

Expert Solution

Answer to Problem 89E

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

Explanation of Solution

To find: the mole fractions of $CH4$ and $O2$ in the given mixture if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

The partial pressure of $CH4$ is given as $0.175 atm$

The partial pressure of $O2$ is given as $0.250 atm$ .

Therefore, the total pressure of the mixture is,

$0.175 atm + 0.250 atm = 0.425 atm$

Equation for finding mole fraction from partial pressure and total pressure is,

$χA = PAPTOTAL$

Therefore,

The mole fraction of $CH4$ is,

$χCH4 = 0.175 atm0.425 atm = 0.412$

The mole fraction of $O2$ is,

$χO2 = 0.250atm0.425 atm = 0.588$

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

b)

Expert Solution

Answer to Problem 89E

Total number of moles of gas in the mixture is $0.161 mol$ .

Explanation of Solution

To find: the total number of moles of gases in the given mixture.

The total number of moles of gases in the given mixture is $0.161 mol$ .

The total pressure of gases presented in the mixture is given as $0.425 atm$ .

The volume of flask is given as $10.5 L$ .

The temperature of flask is given as $65oC = (273+65) K = 338 K$ .

The total number of moles of gas in the mixture is determined by using ideal gas equation According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

Therefore,

The total number of moles of gas in the mixture is,

$Total number of moles = 0.425 atm × 10.5 L 0.08206 L atm/ K mol × 338 K = 0.161 mol$

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

c)

Expert Solution

Answer to Problem 89E

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

Explanation of Solution

To find: the number of grams of $CH4$ and $O2$ in the given mixture.

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

The mole fraction of $CH4$ is calculated as $0.412$ .

The mole fraction of $O2$ is calculated as $0.588$ .

The total number of moles of gases in the given mixture is calculated as $0.161 mol$ .

The number of moles of molecule can be find out by using its mole fraction,
Equation for finding number of moles,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Therefore,

-The number of moles of $CH4$ is,

$nCH4 = 0.412 × 0.161 mol = 6.63 × 10-2 mol$

-The number of moles of $O2$ is,

$nCH4 = 0.588 × 0.161 mol = 9.47 × 10-2 mol$

The number of grams of a substance is determined from its number of moles is,
Equation for finding number of grams is,

$Number of moles × Molecular mass in grams = Number of grams$

-The number of grams of $CH4$ is,

$6.63 × 10-2 mol × 16 g = 1.06 g$

-The number of grams of $O2$ is,

$9.47 × 10-2 mol × 32 g = 3.03 g$

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Answer 5

Chapter 5, Problem 89E

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

a)

Expert Solution

Answer to Problem 89E

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

Explanation of Solution

To find: the mole fractions of $CH4$ and $O2$ in the given mixture if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

The partial pressure of $CH4$ is given as $0.175 atm$

The partial pressure of $O2$ is given as $0.250 atm$ .

Therefore, the total pressure of the mixture is,

$0.175 atm + 0.250 atm = 0.425 atm$

Equation for finding mole fraction from partial pressure and total pressure is,

$χA = PAPTOTAL$

Therefore,

The mole fraction of $CH4$ is,

$χCH4 = 0.175 atm0.425 atm = 0.412$

The mole fraction of $O2$ is,

$χO2 = 0.250atm0.425 atm = 0.588$

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

b)

Expert Solution

Answer to Problem 89E

Total number of moles of gas in the mixture is $0.161 mol$ .

Explanation of Solution

To find: the total number of moles of gases in the given mixture.

The total number of moles of gases in the given mixture is $0.161 mol$ .

The total pressure of gases presented in the mixture is given as $0.425 atm$ .

The volume of flask is given as $10.5 L$ .

The temperature of flask is given as $65oC = (273+65) K = 338 K$ .

The total number of moles of gas in the mixture is determined by using ideal gas equation According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

Therefore,

The total number of moles of gas in the mixture is,

$Total number of moles = 0.425 atm × 10.5 L 0.08206 L atm/ K mol × 338 K = 0.161 mol$

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

c)

Expert Solution

Answer to Problem 89E

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

Explanation of Solution

To find: the number of grams of $CH4$ and $O2$ in the given mixture.

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

The mole fraction of $CH4$ is calculated as $0.412$ .

The mole fraction of $O2$ is calculated as $0.588$ .

The total number of moles of gases in the given mixture is calculated as $0.161 mol$ .

The number of moles of molecule can be find out by using its mole fraction,
Equation for finding number of moles,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Therefore,

-The number of moles of $CH4$ is,

$nCH4 = 0.412 × 0.161 mol = 6.63 × 10-2 mol$

-The number of moles of $O2$ is,

$nCH4 = 0.588 × 0.161 mol = 9.47 × 10-2 mol$

The number of grams of a substance is determined from its number of moles is,
Equation for finding number of grams is,

$Number of moles × Molecular mass in grams = Number of grams$

-The number of grams of $CH4$ is,

$6.63 × 10-2 mol × 16 g = 1.06 g$

-The number of grams of $O2$ is,

$9.47 × 10-2 mol × 32 g = 3.03 g$

Answer 6

Chapter 5, Problem 89E

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

a)

Expert Solution

Answer to Problem 89E

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

Explanation of Solution

To find: the mole fractions of $CH4$ and $O2$ in the given mixture if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

The partial pressure of $CH4$ is given as $0.175 atm$

The partial pressure of $O2$ is given as $0.250 atm$ .

Therefore, the total pressure of the mixture is,

$0.175 atm + 0.250 atm = 0.425 atm$

Equation for finding mole fraction from partial pressure and total pressure is,

$χA = PAPTOTAL$

Therefore,

The mole fraction of $CH4$ is,

$χCH4 = 0.175 atm0.425 atm = 0.412$

The mole fraction of $O2$ is,

$χO2 = 0.250atm0.425 atm = 0.588$

Answer 7

Chapter 5, Problem 89E

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

Answer 8

a)

Expert Solution

Answer to Problem 89E

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

To find: the mole fractions of $CH4$ and $O2$ in the given mixture if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Mole fraction of $CH4$ is $0.412$ .

Mole fraction of $O2$ is $0.588$ .

The partial pressure of $CH4$ is given as $0.175 atm$

The partial pressure of $O2$ is given as $0.250 atm$ .

Therefore, the total pressure of the mixture is,

$0.175 atm + 0.250 atm = 0.425 atm$

Equation for finding mole fraction from partial pressure and total pressure is,

$χA = PAPTOTAL$

Therefore,

The mole fraction of $CH4$ is,

$χCH4 = 0.175 atm0.425 atm = 0.412$

The mole fraction of $O2$ is,

$χO2 = 0.250atm0.425 atm = 0.588$

Answer 13

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

b)

Expert Solution

Answer to Problem 89E

Total number of moles of gas in the mixture is $0.161 mol$ .

Explanation of Solution

To find: the total number of moles of gases in the given mixture.

The total number of moles of gases in the given mixture is $0.161 mol$ .

The total pressure of gases presented in the mixture is given as $0.425 atm$ .

The volume of flask is given as $10.5 L$ .

The temperature of flask is given as $65oC = (273+65) K = 338 K$ .

The total number of moles of gas in the mixture is determined by using ideal gas equation According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

Therefore,

The total number of moles of gas in the mixture is,

$Total number of moles = 0.425 atm × 10.5 L 0.08206 L atm/ K mol × 338 K = 0.161 mol$

Answer 14

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

Answer 15

b)

Expert Solution

Answer to Problem 89E

Total number of moles of gas in the mixture is $0.161 mol$ .

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

To find: the total number of moles of gases in the given mixture.

The total number of moles of gases in the given mixture is $0.161 mol$ .

The total pressure of gases presented in the mixture is given as $0.425 atm$ .

The volume of flask is given as $10.5 L$ .

The temperature of flask is given as $65oC = (273+65) K = 338 K$ .

The total number of moles of gas in the mixture is determined by using ideal gas equation According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

Therefore,

The total number of moles of gas in the mixture is,

$Total number of moles = 0.425 atm × 10.5 L 0.08206 L atm/ K mol × 338 K = 0.161 mol$

Answer 20

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

c)

Expert Solution

Answer to Problem 89E

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

Explanation of Solution

To find: the number of grams of $CH4$ and $O2$ in the given mixture.

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

The mole fraction of $CH4$ is calculated as $0.412$ .

The mole fraction of $O2$ is calculated as $0.588$ .

The total number of moles of gases in the given mixture is calculated as $0.161 mol$ .

The number of moles of molecule can be find out by using its mole fraction,
Equation for finding number of moles,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Therefore,

-The number of moles of $CH4$ is,

$nCH4 = 0.412 × 0.161 mol = 6.63 × 10-2 mol$

-The number of moles of $O2$ is,

$nCH4 = 0.588 × 0.161 mol = 9.47 × 10-2 mol$

The number of grams of a substance is determined from its number of moles is,
Equation for finding number of grams is,

$Number of moles × Molecular mass in grams = Number of grams$

-The number of grams of $CH4$ is,

$6.63 × 10-2 mol × 16 g = 1.06 g$

-The number of grams of $O2$ is,

$9.47 × 10-2 mol × 32 g = 3.03 g$

Answer 21

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of $CH4$ is $0.175 atm$ and $O2$ is $0.250 atm$ .

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.
Partial pressure of a gas in terms of its mole fraction and total pressure is,

` $PA = χA × PTOTAL$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

The number of moles of molecule can be find out by using its mole fraction,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Number of grams of a substance from its number of moles is,

$Number of moles × Molecular mass in grams = Number of grams$

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

$Total number of moles = Total pressure × Volume R × Temperature$

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

Answer 22

c)

Expert Solution

Answer to Problem 89E

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

To find: the number of grams of $CH4$ and $O2$ in the given mixture.

The number of grams of $CH4$ is $1.06 g$ .

The number of grams of $O2$ is $3.03 g$ .

The mole fraction of $CH4$ is calculated as $0.412$ .

The mole fraction of $O2$ is calculated as $0.588$ .

The total number of moles of gases in the given mixture is calculated as $0.161 mol$ .

The number of moles of molecule can be find out by using its mole fraction,
Equation for finding number of moles,

$numbers of moles of molecule A (nA) = molecule fraction of A, ( χA) × total number of moles$

Therefore,

-The number of moles of $CH4$ is,

$nCH4 = 0.412 × 0.161 mol = 6.63 × 10-2 mol$

-The number of moles of $O2$ is,

$nCH4 = 0.588 × 0.161 mol = 9.47 × 10-2 mol$

The number of grams of a substance is determined from its number of moles is,
Equation for finding number of grams is,

$Number of moles × Molecular mass in grams = Number of grams$

-The number of grams of $CH4$ is,

$6.63 × 10-2 mol × 16 g = 1.06 g$

-The number of grams of $O2$ is,

$9.47 × 10-2 mol × 32 g = 3.03 g$

Answer 27

Ch. 5 - Prob. 1RQ Ch. 5 - Prob. 2RQ Ch. 5 - Prob. 3RQ Ch. 5 - Prob. 4RQ Ch. 5 - Prob. 5RQ Ch. 5 - Prob. 6RQ Ch. 5 - Prob. 7RQ Ch. 5 - Prob. 8RQ Ch. 5 - Prob. 9RQ Ch. 5 - Why do real gases not always behave ideally? Under...

Concept explainers

Answer to Problem 89E

Explanation of Solution

Answer to Problem 89E

Explanation of Solution

Answer to Problem 89E

Explanation of Solution

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Chapter 5 Solutions