Concept explainers
a)
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)
Answer to Problem 97E
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: 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)
Answer to Problem 97E
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: 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)
Answer to Problem 97E
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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Chapter 5 Solutions
OWLv2 with MindTap Reader, 4 terms (24 months) Printed Access Card for Zumdahl/Zumdahl/DeCoste’s Chemistry, 10th Edition
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