Chapter 5, Problem 87QAP

Interpretation Introduction

(a)

Interpretation:

The tank with the highest total pressure needs to be determined.

Concept introduction:

According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R are interrelated as below:

$\text{PV = nRT}$

When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:

$\stackrel{\text{Gas 1}}{\overbrace{\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{n}}_{\text{1}}{\text{T}}_{\text{1}}}}}\text{=}\stackrel{\text{Gas2}}{\overbrace{\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{n}}_{\text{2}}{\text{T}}_{\text{2}}}}}$

Here

• P₁ and P₂ are the pressure of gases
• V₁ and V₂ and volume of gases
• n₁ and n₂ number of moles
• T₁ and T₂ are the temperature of gases

Moles are known as the ratio of mass and molar mass. Below is the formula:

$\text{n = }\frac{\text{m}}{\text{MM}}$

Here, MM is molar mass and m is the mass.

The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:

${\text{E}}_{\text{t}}\text{=}\frac{\text{3RT}}{{\text{2N}}_{\text{A}}}$

Here,

E_t = average translational energy of gas

T = temperature in Kelvin

R = Universal gas constant

N_A = Avogadro number

Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:

$\frac{{\text{u}}_{\text{2}}}{{\text{u}}_{\text{1}}}\text{=}{\left(\frac{{\text{MM}}_{\text{1}}}{{\text{MM}}_{\text{2}}}\right)}^{\text{1/2}}$

Here u₁ and u₂ is the rate of effusion for gas1 and gas 2. MM₁ and MM₂ is the molar mass for gas1 and gas 2.

Answer to Problem 87QAP

Tank Y

Explanation of Solution

The given tanks are as follows:

Here, circles represent ${\text{CH}}_{\text{4}}$ gas, square represents oxygen and triangle represents ${\mathrm{SO}}_2$ gas.

The highest total pressure is in the tank Y. Because, tank Y has the maximum amount of gases mixture.

Interpretation Introduction

(b)

Interpretation:

The tank containing highest SO₂ pressure needs to be determined.

Concept introduction:

According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R are interrelated as below:

$\text{PV = nRT}$

When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:

$\stackrel{\text{Gas 1}}{\overbrace{\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{n}}_{\text{1}}{\text{T}}_{\text{1}}}}}\text{=}\stackrel{\text{Gas2}}{\overbrace{\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{n}}_{\text{2}}{\text{T}}_{\text{2}}}}}$

Here

• P₁ and P₂ are the pressure of gases
• V₁ and V₂ and volume of gases
• n₁ and n₂ number of moles
• T₁ and T₂ are the temperature of gases

Moles are known as the ratio of mass and molar mass. Below is the formula:

$\text{n = }\frac{\text{m}}{\text{MM}}$

Here, MM is molar mass and m is the mass.

The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:

${\text{E}}_{\text{t}}\text{=}\frac{\text{3RT}}{{\text{2N}}_{\text{A}}}$

Here,

E_t = average translational energy of gas

T = temperature in Kelvin

R = Universal gas constant

N_A = Avogadro number

Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:

$\frac{{\text{u}}_{\text{2}}}{{\text{u}}_{\text{1}}}\text{=}{\left(\frac{{\text{MM}}_{\text{1}}}{{\text{MM}}_{\text{2}}}\right)}^{\text{1/2}}$

Here, u₁ and u₂ is the rate of effusion for gas1 and gas 2. MM₁ and MM₂ is the molar mass for gas1 and gas 2.

Answer to Problem 87QAP

Tank Y

Explanation of Solution

The given tanks are as follows:

Here, circles represent ${\text{CH}}_{\text{4}}$ gas, square represents oxygen and triangle represents ${\mathrm{SO}}_2$ gas.

Tank Y contains highest partial pressure of SO₂ . This is because, Tank Y has the maximum moles of SO₂ due to which it will have the maximum partial pressure.

Interpretation Introduction

(c)

Interpretation:

The tank with same mass of all the three gases needs to be determined.

Concept introduction:

According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R are interrelated as below:

$\text{PV = nRT}$

When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:

$\stackrel{\text{Gas 1}}{\overbrace{\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{n}}_{\text{1}}{\text{T}}_{\text{1}}}}}\text{=}\stackrel{\text{Gas2}}{\overbrace{\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{n}}_{\text{2}}{\text{T}}_{\text{2}}}}}$

Here

• P₁ and P₂ are the pressure of gases
• V₁ and V₂ and volume of gases
• n₁ and n₂ number of moles
• T₁ and T₂ are the temperature of gases

Moles are known as the ratio of mass and molar mass. Below is the formula:

$\text{n = }\frac{\text{m}}{\text{MM}}$

Here, MM is molar mass and m is the mass.

The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:

${\text{E}}_{\text{t}}\text{=}\frac{\text{3RT}}{{\text{2N}}_{\text{A}}}$

Here,

E_t = average translational energy of gas

T = temperature in Kelvin

R = Universal gas constant

N_A = Avogadro number

Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:

$\frac{{\text{u}}_{\text{2}}}{{\text{u}}_{\text{1}}}\text{=}{\left(\frac{{\text{MM}}_{\text{1}}}{{\text{MM}}_{\text{2}}}\right)}^{\text{1/2}}$

Here, u₁ and u₂ is the rate of effusion for gas1 and gas 2. MM₁ and MM₂ is the molar mass for gas1 and gas 2.

Answer to Problem 87QAP

Tank Z

Explanation of Solution

The given tanks are as follows:

Here, circles represent ${\text{CH}}_{\text{4}}$ gas, square represents oxygen and triangle represents ${\mathrm{SO}}_2$ gas.

Tank Z contain the mass of all three gases same.

$\begin{array}{l}{\text{Mass of O}}_2={\text{2 mol of O}}_2\times {\text{Molar mass of O}}_2\\ \text{ = 2 mol }\times \text{ 32 g/mol }\\ \text{ = }6\text{4 g}\end{array}$

$\begin{array}{l}{\text{Mass of CH}}_4={\text{4 mol of CH}}_4\times {\text{Molar mass of CH}}_4\\ \text{ = 4 mol }\times \text{ 16 g/mol }\\ \text{ = }6\text{4 g}\end{array}$

$\begin{array}{l}{\text{Mass of SO}}_2={\text{1 mol of SO}}_2\times {\text{Molar mass of SO}}_2\\ \text{ = 1 mol }\times \text{ 64 g/mol }\\ \text{ = }6\text{4 g}\end{array}$

Interpretation Introduction

(d)

Interpretation:

The tank with the heaviest content needs to be determined.

Concept introduction:

According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R are interrelated as below:

$\text{PV = nRT}$

When at two different conditions gases are placed, then to determine the changed variable combined gas law is used. Below is the formula of combined gas law:

$\stackrel{\text{Gas 1}}{\overbrace{\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{n}}_{\text{1}}{\text{T}}_{\text{1}}}}}\text{=}\stackrel{\text{Gas2}}{\overbrace{\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{n}}_{\text{2}}{\text{T}}_{\text{2}}}}}$

Here

• P₁ and P₂ are the pressure of gases
• V₁ and V₂ and volume of gases
• n₁ and n₂ number of moles
• T₁ and T₂ are the temperature of gases

Moles are known as the ratio of mass and molar mass. Below is the formula:

$\text{n = }\frac{\text{m}}{\text{MM}}$

Here, MM is molar mass and m is the mass.

The kinetic model of gases is accounted for ideal gas behavior. The formula of average translational energy of gas is as below:

${\text{E}}_{\text{t}}\text{=}\frac{\text{3RT}}{{\text{2N}}_{\text{A}}}$

Here,

E_t = average translational energy of gas

T = temperature in Kelvin

R = Universal gas constant

N_A = Avogadro number

Effusion is known as the leakage of gas molecules from high to low pressure region via a pinhole. For any two gas molecules the formula to determine the time needed for effusion is as below:

$\frac{{\text{u}}_{\text{2}}}{{\text{u}}_{\text{1}}}\text{=}{\left(\frac{{\text{MM}}_{\text{1}}}{{\text{MM}}_{\text{2}}}\right)}^{\text{1/2}}$

Here u₁ and u₂ is the rate of effusion for gas1 and gas 2. MM₁ and MM₂ is the molar mass for gas1 and gas 2.

Answer to Problem 87QAP

Tank Y

Explanation of Solution

The given tanks are as follows:

Here, circles represent ${\text{CH}}_{\text{4}}$ gas, square represents oxygen and triangle represents ${\mathrm{SO}}_2$ gas.

Tank Y contains the heaviest content. This is due to the number of moles of SO₂ is highest in tank Y.