Chapter 13, Problem 97QAP

Interpretation Introduction

Interpretation:

The volume of the mixture of gas at STP and partial pressure of each gas in the mixture at STP should be calculated.

Concept Introduction:

According to ideal gas equation:

$\text{P}\text{V}=\text{n}\text{R}\text{T}$

Here, P is pressure, V is volume, n is number of moles, R is Universal gas constant and T is temperature.

The value of Universal gas constant can be taken as $0.082{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}$.

Mass of gas can be calculated from number of moles and molar mass as follows:

$\text{m}=\text{n}\times \text{M}$

Here, n is number of moles, m is mass and M is molar mass.

Answer to Problem 97QAP

15.65 L, ${\text{P}}_{{\text{O}}_{\text{2}}}=0.2237\text{ atm}$, ${\text{P}}_{{\text{N}}_{\text{2}}}=0.2556\text{ atm}$, ${\text{P}}_{{\text{CO}}_{\text{2}}}=0.1626\text{ atm}$ and ${\text{P}}_{\text{Ne}}=0.3578\text{ atm}$.

Explanation of Solution

Given Information:

The mass of oxygen gas, nitrogen gas, carbon dioxide gas and neon gas is 5 g.

First calculate the number of moles of each gas as follows:

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

Molar mass of oxygen gas is 32 g/mol thus, number of moles will be:

$\begin{array}{c}{\text{n}}_{{\text{O}}_{\text{2}}}=\frac{5\text{ g}}{32\text{ g/mol}}\\ =0.1563\text{ mol}\end{array}$

Molar mass of nitrogen gas is 28 g/mol thus,

$\begin{array}{c}{\text{n}}_{{\text{N}}_{\text{2}}}=\frac{5\text{ g}}{28\text{ g/mol}}\\ =0.1786\text{ mol}\end{array}$

Molar mass of carbon dioxide is 44.01 g/mol thus,

$\begin{array}{c}{\text{n}}_{{\text{CO}}_{\text{2}}}=\frac{5\text{ g}}{44.01\text{ g/mol}}\\ =0.1136\text{ mol}\end{array}$

Molar mass of neon gas is 20.18 g/mol thus,

$\begin{array}{c}{\text{n}}_{\text{Ne}}=\frac{5\text{ g}}{20.18\text{ g/mol}}\\ =0.25\text{ mol}\end{array}$

Number of moles of mixture can be calculated as follows:

${\text{n}}_{\text{mix}}={\text{n}}_{{\text{O}}_{\text{2}}}+{\text{n}}_{{\text{N}}_{\text{2}}}+{\text{n}}_{{\text{CO}}_{\text{2}}}+{\text{n}}_{\text{Ne}}$

Putting the values,

$\begin{array}{c}{\text{n}}_{\text{mix}}=\left(0.1563+0.1786+0.1136+0.25\right)\text{ mol}\\ \text{=0}\text{.6985 mol}\end{array}$

At STP, the value of temperature is 273.15 K and pressure is 1 atm thus, volume can be calculated using the ideal gas equation as follows:

${\text{V}}_{\text{mix}}=\frac{{\text{n}}_{\text{mix}}\text{R}\text{T}}{\text{P}}$

Putting the values,

$\begin{array}{c}\text{V}=\frac{\left(0.6985\text{ mol}\right)\left(0.082{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}\right)\left(273.15\text{ K}\right)}{\left(1\text{ atm}\right)}\\ =15.65\text{ L}\end{array}$

Therefore, volume mixture of gases is $\text{15}\text{.65 L}$.

Partial pressure of each gas at STP can be calculated considering the number of moles of individual gases using the ideal gas equation:

$\text{P}=\frac{\text{n}\text{R}\text{T}}{\text{V}}$

Thus, partial pressure of oxygen gas can be calculated as follows:

$\begin{array}{c}{\text{P}}_{{\text{O}}_{\text{2}}}=\frac{\left(0.1563\text{ mol}\right)\left(0.082{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}\right)\left(273.15\text{ K}\right)}{\left(15.65\text{ L}\right)}\\ =0.2237\text{ atm}\end{array}$

Partial pressure of nitrogen gas can be calculated as follows:

$\begin{array}{c}{\text{P}}_{{\text{N}}_{\text{2}}}=\frac{\left(0.1786\text{ mol}\right)\left(0.082{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}\right)\left(273.15\text{ K}\right)}{\left(15.65\text{ L}\right)}\\ =0.2556\text{ atm}\end{array}$

Partial pressure of carbon dioxide gas can be calculated as follows:

$\begin{array}{c}{\text{P}}_{{\text{CO}}_{\text{2}}}=\frac{\left(0.1136\text{ mol}\right)\left(0.082{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}\right)\left(273.15\text{ K}\right)}{\left(15.65\text{ L}\right)}\\ =0.1626\text{ atm}\end{array}$

Partial pressure of neon gas can be calculated as follows:

$\begin{array}{c}{\text{P}}_{\text{Ne}}=\frac{\left(0.25\text{ mol}\right)\left(0.082{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}\right)\left(273.15\text{ K}\right)}{\left(15.65\text{ L}\right)}\\ =0.3578\text{ atm}\end{array}$.

Conclusion

Therefore, volume of mixture of gases is 15.65 L, partial pressure of oxygen, nitrogen, carbon dioxide and neon gas is 0.2237 atm, 0.2556 atm, 0.1626 atm and 0.3578 atm respectively.