Chapter 13, Problem 75A

Interpretation Introduction

Interpretation:

The mass of the gas is to be calculated for a given pressure and volume of the gas.

Concept introduction:

Ideal gas equation is used to calculate mass of the gas at given temperature and pressure.

According to this law,

$\mathrm{PV}=nRT$

Where

$\mathrm{P}$ is pressure of the gas

$\mathrm{V}$ is volume of the gas

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

Answer to Problem 75A

The mass of the gas is $2.742g$

Explanation of Solution

Ideal gas equation helps to calculate number of moles of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Or

$\mathrm{n}=\frac{PV}{RT}$

Further mass of gas $\mathrm{m}$ is calculated by multiplying number of moles $\mathrm{n}$ with molar mass of the gas $\mathrm{M}$

Given data is:

$\text{V=2L}$

$\text{P=1}\text{.08}\text{atm}$

$\begin{array}{c}\text{T=15°C}\\ \text{=15+273}\\ \text{=288K}\end{array}$

$\text{R=}0.0821Latm{K}^{-1}mo{l}^{-1}$

On substituting the values in the formula:

$\begin{array}{c}\mathrm{n}=\frac{1.08\times 2}{\begin{array}{l}0.0821\times 288\end{array}}\\ =0.0914mol\end{array}$

So $\mathrm{m}$ is given by

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

The given gas is ${\mathrm{C}}_2{H}_6$.

The formula to calculate molar mass is,

$\mathrm{Molar}mass=\left(N_1\times x_1\right)+\left(N_2\times x_2\right)+\mathrm{...}$

Where,

• ${\mathrm{N}}_1$ represents the number of atoms of first element in chemical formula.
• ${\mathrm{x}}_1$ represents the atomic mass of first element.
• ${\mathrm{N}}_2$ represents the number of atoms of second element in chemical formula.
• ${\text{x}}_1$ represents the atomic mass of second element.

Atomic mass of carbon is $12gmo{l}^{-1}$

Atomic mass of hydrogen is $1gmo{l}^{-1}$

Hence,

$\begin{array}{c}M=2\times 12+6\times 1\\ =24+6\\ =30gmo{l}^{-1}\end{array}$

$\begin{array}{c}\mathrm{m}=30\times 0.0914\\ =2.742g\end{array}$

Therefore mass of the gas is $2.742g$

Conclusion

The mass of the gas is $2.742g$.