Chapter 13.2, Problem 28PP

Interpretation Introduction

Interpretation:

The pressure of the gas is to be calculated when volume, temperature and number of moles of the gas are given.

Concept introduction:

Ideal gas equation helps to calculate pressure of a gas at given temperature and volume. 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 28PP

The pressure of the gas is $5.14atm$

Explanation of Solution

Given information:

The Number of moles of gas is $0.108mol$

The volume of the gas $\mathrm{V}=0.505L$

Gas constant is $0.0821Latm{K}^{-1}mo{l}^{-1}$

The temperature of gas $\mathrm{T}=20C$

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

$\mathrm{PV}=nRT$

Or

$\mathrm{P}=\frac{nRT}{V}$

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

To convert temperature into Kelvin,

$\begin{array}{c}\mathrm{T}\left(K\right)=T\left(C\right)+273\\ =20+273\\ =293K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}P=\frac{nRT}{V}\\ =\frac{0.108\times 0.0821\times 293}{0.505}\\ =5.14atm\end{array}$

Therefore, pressure of the gas is $5.14atm$

Conclusion

The pressure of the gas is $5.14atm$.