Chapter 13, Problem 60A

Interpretation Introduction

Interpretation: The pressure of the gas is to be calculated when pressure and temperature of the gas are given at two conditions.

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 the pressure of the gas

  $\mathrm{V}$ is the 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 60A

The pressure of the gas is $\text{74}\text{.8 kPa}$

Explanation of Solution

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

  $\mathrm{PV}=nRT$

Or

  $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Here,

  $\begin{array}{l}{\text{P}}_{\text{1}}\text{=108 KPa}\\ {\text{V}}_{\text{1}}\text{=500 mL}\\ {\text{V}}_{\text{2}}\text{=700 mL}\\ {\text{T}}_{\text{1}}\text{=10 °C}\\ {\text{T}}_{\text{1}}{\text{(K)=T}}_{\text{1}}\text{(°C)+273}\\ \text{=10+273}\\ \text{=283 K}\\ {\text{T}}_{\text{2}}\text{=21}\text{°C}\\ \text{=21+273}\\ \text{=294 K}\end{array}$

Now substituting the values into the formula,

  $\begin{array}{c}{\text{P}}_{\text{2}}\text{=}\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}{\text{T}}_{\text{2}}}{{\text{V}}_{\text{2}}{\text{T}}_{\text{1}}}\\ \text{=}\frac{\text{108×500×294}}{\text{750×283}}\\ \text{=74}\text{.8 kPa}\end{array}$

Therefore pressure of the gas is $\text{74}\text{.8 kPa}$ .

Conclusion

The pressure of the gas is $\text{74}\text{.8 kPa}$ .