Chapter 13, Problem 69A

Interpretation Introduction

Interpretation:

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

Concept introduction:

Ideal gas equation helps to calculate number of the moles of a gas at given temperature, volume 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 69A

The number of moles of the gas at $25°C$ is $0.286mol$ and at $49°C$ is $0.265mol$

Explanation of Solution

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

$\mathrm{PV}=nRT$

Or

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

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

Now

$\mathrm{V}=2L$

$\text{P=3}\text{.50}\text{atm}$

$\text{R=}0.0821{\text{LatmK}}^{\text{-1}}{\text{mol}}^{\text{-1}}$

$\mathrm{T}=25C$

To convert temperature into Kelvin,

$\begin{array}{c}\mathrm{T}\left(K\right)=T\left(C\right)+273\\ =25+273\\ =298K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{3.50\times 2}{0.0821\times 298}\\ =0.286mol\end{array}$

Now temperature is changed to $49°C$, so applying the formula again:

$\begin{array}{c}\mathrm{T}\left(K\right)=T\left(C\right)+273\\ =49+273\\ =322K\end{array}$

$\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{3.50\times 2}{0.0821\times 322}\\ =0.265mol\end{array}$

Conclusion

The number of moles of the gas at $25°C$ is $0.286mol$ and at $49°C$ is $0.265mol$