Chapter 13, Problem 14STP

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:

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

  $PV=n\text{R}T$

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 14STP

A

Explanation of Solution

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

  $PV=n\text{R}T$

Or

  $P=\frac{n\text{R}T}{V}$

Given data is:

  $\text{m=0}\text{.0468}\text{g}$

  $\mathrm{V}=4L$

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

  $\mathrm{T}=35°C$

To convert temperature into Kelvin,

  $\begin{array}{c}\mathrm{T}\left(K\right)=T\left(°C\right)+273\\ =35+273\\ =308K\end{array}$

The given gas is ${\text{NH}}_{\text{3}}$ .

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

The atomic mass of Nitrogen is $14gmo{l}^{-1}$

The atomic mass of Hydrogen is $1gmo{l}^{-1}$

Hence,

  $\begin{array}{c}M=1\times 14+3\times 1\\ =14+3\\ =17gmo{l}^{-1}\end{array}$

Further, the number of moles $\mathrm{n}$ is calculated by using the formula:

  $\begin{array}{c}\mathrm{n}=\frac{m}{M}\\ =\frac{0.0468}{17}\\ =0.00275mol\end{array}$

  $\mathrm{m}$ denotes the mass of gas

  $\mathrm{M}$ denotes the molar mass of gas

Now substituting the values into the formula,

  $\begin{array}{c}P=\frac{n\text{R}T}{V}\\ =\frac{0.00275\times 0.0821\times 308}{4}\\ =0.0174atm\end{array}$

Therefore, the pressure of the gas is $0.0175atm$

Conclusion

On putting the value in the formula, it’s clear that option A is correct.