Chapter 14, Problem 67A

Interpretation Introduction

Interpretation: The pressure in the container containing 4.50 g of methane gas of volume 2.0 L at $35{}^{\text{o}}\text{C}$ needs to be calculated.

Concept Introduction: The relation between pressure, volume, number of moles, and temperature is as follows:

  $PV=nRT$

Here, P is pressure, V is volume, n is the number of moles, R is the Universal gas constant and T is temperature.

Explanation of Solution

To calculate the pressure, the number of moles of methane gas needs to be calculated first. Molar mass of methane gas is 16.04 g/mol. Number of moles is calculated as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is molar mass.

Substitute the values,

  $\begin{array}{c}n=\frac{4.50\text{ g}}{\text{16}\text{.04 g/mol}}\\ =0.28\text{ mol}\end{array}$

Now, the pressure of the gas is calculated as follows:

  $P=\frac{nRT}{V}$

Here, the temperature must be in K thus,

  $\begin{array}{c}T=35+273.15\\ =308.15\text{ K}\end{array}$

Substitute the values,

  $\begin{array}{c}P=\frac{\left(0.28\text{ mol}\right)\left(0.082\text{ L atm/mol K}\right)\left(308.15\text{ K}\right)}{\left(2\text{ L}\right)}\\ =3.54\text{ atm}\end{array}$

Therefore, the pressure of methane gas is 3.54 atm.