Chapter 13.1, Problem 7PP

To determine

To Calculate: Themass of the helium gas.

Answer to Problem 7PP

  $5.1\times {10}^{\text{2}}\text{g}$

Explanation of Solution

Given data:

Pressure, $P=15.5\times {\text{10}}^{\text{6}}\text{Pa}$

Temperature, $T=293\text{K}$

Volume, $V=0.020{\text{m}}^{\text{3}}$

Value of gas constant, $R=8.31\text{Pa}\cdot {\text{m}}^{\text{3}}\text{/mol}\cdot \text{K}$

The molar mass of helium gas is $4.00\text{g/mol}$ .

Formula used:

From the ideal gas law:

  $PV=nRT$

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

Molar mass of gas, $M=\frac{m}{n}$

Mass of gas, $m=Mn$

Where, n is the number of moles.

Calculation:

After rearranging the ideal gas law, calculate the number of moles:

  $\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{\left(\text{15}{\text{.5×10}}^{\text{6}}\text{Pa}\right)\left(\text{0}\text{.020}{\text{m}}^{\text{3}}\right)}{\left(\text{8}\text{.31}\text{Pa}\cdot {\text{m}}^{\text{3}}\text{/mol}\cdot \text{K}\right)\left(\text{293K}\right)}\\ =127.3\text{mol}\end{array}$

Now, calculate the mass of gas,

  $\begin{array}{c}m=\left(\text{127}\text{.3}\text{mol}\right)\left(\text{4}\text{.00}\text{g/mol}\right)\\ =5.1\times {10}^{\text{2}}\text{g}\end{array}$

Conclusion:

The mass of the helium gas is $5.1\times {10}^{\text{2}}\text{g}$ .