Determine the value of the gas constant, $R$, in units of $\mathrm{ft}^{3} \mathrm{~atm} / \mathrm{lb} \mathrm{mol}{ }^{\circ} \mathrm{R}$ ), starting with the value of the standard molar volume of a perfect gas (i.e., $22.4 \mathrm{~m}^{3} / \mathrm{kg} \mathrm{mol}$ ).