\(120 \mathrm{~cm}^3\) of gas was collected at \(20^{\circ} \mathrm{C}\) and \(745 \mathrm{~mm}\) of mercury pressure. Find the volume of gas at standard temperature and pressure ____________
A. \(1605.7 \mathrm{~cm}^3\) B. \(917.8 \mathrm{~cm}^3\) C. \(305.1 \mathrm{~cm}^3 \) D. \(109.6 \mathrm{~cm}^3\)
Correct Answer: D
Explanation
\(109.6 \mathrm{~cm}^3\) given: \begin{array}{l} V_1=120 \mathrm{~cm}^3 \\ T_1=20^{\circ} \mathrm{C}+273=293 \mathrm{~K} \\ P_1=745 \mathrm{mmHg} \end{array} at s.t.p. \(\mathrm{P}_2=760 \mathrm{mmHg}\) \(T_2=273 \mathrm{~K}\) using the general gas equation \begin{array}{l} \frac{\mathrm{P}_1 \mathrm{~V}_1}{\mathrm{~T}_1}=\frac{\mathrm{P}_2 \mathrm{~V}_2}{\mathrm{~T}_2} \\ \Rightarrow \mathrm{V}_2=\frac{\mathrm{P}_1 \mathrm{~V}_1 \mathrm{~T}_2}{\mathrm{~T}_1 \mathrm{P}_2} \end{array} \begin{array}{l} V_2=\frac{745 \times 120 \times 273}{293 \times 760}=\frac{24406200}{22680} \\ V_2=109.60 \mathrm{~cm}^3 \end{array}