Question

\(500\text{ C.C}\) each of hydrogen at \(700\text{ mm Hg}\) pressure and oxygen at \(600\text{ mm Hg}\) pressure are put together in a vessel of \(1\) litre capacity. The final pressure of the gas mixture will be _ _ _ _ mm Hg

• A. \(600\)
• B. \(700\)
• C. \(375\)
• D. \(650\)

Hint:

For mixing ideal gases at constant temperature, use \(P=\frac{\sum P_iV_i}{V_{\text{final}}}\).

Answer 1

The Correct Option is D

We are given two gases. Hydrogen: \[ V_1=500\text{ C.C.},\qquad P_1=700\text{ mm Hg}. \] Oxygen: \[ V_2=500\text{ C.C.},\qquad P_2=600\text{ mm Hg}. \] Final vessel volume is: \[ V=1\text{ litre}=1000\text{ C.C.}. \] For ideal gases at constant temperature, final pressure of mixture is obtained from: \[ P=\frac{P_1V_1+P_2V_2}{V}. \] Substitute values: \[ P=\frac{700(500)+600(500)}{1000}. \] \[ P=\frac{350000+300000}{1000}. \] \[ P=\frac{650000}{1000}. \] \[ P=650\text{ mm Hg}. \] Therefore, the final pressure of the gas mixture is: \[ 650\text{ mm Hg}. \]