Question

To an evacuated vessel with a movable piston under a total pressure of 1 atm, 0.1 mol of He and an unknown compound (vapour pressure 0.68 atm at 0${}^o$C) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0${}^o$C is close to:

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is A 7

Let X be the unknown compound. Its partial pressure (0.68 atm) is equal to the product of the mole fraction $\left(X_X\right)$ and the total pressure which is 1 atm. So, mole fraction will be same as partial pressure for X gas.

Thus the mole fraction of X is $X_X=0.68=\frac{n_X}{n_X+n_{He}}$.

But $n_{He}=0.1$

Thus $n_X=\frac{0.68\times 0.1}{1-0.68}=0.2125$ moles.

The total number of moles $n=0.1+0.2125=0.3125$

The ideal gas equation is $PV=nRT$

Thus, the total volume (in litre) of the gases $V=\frac{nRT}{P}=\frac{0.3125\times 0.082\times 273}{1}=6.99\approx 7L$.

Option A is correct.