Question

To an evacuated vessel with a movable piston under the external pressure of 1atm, 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm, at $0{}^\circ$C) are introduced. Considering the ideal gas behaviour determines the total volume (in litre) of the gases at $0{}^\circ$C.

Answer 1

partial pressure of any component is a product of vapour pressure of pure component and its mole fraction. The number of moles of unknown compounds can be calculated using this. The ideal gas equation is
$PV=nRT$

Complete step by step solution:
-Let us consider an unknown compound as X. As given in data, vapour pressure exerted by an unknown compound is 0.68 atm.
-Partial vapour pressure 0.68 atm is equal to the product of mole fraction and total pressure which is 1 atm as given in data.
So the mole fraction of any component is the ratio of the number of moles of that component to the number of moles of all components present. So mole fraction of compound x can be written as follows:
${{X}_{X}}=\dfrac{{{n}_{x}}}{{{n}_{x}}+{{n}_{He}}}$
Number of moles of He is 0.1 mol.
${{n}_{x}}$=0.2125 moles so total number of moles are 0.1+0.2125=0.3125
Ideal gas equation is $PV=nRT$
$0{}^\circ$C is equal to 273 k.
the total volume (in litre) of the gases at $0{}^\circ$C, $\dfrac{nRT}{P}=\dfrac{0.3125\times 0.082\times 273}{1}$=7L

Hence, the total volume (in litre) of the gases at $0{}^\circ$C is $7L$.

Note: As per given in data, external pressure is 1 atm. Out of this 1 atm, 0.68 atm is exerted by an unknown compound so (1-0.68 =0.32 atm) is the pressure exerted by helium. So another method to calculate the total volume of gases is
$PV=nRT$
V= $\dfrac{0.1\times 0.082\times 273}{0.32}$= 7L