Question

A rigid, 5.00-L container is filled with enough Ne so that the pressure is 0.645 atm at 25.7°C. A quantity of F2 is added to the container so that the new pressure is 1.290 atm at 25.7°C. Finally, a quantity of CH4 is added to the container so that the final pressure of the mixture is 1.674 atm at 25.7°C. What is the mole fraction of each component of the mixture?

Answer 1

Sol :-

Given,

Partial pressure of Ne (P_Ne) = 0.645 atm  

Total pressure (P_T) = 1.674 atm

From Dalton law of partial pressure " At constant volume and temperature, the total pressure of the non-reacting gaseous mixture will be the sum of the partial pressure of each individual gas.

So,

Partial pressure of F₂ (P_F2) = 1.290 atm - 0.645 atm = 0.645 atm

Similarly,

Partial pressure of CH₄ (P_CH4) = 1.674 atm - (0.645 + 0.645) atm = 0.384 atm

Also, from the application of Dalton law of partial pressure:

Partial pressure of a gas (P_gas) = Total pressure (P_T) x Mole fraction of a gas (X_gas)

So,

X_gas = P_gas / P_T

Now,

X_Ne = P_Ne / P_T

= 0.645 atm / 1.674 atm

= 0.385

Similarly,

X_F2 = P_F2 / P_T

= 0.645 atm / 1.674 atm

= 0.385

and

X_CH4 = P_CH4 / P_T

= 0.384 atm/ 1.674 atm

= 0.230

Hence, Mole fraction of Ne = 0.385 Mole fraction of F2 = 0.385 and Mole fraction of CH4 = 0.230