Question

A 1.0 L container at 298 K contains 1 mole of hydrogen and 2 mole of methane gases. The partial pressures of the two gases and the total pressure is

Select one:

a. pH2 = 24.44 atm, p CH4 = 48.87 atm, P total = 73.31 atm

b. pH2 = 24.44 atm, p CH4 = 24.44 atm, P total = 48.87 atm

c. pH2 = 24.44 atm, p CH4 = 48.87 atm, P total = 24.44 atm

d. pH2 = 48.87 atm, p CH4 = 48.87 atm, P total = 97.74 atm

Answer 1

Correct option. A

Ans. Equal moles of two gases have same volume and pressure under identical conditions of temperature.

Since volume of vessel is fixed at 1.0 L and temperature is fixed at 298 K- the pressure exerted by a gas is directly proportional to number of moles.

Let the pressure exerted by 1 mol gas under given conditions = Y atm.

So,

            Pressure exerted by 1 mol H₂ = Y atm

            Pressure exerted by 2 mol CH₄ = 2 Y atm

            Total pressure = Y atm + 2Y atm = 3Y atm

So, the ratio-

            p(H2) : p (CH4) : total pressure = 1: 2: 3

Now, check which option fulfils 1: 2: 3 ratio-

Option A. p(H2) : p (CH4) : total pressure = 24.44 : 48.87 : 73.31 = 1: 2: 3 (approx)

The ratio is same as 1 : 2: 3. So, it is Correct.

Option B: p(H2) : p (CH4) : total pressure = 24.44 : 24.44: 48.87 = 1: 1: 2 (approx)

Ratio is Not equal to 1: 2: 3. So, it’s incorrect.

Option C: p(H2) : p (CH4) : total pressure = 24.44 : 48.87: 24.44 = 1: 2: 1 (approx)

Ratio is Not equal to 1: 2: 3. So, it’s incorrect.

Option D: p(H2) : p (CH4) : total pressure = 48.87 : 48.87: 97.74 = 1: 1: 2 (approx)

Ratio is Not equal to 1: 2: 3. So, it’s incorrect.