Equal numbers of moles of he(g), ar(g), and ne(g) are placed in a glass vessel at room temperature. if the vessel has a pinhole-sized leak, which of the following will be true regarding the relative values of the partial pressures of the gases remaining in the vessel after some of the gas mixture has effused?

The option that will be true regarding the relative values of the partial pressures of the gases remaining in the vessel after some of the gas mixture has effused is;

A) Pressure He < Pressure Ne < Pressure Ar

The missing options are;

a) Pressure He < Pressure Ne < Pressure Ar

b) Pressure He < Pressure Ar < Pressure Ne

c) Pressure Ar < Pressure Ne < Pressure He

d) Pressure He = Pressure Ar = Pressure Ne

Now, to answer this question, let us first write the formula for graham's law of diffusion/effusion.

r ∝ 1/√M

Where;

r is rate of diffusion/effusion

M is molar mass

In effusion, there is usually a barrier with very small holes that prevents the gas from expanding very fast into a new volume. Thus, we can say that the heavier the gas, the lesser the effusion rate and the lighter the gas, the faster the effusion rate.

Now, the pressure of the heavier gas is usually higher than that of the lighter ones.

The molar mass of the given gases are;

Molar mass of He = 4 g/mol

Molar mass of Ne = 20.18 g/mol

Molar mass of Ar = 39.95 g/mol

From the effusion equation, we see that the rate of effusion is inversely proportional to the molar mass.

Thus, the higher the molar mass, the lesser the effusion rate and as such, the higher the pressure since it is a heavy gas.

Thus, Ar has the highest Molar mass and will have the highest pressure. Next is Neon(Ne), then Helium(He).

Thus, in conclusion;

Pressure He < Pressure Ne < Pressure Ar

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VP as function of time => VP(Ar) > VP(Ne) > VP(He).

Explanation:

Effusion rate of the lighter particles will be higher than the heavier particles. That is, the lighter particles will leave the container faster than the heavier particles. Over time, the vapor pressure of the greater number of heavier particles will be higher than the vapor pressure of the lighter particles.

=> VP as function of time => VP(Ar) > VP(Ne) > VP(He).

Review Graham's Law => Effusion Rate ∝ 1/√formula mass.

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