'A' Level Chemistry Problem Analysis: Inert Gas Equilibria

QN: What happens to position of equilibrium when an inert gas (eg. helium) is added at constant volume (eg. in a steel vessel)?

Thought process:

Adding helium to the equilibrium mixture at constant volume increases the total gas pressure and decreases the mole fractions of all 3 gases, but the partial pressure of each gas given by the product of its (reduced) mole fraction and the (increased) total pressure does not change. Hence, position of equilibrium does not change.

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QN: What happens to position of equilibrium when an inert gas (eg. helium) is added at constant pressure, but not constant volume?

Thought process:

The important effect is on the partial pressure (mole fraction x total pressure) of reactants versus products, and since the mole fractions of the gases are now reduced (on addition of helium), their partial pressures are also reduced (since total pressure remains the same).

Another way to think about it, is that with increased volume, the concentrations/molarities of the reactant and product gases, all decrease.

Since on the RHS of equation (or numerator of Qc or Kc expression) has 2 gaseous terms (each unimolar), while the LHS of equation (or denominator of Qc or Kc expression) has only 1 (unimolar) gaseous term, in effect, the decrease in RHS or numerator is greater than the decrease in LHS or denominator, which translates into Qc < Kc, and the position of equilibrium (Kc) now is shifted to the right of Qc, so the net reaction is the forward reaction to produce more moles of gas until Qc = Kc.

So to summarize, the effect on total pressure is not important, it is relative concentrations/molarities or partial pressures (ie LHS vs RHS), which determines positional shifts of equilibrium (ie. Qc vs Kc).

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