This system has an equilibrium constant of 50. 5 at 448°C: H2(g) I2(g) ↔ 2HI(g). What is the reaction quotient, Q, for this system when [H2] = 0. 200 M, [I2] = 0. 100 M, and [HI] = 3. 00 M?.

The reaction quotient Q is a measure of the relative amount of products and reactants present in a reaction at a given time when a reaction has not yet reached equilibrium.

For the reaction aA + bB ⇄ cC + dD, Q adopts the expression:

[tex]Q=\frac{[C]^{c}[D]^{d} }{[A]^{a} [B]^{b} }[/tex]

That is, Q is defined as the ratio between the equilibrium concentrations of products and reactants raised to their respective stoichiometric coefficients, at a given temperature.

Comparison between Q and Kc

Comparing Q with Kc allows us to find out the state and evolution of the system:

If the reaction quotient equals the equilibrium constant, Q = Kc, the system has reached chemical equilibrium.
If the reaction quotient is greater than the equilibrium constant, Q > Kc, the system is not in equilibrium. In this case the forward reaction predominates and there will be more product present than is obtained at equilibrium. Therefore, that product is used to favor the reverse reaction and reach equilibrium. Then the system will evolve to the left to increase the concentration of reactants.
If the reaction quotient is less than the equilibrium constant, Q < Kc, the system is not in equilibrium. The concentration of the reactants is higher than it would be at equilibrium, so the forward reaction predominates. Thus, the system will evolve to the right to increase the concentration of products.

Q for this system

In this case the system is:

H₂(g) + I₂(g) ↔ 2 HI(g)

So, Q adopts the expression:

[tex]Q=\frac{[HI]^{2} }{[H_{2} ] [I_{2} ] }[/tex]

You know:

[H₂] = 0. 200 M
[I₂] = 0. 100 M
[HI] = 3. 00 M

Replacing in the expression of Q:

[tex]Q=\frac{(3 M)^{2} }{(0.2 M) (0.1 M)}[/tex]

Solving:

[tex]Q=\frac{9 M^{2} }{0.02 M^{2} }[/tex]

Q= 450

Finally, the reaction quotient Q has a value of 450.

In this case, the reaction quotient is greater than the equilibrium constant, Q > Kc. Then, the system is not in equilibrium. The forward reaction predominates and the system will evolve to the left to increase the concentration of reactants.

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