Equilibrium

Reaction Quotient (Q) - AP Chemistry Rundown

The reaction quotient, denoted as Q, is a concept closely related to equilibrium. It provides a snapshot of the relative amounts of reactants and products present in a reaction at any given point in time. Comparing Q to the equilibrium constant, K, allows us to predict the direction a reversible reaction will shift to reach equilibrium.

Definition and Calculation

The reaction quotient, Q, is calculated using the same formula as the equilibrium constant, K, but with non-equilibrium concentrations or partial pressures.

• For a general reversible reaction:

  $$ aA + bB \rightleftharpoons cC + dD $$

• The reaction quotient, Q, is:

  $$ Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} $$
  Where:

  • [A], [B], [C], and [D] are the concentrations of reactants and products at a specific time.
  • a, b, c, and d are the stoichiometric coefficients from the balanced chemical equation.

  Note: If dealing with gases, partial pressures are used instead of concentrations. $$ Q_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b} $$
  Concentration vs Pressure

Comparing Q and K

The comparison of Q and K is crucial for predicting the direction of a reaction shift.

1. Q < K: The ratio of products to reactants is less than at equilibrium. The reaction will shift to the right, favoring the formation of more products to reach equilibrium.

2. Q > K: The ratio of products to reactants is greater than at equilibrium. The reaction will shift to the left, favoring the formation of more reactants to reach equilibrium.

3. Q = K: The system is at equilibrium. There is no net change in the concentrations of reactants and products. Le Chatelier’s Principle

Applications

• Predicting Reaction Direction: The primary use of Q is to determine which direction a reversible reaction will proceed to reach equilibrium.

• Calculating Equilibrium Concentrations: When combined with an ICE table (Initial, Change, Equilibrium), Q can help determine equilibrium concentrations, especially when initial conditions are not at equilibrium.

• Analyzing Reaction Progress: Q can be used to track the progress of a reaction and determine how close it is to reaching equilibrium.

Example Problem

Consider the following reaction:

$$ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) $$
At a certain point in time, the partial pressures are: $$ P_{N_2} = 2 \ atm $$ , $$ P_{H_2} = 1 \ atm $$ , and $$ P_{NH_3} = 3 \ atm $$ . The equilibrium constant, $$ K_p $$ , for this reaction at the given temperature is 8.

1. Calculate Q:

   $$ Q_p = \frac{(P_{NH_3})^2}{(P_{N_2})(P_{H_2})^3} = \frac{(3)^2}{(2)(1)^3} = \frac{9}{2} = 4.5 $$

2. Compare Q and K:

   $$ Q_p = 4.5 $$ and $$ K_p = 8 $$
   Since $$ Q_p < K_p $$ , the reaction will shift to the right to reach equilibrium, favoring the formation of more ammonia ( $$ NH_3 $$ ). ICE Tables

Common Mistakes to Avoid

• Using Equilibrium Concentrations to Calculate Q: Remember that Q is calculated using non-equilibrium concentrations or partial pressures. Using equilibrium values will simply give you K.

• Forgetting Stoichiometry: The stoichiometric coefficients from the balanced equation are crucial for the correct calculation of Q. Make sure to raise the concentrations or partial pressures to the appropriate powers.

• Incorrectly Comparing Q and K: Double-check whether Q is greater than, less than, or equal to K to accurately predict the direction of the shift.

• Units: K and Q are dimensionless, but concentrations and partial pressures must be in consistent units (e.g., Molarity(M) for concentrations, atm or kPa for partial pressures).