The Equilibrium Law: Predicting Chemical Outcomes
What is a Reversible Reaction?
In many chemical reactions, the reactants are completely converted into products. However, in a reversible reaction, the reaction can proceed in both the forward and reverse directions simultaneously. Imagine a busy street where people are constantly walking from one sidewalk to the other. Even though individuals are moving in both directions, the overall number of people on each sidewalk remains constant. This is the essence of a state called dynamic equilibrium.
Dynamic equilibrium is reached when the rate of the forward reaction (reactants turning into products) equals the rate of the reverse reaction (products turning back into reactants). At this point, the concentrations of all reactants and products remain constant over time, even though the reactions have not stopped. It is a dynamic, not a static, state.
Introducing the Equilibrium Constant Expression
The Equilibrium Law gives us a mathematical way to describe this state. For a general reversible reaction:
Where A and B are reactants, C and D are products, and a, b, c, and d are their respective coefficients in the balanced equation, the equilibrium constant expression is written as:
Here, Kc is the equilibrium constant with respect to concentration. The square brackets [ ] represent the molar concentration (moles per liter, M) of each substance at equilibrium. It is crucial to remember that the concentrations of the products are always in the numerator, and the concentrations of the reactants are always in the denominator.
What Does the Value of K Tell Us?
The numerical value of the equilibrium constant provides immediate insight into the position of equilibrium, or in other words, the relative amounts of products and reactants present at equilibrium.
| Value of K | Interpretation | Description at Equilibrium |
|---|---|---|
| $ K >> 1 $ (K is very large) | Products are favored. | The numerator (products) is much larger than the denominator (reactants). The equilibrium mixture consists mostly of products. |
| $ K << 1 $ (K is very small) | Reactants are favored. | The denominator (reactants) is much larger than the numerator (products). The equilibrium mixture consists mostly of reactants. |
| $ K \approx 1 $ (K is close to 1) | Neither is strongly favored. | The concentrations of products and reactants are comparable. |
A Practical Example: The Haber Process
Let's apply the Equilibrium Law to a reaction of immense industrial importance: the synthesis of ammonia[1] from nitrogen and hydrogen, known as the Haber process.
The balanced chemical equation is:
According to the Equilibrium Law, the equilibrium constant expression for this reaction is:
At a certain temperature, the value of Kc might be 6.0 x 10-2. Since this value is less than 1, we know that the equilibrium position lies to the left; the reaction mixture at equilibrium contains more nitrogen and hydrogen reactants than ammonia product. This is a key challenge in the industrial process, which is why specific conditions (high pressure, moderate temperature) are used to shift the equilibrium towards producing more ammonia, guided by Le Chatelier's principle.
The Reaction Quotient (Q): Predicting the Direction of Change
How can we tell if a reaction mixture is at equilibrium, and if not, which way it will proceed to reach equilibrium? We use a very similar expression called the reaction quotient, Q.
The expression for Q has the exact same form as the expression for K. The critical difference is that Q is calculated using the initial concentrations (or pressures) of the reactants and products, which may or may not be the equilibrium concentrations.
By comparing Q to K, we can predict the direction in which the reaction will proceed:
- If Q < K: The reaction will proceed in the forward direction (to the right) to produce more products until Q = K.
- If Q > K: The reaction will proceed in the reverse direction (to the left) to produce more reactants until Q = K.
- If Q = K: The reaction is at equilibrium, and no net change will occur.
Equilibrium Involving Gases and Partial Pressures (Kp)
For reactions involving gases, it is often more convenient to measure pressures rather than concentrations. The Equilibrium Law can be written using the partial pressures[2] of the gases. This constant is denoted as Kp.
For the general reaction: $ aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g) $
Where P_A, P_B, etc., are the partial pressures of the gases at equilibrium. The relationship between Kc and Kp is given by the formula: $ K_p = K_c (RT)^{\Delta n} $, where R is the gas constant, T is the temperature in Kelvin, and $ \Delta n $ is the change in the number of moles of gas (moles of products - moles of reactants).
Important Questions
Does the equilibrium constant change with concentration or pressure?
No. The equilibrium constant, K, is only dependent on temperature. Changing the concentration of a reactant or product, or changing the total pressure (for gaseous reactions), will shift the position of equilibrium (as predicted by Le Chatelier's principle) but will not change the value of K itself. The system will adjust until the ratio of concentrations (or pressures) once again equals the constant K.
What is not included in the equilibrium constant expression?
Pure solids (s) and pure liquids (l) are not included in the equilibrium constant expression. Their concentrations are effectively constant and are incorporated into the value of K. For example, in the reaction $ CaCO_{3}(s) \rightleftharpoons CaO(s) + CO_{2}(g) $, the equilibrium expression is simply $ K_p = P_{CO_{2}} $ or $ K_c = [CO_{2}] $. The solids do not appear in the expression.
How is the equilibrium constant for a reverse reaction related to the forward reaction?
The equilibrium constant for a reverse reaction is the reciprocal of the equilibrium constant for the forward reaction. If the forward reaction $ A \rightleftharpoons B $ has a constant $ K_{forward} $, then the reverse reaction $ B \rightleftharpoons A $ has a constant $ K_{reverse} = 1 / K_{forward} $.
Conclusion
Footnote
[1] Ammonia (NH3): A colorless gas with a pungent smell, widely used as a fertilizer and in the production of many chemicals.
[2] Partial Pressure: The pressure that a single gas in a mixture would exert if it occupied the entire volume alone. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas.