7.6 - Properties of the Equilibrium Constant - notes
7.6 - Properties of the Equilibrium Constant
Understanding the equilibrium constant (K)
In chemical reactions, equilibrium is reached when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The equilibrium constant, denoted as K, is a numerical value that describes the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their stoichiometric coefficients. This constant provides insight into the extent of a reaction and whether it favors products or reactants.
Key characteristics of the equilibrium constant
- Fixed value at a given temperature - K remains constant for a specific reaction at a particular temperature, regardless of initial concentrations.
- Indicator of reaction direction - A large K value indicates the reaction favors products, while a small K value suggests reactants are favored.
- Mathematical expression - For a general reaction aA + bB ⇌ cC + dD, the equilibrium constant is expressed as: where brackets denote molar concentrations at equilibrium.
Understanding how K behaves under different manipulations is crucial for predicting the behavior of complex, multistep reactions.
Reversing a reaction and its effect on K
When a chemical reaction is reversed, the products become reactants and vice versa. This change directly impacts the equilibrium constant for the reaction.
Impact of reaction reversal
- Inversion of K - If the original reaction has an equilibrium constant K, the reversed reaction will have an equilibrium constant of 1/K.
- Reasoning behind inversion - Since the numerator (products) and denominator (reactants) of the K expression swap places, the value becomes the reciprocal of the original K.
For example, consider the reaction N2 + 3H2 ⇌ 2NH3 with K = 0.5. If reversed to 2NH3 ⇌ N2 + 3H2, the new equilibrium constant becomes 1/0.5 = 2.0. This shows that reversing a reaction inverts the preference for products or reactants.
Multiplying reaction coefficients and its effect on K
Sometimes, the stoichiometric coefficients of a reaction are scaled by a factor to balance or adjust the reaction equation. This scaling alters the equilibrium constant in a specific way.
Effect of coefficient multiplication
- Raising K to a power - If all stoichiometric coefficients in a reaction are multiplied by a factor c, the equilibrium constant for the new reaction becomes Kc.
- Cause of this change - Each concentration term in the K expression is raised to a power equal to its coefficient. Multiplying coefficients by c means each exponent is also multiplied by c, resulting in the entire K being raised to the power of c.
For instance, for the reaction H2 + I2 ⇌ 2HI with K = 4, if the coefficients are doubled to 2H2 + 2I2 ⇌ 4HI, the new equilibrium constant is 42 = 16. This demonstrates how scaling a reaction amplifies the equilibrium constant.
Combining reactions and their equilibrium constants
In many chemical processes, an overall reaction is the result of multiple individual reactions occurring in sequence. The equilibrium constant for the overall reaction can be determined from the constants of the individual steps.
Rule for combining reactions
- Product of individual K values - When reactions are added together to form an overall reaction, the equilibrium constant for the overall reaction is the product of the equilibrium constants of the individual reactions.
- Why this happens - Adding reactions means combining their equilibrium expressions. Since K is a ratio of products to reactants, multiplying the individual K values accounts for the cumulative effect of each step on the overall equilibrium.
Consider two reactions:
- A ⇌ B with K1 = 2
- B ⇌ C with K2 = 3
When added to form the overall reaction A ⇌ C, the equilibrium constant is K1 × K2 = 2 × 3 = 6. This multiplicative property allows chemists to predict the feasibility of complex reaction pathways.
Applying manipulations to the reaction quotient (Q)
The reaction quotient, Q, is a measure similar to K, but it represents the ratio of product to reactant concentrations at any point during a reaction, not just at equilibrium. Because Q and K share the same mathematical form, the manipulations applied to K are also valid for Q.
Similarities between K and Q
- Identical algebraic structure - For a reaction aA + bB ⇌ cC + dD, Q is calculated as: just like K, but using concentrations at a specific moment.
- Same rules apply - Reversing a reaction inverts Q, multiplying coefficients raises Q to that power, and combining reactions multiplies their Q values.
- Purpose of Q - Q helps predict the direction a reaction will proceed to reach equilibrium by comparing it to K. If Q < K, the reaction favors products; if Q > K, it favors reactants; if Q = K, the system is at equilibrium.
This parallel behavior ensures consistency when analyzing reactions before they reach equilibrium, allowing for dynamic predictions during reaction progress.
Worked example - Calculating K for a reversed reaction
Consider the reaction 2NO2 ⇌ N2O4 with an equilibrium constant K = 8.0. Calculate the equilibrium constant for the reversed reaction N2O4 ⇌ 2NO2.
Step 1: Identify the rule
When a reaction is reversed, the equilibrium constant is inverted.
Step 2: Apply the rule
Original K = 8.0
For the reversed reaction, new K = 1 / 8.0 = 0.125
Step 3: Final answer
The equilibrium constant for the reversed reaction is 0.125.
Worked example - Calculating K for a scaled reaction
For the reaction CO + 1/2 O2 ⇌ CO2 with K = 2.0, calculate the equilibrium constant when the coefficients are multiplied by 2 to give 2CO + O2 ⇌ 2CO2.
Step 1: Identify the rule
When the stoichiometric coefficients are multiplied by a factor c, the equilibrium constant becomes Kc.
Step 2: Apply the factor
Here, the factor c = 2.
New K = (2.0)2 = 4.0
Step 3: Final answer
The equilibrium constant for the scaled reaction is 4.0.
Worked example - Calculating K for combined reactions
Two reactions are combined to form an overall reaction:
- A ⇌ B with K1 = 1.5
- B ⇌ C with K2 = 2.0
Calculate the equilibrium constant for the overall reaction A ⇌ C.
Step 1: Identify the rule
When reactions are added, the overall equilibrium constant is the product of the individual K values.
Step 2: Multiply the K values
Koverall = K1 × K2 = 1.5 × 2.0 = 3.0
Step 3: Final answer
The equilibrium constant for the overall reaction is 3.0.