Question

Explain how to write an equilibrium constant expression.

Short answer

To write an equilibrium constant expression, first understand that it is a measure of the extent to which a reaction proceeds and the mixture of reactants and products at equilibrium. Consider a general reversible reaction: \(aA + bB \rightleftharpoons cC + dD\). The equilibrium constant (K) is given by: \[K = \frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b}\], where the powers (a, b, c, d) represent the coefficients in the balanced equation, and [A], [B], [C], and [D] represent the equilibrium concentrations. Remember, only gases and aqueous species are included in the expression. For example, in the reaction \(2 NO_2(g) \rightleftharpoons N_2O_4(g)\), the equilibrium constant expression is: \[K = \frac{[N_2O_4]}{[NO_2]^2}\].

Step-by-step solution

Understanding Chemical Equilibrium

In a chemical reaction, reactants convert into products, but sometimes, not all reactants are completely consumed. In such cases, a mixture of reactants and products will coexist. The reaction is said to be in a state of equilibrium when the rate of the forward reaction (where reactants are transforming into products) is equal to the rate of the reverse reaction (where products are transforming back into reactants). At equilibrium, the concentration of the reactants and products remains constant but not necessarily equal.

Defining Equilibrium Constant

The equilibrium constant (K) is a measure of the extent to which a reaction proceeds and the mixture of reactants and products at equilibrium. It relates the concentrations of reactants and products at equilibrium. For a general reversible reaction: \(aA + bB \rightleftharpoons cC + dD\) where a, b, c, and d are the stoichiometric coefficients of the species A, B, C, and D respectively, the equilibrium constant is given by: \[K = \frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b}\] Here, [A], [B], [C], and [D] represent the equilibrium concentrations of the species A, B, C, and D, respectively, and the powers (a, b, c, d) represent the coefficients in the balanced equation.

Important Points to Remember

When writing an equilibrium constant expression, it's important to keep these points in mind: 1. The equilibrium constant expression is written using only gases and aqueous species. Pure solids and pure liquids do not appear in the expression. 2. Do not include coefficients as the concentration or pressure of the substance in the expression, instead, raise the concentration or pressure to the power of the coefficient. 3. The equilibrium constant is temperature dependent and changes with any change in the temperature.

Example

For example, consider the following reaction at equilibrium: \(2 NO_2(g) \rightleftharpoons N_2O_4(g)\) To write the equilibrium constant expression, we can follow these steps: 1. Identify the reactants and products: Reactants are NO2 and products are N2O4. 2. Write the expression for K: \[K = \frac{[N_2O_4]}{[NO_2]^2}\] 3. Remember that only gases and aqueous species are included in the expression, which is already achieved in this example. So, the equilibrium constant expression for this reaction is: \[K = \frac{[N_2O_4]}{[NO_2]^2}\]

Key concepts

Chemical Equilibrium

Chemical equilibrium is a fascinating concept that plays a vital role in understanding chemical reactions. Imagine a situation where a chemical reaction is taking place, and both reactants and products are present. As the reaction progresses, reactants are being transformed into products, but at the same time, products might also be changing back into reactants. When the rate at which reactants convert into products equals the rate at which products revert back to reactants, the system is said to be at equilibrium. At this point, the concentrations of reactants and products remain steady even though the reactions are still occurring. This dynamic balance is characteristic of chemical equilibrium. It doesn't mean the reactants and products are equal in concentration; rather, their concentrations are constant over time.

Reaching this state is crucial for several natural processes, such as cellular respiration and photosynthesis, and it is essential in various industrial processes.

Reversible Reactions

To fully grasp chemical equilibrium, it's essential to understand reversible reactions. These are reactions where the transformation from reactants to products and the reverse transformation from products back to reactants occur simultaneously. Unlike irreversible reactions, which proceed in one direction until the reactants are used up, reversible reactions can establish an equilibrium state.

In a closed system where reversible reactions occur, both the forward and reverse paths are active. For example, in a simple reaction represented by A + B ⇌ C + D, the forward reaction (A + B forming C + D) happens just as the reverse reaction (C + D forming A + B).

The hallmark of a reversible reaction is this ability to reach a state where both product and reactant formation rates are balanced, maintaining a stable system known as equilibrium. Understanding these reactions helps predict the behavior of many chemical processes.

Equilibrium Concentrations

Equilibrium concentrations refer to the concentrations of reactants and products present in a chemical system when it has reached equilibrium. These concentrations are key to understanding how far a reaction has progressed and which direction the reaction favors.

The equilibrium constant expression, represented by the letter K, gives us a mathematical way to calculate these concentrations. For any given chemical reaction at equilibrium, such as the general equation:\[ aA + bB \rightleftharpoons cC + dD \]the equilibrium constant (K) is expressed as:\[ K = \frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b} \]Here, \([A]\) and \([B]\) are the equilibrium concentrations of the reactants, while \([C]\) and \([D]\) are those of the products. The exponents correspond to the stoichiometric coefficients in the reaction.

This equilibrium constant depends on temperature, highlighting the conditions under which the reaction favors the forward or reverse pathway.

Reaction Stoichiometry

Reaction stoichiometry involves using the coefficients of a balanced chemical equation to relate amounts of reactants and products. It's a critical aspect when writing the equilibrium constant expression as it determines the powers to which concentrations are raised. These coefficients provide the proportion in which substances react or form.

Take the reaction 2NO₂(g) ⇌ N₂O₄(g) as an example. Here, the coefficient 2 in front of NO₂ tells us that two moles of nitrogen dioxide react to form one mole of dinitrogen tetroxide. In the equilibrium constant expression:\[ K = \frac{[N_2O_4]}{[NO_2]^2} \]the exponent 2 in \([NO_2]^2\) comes from this stoichiometric coefficient.

By understanding the stoichiometry of a reaction, you can accurately determine and calculate the equilibrium concentrations, making it an indispensable tool in analyzing chemical reactions.