Question

\(\begin{array}{c}{\text { Consider the reaction: }} \\\ {\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)}\end{array}\)

Short answer

The equilibrium constant (K) for the reaction is represented by the expression K = \frac{{[HI]^2}}{{[H2][I2]}}. The values of [HI], [H2], and [I2] need to be substituted to calculate K, or K can be used to find any missing equilibrium concentration.

Step-by-step solution

Write the equation for the equilibrium constant

For the given chemical reaction, the equilibrium constant (K) expression is written based on the law of mass action. In this case, K is the ratio of the product of the concentrations of the products raised to their stoichiometric coefficients to the product of the concentrations of the reactants raised to their stoichiometric coefficients.

Define the equilibrium concentrations

Let the equilibrium concentrations of H2, I2, and HI be represented by [H2], [I2], and [HI], respectively. These concentrations are usually given in moles per liter (mol/L).

Substitute equilibrium concentrations into the K expression

If the equilibrium concentrations are given or can be calculated, substitute them into the equilibrium constant expression formulated in step 1. Solve for K if all the equilibrium concentrations are known, or solve for the unknown concentration(s) if K is given.

Key concepts

Chemical Equilibrium

One essential concept in chemistry is the idea of chemical equilibrium, which occurs when a reversible chemical reaction has reached a state where the forward and backward reaction rates are equal. This balance means that the concentrations of the reactants and products remain constant over time – they do not necessarily have to be equal to each other.

For example, in the reversible reaction involving hydrogen gas (H₂) and iodine gas (I₂) forming hydrogen iodide (HI), the system reaches equilibrium when the rate at which H₂ and I₂ react to form HI is equal to the rate at which HI decomposes back into H₂ and I₂. It's important to understand that reaching equilibrium does not mean that the reactants and products cease to react; they still do so but in such a way that the amount of each substance remains unchanged.

Law of Mass Action

The Law of Mass Action is a principle that allows us to quantify the state of chemical equilibrium. It posits that the rate of a reaction is directly proportional to the product of the concentrations of the reactants, each raised to the power of a coefficient that represents their stoichiometric coefficient in the balanced equation.

This principle can be used to derive the equilibrium constant expression, which involves the concentrations of products and reactants at equilibrium. For the reaction in question, the Law of Mass Action tells us that the rate of formation of HI is proportional to the concentrations of H₂ and I₂, and the rate of the reverse reaction is proportional to the concentration of HI squared, because 2 molecules of HI are involved.

Stoichiometric Coefficients

In the context of chemical reactions, stoichiometric coefficients are the numbers placed in front of compounds in a chemical equation to balance it in accordance with the law of conservation of mass. These coefficients indicate the ratio of reactants and products that react with each other. When writing the equilibrium constant expression, it's crucial to raise the concentration of each chemical to the power of its stoichiometric coefficient.

In our example with the hydrogen and iodine reaction, the stoichiometric coefficient for H₂ and I₂ is 1, while for HI it is 2. It's important to consider these coefficients carefully, as they greatly influence the value of the equilibrium constant and the overall dynamics of the reaction.

Equilibrium Concentrations

The term equilibrium concentrations refers to the concentrations of reactants and products in a reaction mixture when the system is at equilibrium. These concentrations can be determined experimentally or calculated if the equilibrium constant is known.

In our example, we would denote the equilibrium concentration of hydrogen as [H₂], iodine as [I₂], and hydrogen iodide as [HI]. Knowledge of these values is critical because they allow chemists to predict the position of equilibrium, the extent of the reaction, and even the direction in which the reaction will need to shift if any changes occur in the system's conditions (such as changing concentrations, pressure, temperature, or volume).