# CH: Equilibrium # Equilibrium

Reaction equilibrium refers to a state where the forward and reverse reactions occur at equal rates. It is important to note that the concentrations of reactants and products remain constant, even though the individual molecules continue to react. The equilibrium position can be influenced by factors such as temperature, pressure, and the concentrations of reactants and products. The position of the equilibrium can be described in terms of the equilibrium constant (Kc), which expresses the ratio of the concentrations of products to reactants at equilibrium.

## ICE tables

An ICE table (I = initial, C = change, E = equilibrium) is a tabular method used to calculate the concentrations or quantities of species involved in a chemical equilibrium. It helps in determining the equilibrium constant (K) for a given reaction.

Here’s a step-by-step explanation of how to use an ICE table:

Identify the balanced chemical equation: Start by writing down the balanced equation for the chemical reaction in question. For example, let’s consider the reaction:

A + 2B ⇌ C + D

1. Set up the ICE table: Draw a table with three columns labeled “Initial,” “Change,” and “Equilibrium.” List the species involved in the reaction in the rows.
2. Fill in the initial concentrations/amounts: In the “Initial” column, write down the initial concentrations (if the reaction is in a solution) or amounts (if the reaction involves gases or solids) of each species involved. These values are usually given in the problem or can be determined experimentally.
3. Determine the changes in concentration/amount: In the “Change” column, calculate the changes in the concentrations or amounts of the species. This is done by considering the stoichiometry of the reaction. For example, if the reaction proceeds by consuming one mole of A and two moles of B for each mole of C produced, you would subtract the appropriate values from the initial amounts.
4. Express the changes in terms of x: In many cases, the change in concentration/amount is represented by a variable, commonly denoted as x. This variable represents the change at equilibrium. For example, if the change in the concentration of A is -x, the change in the concentration of B is -2x (based on the stoichiometry of the reaction).
5. Calculate the equilibrium concentrations/amounts: In the “Equilibrium” column, add the initial concentrations/amounts to the changes calculated in the previous step. This will give you the concentrations/amounts of each species at equilibrium.
1. Set up the equilibrium expression: Write down the expression for the equilibrium constant (K) based on the balanced chemical equation. For the example reaction, the equilibrium expression would be: K = [C][D] / [A][B]2
2. Substitute the equilibrium concentrations/amounts into the equilibrium expression: Plug in the equilibrium concentrations/amounts from the ICE table into the equilibrium expression. If any concentration/amount contains “x,” substitute it with the appropriate expression involving “x.” This will give you an equation in terms of “x.”
3. Solve for “x”: Solve the equation obtained in the previous step to determine the value of “x.” This can be done through algebraic manipulation. Often, if the x value is extremely small, this step is omitted. So, be sure to check with your instructor on how this step should be approached.
4. Calculate the equilibrium concentrations/amounts: Substitute the value of “x” obtained into the expressions for the equilibrium concentrations/amounts. This will give you the final values for the concentrations/amounts of each species at equilibrium.
5. Calculate the equilibrium constant: Use the equilibrium concentrations/amounts to calculate the value of the equilibrium constant (K) by substituting them into the equilibrium expression.

By following these steps, an ICE table allows you to systematically analyze chemical equilibria and calculate the concentrations/amounts of species involved at equilibrium, as well as the corresponding equilibrium constant.

## Le Châtelier's principle

Le Châtelier’s principle is a fundamental concept in chemistry that describes how a system at equilibrium responds to changes in conditions. It states that if a stress is applied to a system at equilibrium, the system will adjust itself in order to re-establish the equilibrium.

Several factors can influence the position of an equilibrium, including changes in concentration, pressure (for gas-phase reactions), temperature, and the addition or removal of a catalyst.

Change in concentration: If you increase the concentration of a reactant or decrease the concentration of a product, the equilibrium will shift in the forward direction (towards the products). Conversely, if you increase the concentration of a product or decrease the concentration of a reactant, the equilibrium will shift in the reverse direction (towards the reactants).

Change in volume or pressure: When pressure or volume is changed, the equilibrium position of the reaction can be affected. Here’s how it works:

• Increase in pressure/decrease in volume: If the pressure is increased or the volume is decreased, the system will respond by shifting the equilibrium in the direction that reduces the total number of moles of gas. This shift occurs to alleviate the increase in pressure and to decrease the concentration of gas species.
• Decrease in pressure/increase in volume: If the pressure is decreased or the volume is increased, the system will respond by shifting the equilibrium in the direction that increases the total number of moles of gas. This shift occurs to compensate for the decrease in pressure and to increase the concentration of gas species.
• In summary, changes in pressure or volume can shift the equilibrium position of a gas-phase reaction. Increasing the pressure or decreasing the volume favors the side with fewer moles of gas, while decreasing the pressure or increasing the volume favors the side with more moles of gas.

Change in temperature: The effect of temperature change depends on whether the reaction is endothermic or exothermic.

• In exothermic reactions, heat is released as a product. When heat is added to an exothermic reaction at equilibrium, the system will respond by shifting in the reverse direction to absorb the excess heat. If heat is removed from the reaction, the system will respond by shifting in the forward direction.
• In endothermic reactions, heat is required as a reactant. When heat is added to an endothermic reaction at equilibrium, the system will respond by favoring the forward reaction. When heat is removed, the system will respond by shifting in the reverse direction.

For example, the decomposition of dinitrogen tetroxide is an endothermic (heat-consuming) process. For purposes of applying Le Chatelier’s principle, heat may be viewed as a reactant:

Heat + N2O4(g) 2NO2(g)

Raising the temperature of the system is similar to increasing the amount of a reactant, and so the equilibrium will shift to the right (favor the forward reaction). Lowering the system temperature will likewise cause the equilibrium to shift left (favor the reverse reaction). For exothermic processes, heat is viewed as a product of the reaction and so the opposite temperature dependence is observed.

Addition or removal of a catalyst: Adding or removing a catalyst does not affect the position of the equilibrium. However, it can increase the rate at which equilibrium is reached by providing an alternative reaction pathway with a lower activation energy.

It’s important to note that Le Châtelier’s principle provides qualitative predictions about the direction of the shift in equilibrium. It helps understand how the system responds to changes but does not quantitatively predict the extent of the shift. For detailed quantitative analysis, other methods such as equilibrium constants or ICE tables are used.