Calculating Chemical Equilibrium

Chemical equilibrium refers to the state in which the concentrations of reactants and products in a chemical reaction remain constant over time. At equilibrium, the forward and reverse reactions occur at the same rate, resulting in no net change in the concentration of reactants and products. This article explains the principles of chemical equilibrium, how to calculate equilibrium constants, and how to apply these calculations to various chemical reactions.

Calculating Chemical Equilibrium

Understanding Chemical Equilibrium

Dynamic Nature of Equilibrium

Chemical equilibrium is dynamic, meaning that even though the macroscopic properties (concentration, pressure, etc.) remain constant, the individual molecular reactions continue to occur. The rates of the forward and reverse reactions are equal at equilibrium.

Equilibrium Constant (K)

The equilibrium constant $K$ is a value that expresses the ratio of the concentrations of products to reactants at equilibrium. It is specific to a given reaction at a particular temperature. For a general reaction:

$aA+bB\rightleftharpoons cC+dD$

the equilibrium constant $K$ is given by:

K=[C]c[D]d[A]a[B]bK = \frac{[C]^c [D]^d}{[A]^a [B]^b}K=[A]a[B]b[C]c[D]d​

where $[A]$, $[B]$, $[C]$, and $[D]$ are the concentrations of the reactants and products at equilibrium, and $a$, $b$, $c$, and $d$ are their respective coefficients in the balanced chemical equation.

Calculating Equilibrium Constants

Homogeneous Equilibria

In homogeneous equilibria, all reactants and products are in the same phase (e.g., all gases or all solutions). The equilibrium constant expression is straightforward and involves concentrations. For example, for the reaction:

N2(g)+3H2(g)⇌2NH3(g)\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)N2​(g)+3H2​(g)⇌2NH3​(g)

the equilibrium constant KcK_cKc​ (for concentration) is:

Kc=[NH3]2[N2][H2]3K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}Kc​=[N2​][H2​]3[NH3​]2​

Heterogeneous Equilibria

In heterogeneous equilibria, reactants and products are in different phases. Only the concentrations of species in the aqueous or gaseous phase are included in the equilibrium constant expression. Solids and liquids are omitted from the equilibrium expression because their concentrations do not change significantly.

For example, in the reaction:

CaCO3(s)⇌CaO(s)+CO2(g)\text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g)CaCO3​(s)⇌CaO(s)+CO2​(g)

the equilibrium constant KpK_pKp​ (for partial pressures) is:

Kp=PCO2K_p = P_{\text{CO}_2}Kp​=PCO2​​

Using Equilibrium Constants

To use equilibrium constants effectively, you must understand their implications. A large $K$ value indicates that the reaction favors the formation of products, while a small $K$ value suggests that the reactants are favored.

Calculating Equilibrium Concentrations

Initial Concentrations and Change in Concentration

To calculate the equilibrium concentrations, follow these steps:

1. Write the Balanced Chemical Equation: Identify the balanced equation for the reaction.
2. Set Up an ICE Table: Create an Initial, Change, Equilibrium (ICE) table to organize the initial concentrations, changes in concentrations, and equilibrium concentrations.For example, for the reaction:

   $\text{A}(g)+\text{B}(g)\rightleftharpoons \text{C}(g)$

   with initial concentrations [A]0[A]_0[A]0​, [B]0[B]_0[B]0​, and [C]0[C]_0[C]0​, the ICE table would look like:

   Species	Initial	Change	Equilibrium
   A	[A]_0	-x	[A]_0 – x
   B	[B]_0	-x	[B]_0 – x
   C	[C]_0	+x	[C]_0 + x

3. Substitute into the Equilibrium Expression: Use the equilibrium concentrations in the expression for $K$ and solve for $x$. Substitute the value of $x$ back into the ICE table to find the equilibrium concentrations.

Example Calculation

Consider the reaction:

N2(g)+3H2(g)⇌2NH3(g)\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)N2​(g)+3H2​(g)⇌2NH3​(g)

with an equilibrium constant KcK_cKc​ of 0.500 and initial concentrations [N2]0=1.00 M[\text{N}_2]_0 = 1.00 \, \text{M}[N2​]0​=1.00M and [H2]0=1.00 M[\text{H}_2]_0 = 1.00 \, \text{M}[H2​]0​=1.00M. Assume [NH3]0=0 M[\text{NH}_3]_0 = 0 \, \text{M}[NH3​]0​=0M. Set up the ICE table:

Substitute into the equilibrium expression:

Kc=[NH3]2[N2][H2]3K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}Kc​=[N2​][H2​]3[NH3​]2​

0.500=(2x)2(1.00−x)(1.00−3x)30.500 = \frac{(2x)^2}{(1.00 – x)(1.00 – 3x)^3}0.500=(1.00−x)(1.00−3x)3(2x)2​

Solve for $x$ to find the equilibrium concentrations of [N2][\text{N}_2][N2​], [H2][\text{H}_2][H2​], and [NH3][\text{NH}_3][NH3​].

Le Chatelier’s Principle

Le Chatelier’s Principle states that if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the system will shift to counteract the change and restore equilibrium.

Concentration Changes

If you increase the concentration of a reactant, the system will shift toward the formation of more products. Conversely, increasing the concentration of a product will shift the equilibrium toward the reactants.

Pressure Changes

For gaseous reactions, increasing the pressure shifts the equilibrium toward the side with fewer moles of gas. Decreasing the pressure favors the side with more moles of gas.

Temperature Changes

Changing the temperature affects the equilibrium position. For exothermic reactions, increasing the temperature shifts the equilibrium toward the reactants. For endothermic reactions, increasing the temperature shifts the equilibrium toward the products.

Conclusion

Calculating chemical equilibrium involves understanding equilibrium constants, setting up and solving ICE tables, and applying Le Chatelier’s Principle to predict shifts in equilibrium. Mastery of these concepts allows chemists to predict reaction outcomes and optimize conditions for desired results in both laboratory and industrial settings.