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Calculate Kc for The Following Equilibrium at A Particular Temperature

Reviewed by Calculator Editorial Team

The equilibrium constant (Kc) is a fundamental concept in chemical equilibrium that describes the ratio of product concentrations to reactant concentrations at a given temperature. This calculator helps you determine Kc for any chemical reaction at a specific temperature.

What is Kc?

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. It's specific to a particular temperature and chemical reaction.

For a general reaction:

aA + bB ⇌ cC + dD

The equilibrium constant expression is:

Kc = [C]c[D]d / [A]a[B]b

Where [A], [B], [C], and [D] represent the molar concentrations of the reactants and products at equilibrium.

How to Calculate Kc

To calculate Kc, you need to know the concentrations of all reactants and products at equilibrium. The steps are:

  1. Write the balanced chemical equation
  2. Determine the equilibrium concentrations of all species
  3. Write the equilibrium constant expression
  4. Substitute the equilibrium concentrations into the expression
  5. Calculate the numerical value of Kc

For reactions that involve solids or liquids, their concentrations are not included in the equilibrium constant expression because their concentrations are essentially constant.

Formula

The general formula for calculating Kc is:

Kc = [Products]coefficients / [Reactants]coefficients

Where:

  • [Products] = Concentrations of all products
  • [Reactants] = Concentrations of all reactants
  • coefficients = Stoichiometric coefficients from the balanced chemical equation

For example, for the reaction:

2A + B ⇌ C + 3D

The equilibrium constant expression would be:

Kc = [C][D]3 / [A]2[B]

Example Calculation

Let's calculate Kc for the reaction:

N2(g) + 3H2(g) ⇌ 2NH3(g)

At equilibrium, the concentrations are:

  • [N2] = 0.10 M
  • [H2] = 0.20 M
  • [NH3] = 0.30 M

The equilibrium constant expression is:

Kc = [NH3]2 / [N2][H2]3

Substituting the values:

Kc = (0.30)2 / (0.10)(0.20)3 = 0.09 / 0.0008 = 112.5

So, Kc = 112.5 at this temperature.

Temperature Dependence

The value of Kc is temperature-dependent. As temperature changes, the equilibrium position shifts, and thus Kc changes. This relationship is described by the van't Hoff equation:

ln(K2/K1) = -ΔH°/R (1/T2 - 1/T1)

Where:

  • K1 and K2 = Equilibrium constants at temperatures T1 and T2
  • ΔH° = Enthalpy change of the reaction
  • R = Universal gas constant (8.314 J/mol·K)

This equation shows that for exothermic reactions (ΔH° < 0), Kc increases with temperature, while for endothermic reactions (ΔH° > 0), Kc decreases with temperature.

FAQ

What units are used for Kc?
Kc is a dimensionless quantity because it's a ratio of concentrations. The units cancel out in the expression.
Can Kc be greater than 1?
Yes, if the products are favored at equilibrium, Kc will be greater than 1. If the reactants are favored, Kc will be less than 1.
How does pressure affect Kc?
Pressure affects Kc only for gaseous reactions. According to Le Chatelier's principle, increasing pressure favors the side with fewer moles of gas, which changes Kc.
What if a reactant or product is a solid or liquid?
Solids and liquids are not included in the Kc expression because their concentrations are essentially constant and don't change during the reaction.