Equilibrium Constant Calculations: Videos & Practice Problems

Understanding the equilibrium constant (K_c) is crucial in chemical reactions. It can be calculated using the concentrations of reactants and products at equilibrium. For gaseous reactions, K_c is derived from the ratio of the products' concentrations to the reactants', each raised to the power of their stoichiometric coefficients. In a given example, the K_c is determined by plugging in the equilibrium concentrations of methane, carbon dioxide, carbon monoxide, and hydrogen gas into the expression:

K_c=[CO]²[H₂]²[CH₄][CO₂] The resulting value, after considering significant figures, gives us the equilibrium constant for the reaction, which is dimensionless and in this case, is 0.0335. This figure reflects the ratio of product and reactant concentrations at equilibrium, a fundamental concept in chemical thermodynamics.

Equilibrium Constant Calculation

In chemical equilibrium, the equilibrium constant \( K_c \) can be calculated when the equilibrium concentrations of all reactants and products are known. This constant is a crucial aspect of understanding the dynamics of a chemical reaction at equilibrium. It is defined by the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced chemical equation. Notably, solids and pure liquids are excluded from this expression.

For example, consider the reaction where the equilibrium mixture contains 0.255 M of methane (\( CH_4 \)), 1.10 M of carbon dioxide (\( CO_2 \)), 0.388 M of carbon monoxide (\( CO \)), and 0.250 M of hydrogen gas (\( H_2 \)). The equilibrium constant \( K_c \) can be expressed as:

\[K_c = \frac{[CO]^2 \cdot [H_2]^2}{[CH_4] \cdot [CO_2]}\]

Substituting the given concentrations into the equation, we have:

\[K_c = \frac{(0.388)^2 \cdot (0.250)^2}{(0.255) \cdot (1.10)}\]

Calculating this yields an initial value of approximately 0.033543762. Since the equilibrium constant is a dimensionless quantity, it does not carry units. To express \( K_c \) with the appropriate significant figures, we round the result to three significant figures, resulting in:

\[K_c = 0.035\]

This value represents the equilibrium constant for the given reaction, providing insight into the relationship between the concentrations of the reactants and products at equilibrium.

The reaction: 2 NO(g) + Br₂(g) ⇌ 2 NOBr(g), has a K_p of 2.5 x 10² at 35°C. Calculate the equilibrium concentration of NOBr, if equilibrium concentrations of NO and Br₂ are 0.2 atm and 0.050 atm, respectively.

• A. 2 atm
• B. 0.7 atm
• C. 1 atm
• D. 0.5 atm

Answer: (B)

For the reaction below, K_c = 1.5 at a constant temperature. A 3.2 L flask contains an equilibrium mixture of 3 compounds: 3.7 g of NH₄HS, 70. g of NH₃ and unknown amount of H₂S. What is the mass (grams) of H₂S produced at equilibrium?
NH₄HS(s) ⇌ NH₃(g) + H₂S(g)

• A. 12.4 g H₂S
• B. 433 g H₂S
• C. 130 g H₂S
• D. 210 g H₂S

Answer: (C)

Here’s what students ask on this topic:

How do you calculate the equilibrium constant?

To calculate the equilibrium constant (K), you first need to understand that it is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their respective coefficients from the balanced chemical equation.

Here's a step-by-step guide:

1. Write down the balanced chemical equation for the reaction.
2. Identify the reactants and products along with their coefficients.
3. At equilibrium, measure the concentrations of each reactant and product in moles per liter (M).
4. Use the expression for the equilibrium constant, K, which is given by:

K = ^{[C]c [D]d} / _{[A]^a [B]^b}

where:

• [A] and [B] are the molar concentrations of the reactants,
• [C] and [D] are the molar concentrations of the products,
• a, b, c, and d are the coefficients of the reactants and products from the balanced equation.

5. Plug in the equilibrium concentrations into the expression and calculate the value of K.

Remember that for gases, partial pressures can be used instead of concentrations, leading to the equilibrium constant for pressure, K_p. Also, solids and pure liquids do not appear in the expression as their concentrations do not change.

How can the equilibrium constant be calculated without concentrations?

The equilibrium constant (K) for a chemical reaction can be calculated without directly using concentrations if you have access to the standard Gibbs free energy change (ΔG°) for the reaction. This is because ΔG° and K are related through the equation:

$\mathrm{\Delta G°}=-RTln\left(K\right)$

Where:

• ΔG° is the standard Gibbs free energy change in joules per mole (J/mol)
• R is the universal gas constant (8.314 J/mol·K)
• T is the temperature in Kelvin (K)
• K is the equilibrium constant

To find K without concentrations, you would rearrange the equation to solve for K:

$K=e^{\frac{-\mathrm{\Delta G°}}{RT}}$

You'll need to know the value of ΔG° at a given temperature to use this equation. This information can often be found in thermodynamic tables or calculated from standard enthalpy (ΔH°) and entropy (ΔS°) changes using the equation:

How do you calculate the equilibrium constant for a reaction?

To calculate the equilibrium constant (K) for a reaction, you need to know the balanced chemical equation and the concentrations of the reactants and products at equilibrium. The general formula for the equilibrium constant of a reaction is:

$K=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

Here, [A], [B], [C], and [D] represent the molar concentrations of the reactants and products at equilibrium, and a, b, c, and d are the stoichiometric coefficients from the balanced chemical equation.

For a generic reaction:

$aA+bB\rightleftharpoons cC+dD$

You would raise the concentration

How do you calculate the equilibrium constant, K_c?

To calculate the equilibrium constant, K_c, for a chemical reaction, you need to know the balanced chemical equation and the concentrations of the reactants and products at equilibrium. The equilibrium constant is a ratio of the concentrations of the products raised to the power of their coefficients to the concentrations of the reactants raised to the power of their coefficients.

Here's the general formula for a reaction aA + bB → cC + dD:

$K{c}_{}=\frac{\left[C\right]c^{}\left[D\right]d^{}}{\left[A\right]a^{}\left[B\right]b^{}}$

Where:

• [A], [B], [C], and [D] are the molar concentrations of the reactants and products at equilibrium.
• a, b, c, and d are the stoichiometric coefficients of the reactants and products from the balanced equation.

Remember that only gases and aqueous solutions are included in the expression. Pure solids and liquids do not appear in the K_c expression. Make sure to use equilibrium concentrations, not initial concentrations, and ensure that all concentrations are