Easy Equilibrium Constant (Kc) Practice Questions

Concept Explanation

The equilibrium constant ($K_c$) is a numerical value that describes the relative concentrations of reactants and products in a chemical system at dynamic equilibrium at a specific temperature. When a reversible reaction reaches equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of all species remain constant over time. According to the Law of Mass Action, the $K_c$ expression is written as the product of the molar concentrations of the products divided by the product of the molar concentrations of the reactants, each raised to the power of their stoichiometric coefficients.

For a general reaction: $aA + bB \rightleftharpoons cC + dD$, the expression is:

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

Key rules for writing $K_c$ expressions include:

• Only species in the aqueous (aq) or gaseous (g) states are included in the expression.

• Pure solids (s) and liquids (l) have constant concentrations and are omitted from the $K_c$ formula.

• The value of $K_c$ is temperature-dependent; changing the temperature will change the value of the constant.

• A large $K_c$ (> 1) indicates that products are favored at equilibrium, while a small $K_c$ (< 1) indicates that reactants are favored.

Understanding these basics is essential before moving on to more complex topics like Ka and Kb calculations or investigating strong vs weak acids, where equilibrium principles are applied to ionic dissociation.

Solved Examples

Below are three fully worked examples to demonstrate how to write expressions and calculate values for the equilibrium constant (Kc).

1. Writing an Expression: Write the $K_c$ expression for the reaction: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$.

   1. Identify the products: $NH_3$ with a coefficient of 2.

   2. Identify the reactants: $N_2$ (coefficient 1) and $H_2$ (coefficient 3).

   3. Place products in the numerator and reactants in the denominator, raising each to the power of their coefficient.

   4. Solution: $K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$

2. Calculating $K_c$ from Concentrations: For the reaction $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$, the equilibrium concentrations are $[H_2] = 0.10 \text{ M}$, $[I_2] = 0.20 \text{ M}$, and $[HI] = 0.40 \text{ M}$. Calculate $K_c$.

   1. Write the expression: $K_c = \frac{[HI]^2}{[H_2][I_2]}$.

   2. Substitute the values: $K_c = \frac{(0.40)^2}{(0.10)(0.20)}$.

   3. Calculate the numerator: $0.16$.

   4. Calculate the denominator: $0.02$.

   5. Final Answer: $K_c = 8.0$.

3. Handling Heterogeneous Equilibria: Write the $K_c$ expression for $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$.

   1. List all species: $CaCO_3(s)$, $CaO(s)$, and $CO_2(g)$.

   2. Apply the rule: Omit solids and liquids.

   3. $CaCO_3$ and $CaO$ are both solid (s), so they are excluded.

   4. Solution: $K_c = [CO_2]$.

Practice Questions

Test your knowledge with these easy equilibrium constant (Kc) practice questions. Ensure you pay attention to the physical states of each substance.

1. Write the equilibrium constant expression for the following reaction: $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$.

2. In a 1.0 L flask, the equilibrium concentrations for the reaction $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$ are $[PCl_5] = 0.5 ext{ M}$, $[PCl_3] = 0.2 ext{ M}$, and $[Cl_2] = 0.2 ext{ M}$. Calculate the value of $K_c$.

3. Identify which species should be excluded from the $K_c$ expression for this reaction: $Mg(s) + 2HCl(aq) \rightleftharpoons MgCl_2(aq) + H_2(g)$.

4. Write the $K_c$ expression for the decomposition of liquid water into its gaseous elements: $2H_2O(l) \rightleftharpoons 2H_2(g) + O_2(g)$.

5. At a certain temperature, $K_c = 50.0$ for the reaction $H_2 + I_2 \rightleftharpoons 2HI$. If the equilibrium concentrations of $H_2$ and $I_2$ are both $0.02 ext{ M}$, what is the equilibrium concentration of $HI$?

6. For the reaction $CO(g) + Cl_2(g) \rightleftharpoons COCl_2(g)$, the equilibrium concentrations are $[CO] = 1.2 ext{ M}$, $[Cl_2] = 0.05 ext{ M}$, and $[COCl_2] = 0.15 ext{ M}$. Calculate $K_c$.

7. True or False: If you double the coefficients of a balanced chemical equation, the value of $K_c$ remains the same.

8. Write the $K_c$ expression for the reaction: $NH_4Cl(s) \rightleftharpoons NH_3(g) + HCl(g)$.

9. A reaction has a $K_c$ value of $1.5 \times 10^{-10}$. At equilibrium, does the mixture contain mostly reactants or mostly products?

10. Calculate $K_c$ for the reaction $A + B \rightleftharpoons 2C$ if the equilibrium concentrations are $[A] = 0.4 ext{ M}$, $[B] = 0.4 ext{ M}$, and $[C] = 0.8 ext{ M}$.

Answers & Explanations

1. Answer: $K_c = \frac{[SO_3]^2}{[SO_2]^2[O_2]}$. All species are gases, so they are all included. The coefficients become exponents.

2. Answer: $0.08$. $K_c = \frac{[PCl_3][Cl_2]}{[PCl_5]} = \frac{(0.2)(0.2)}{0.5} = \frac{0.04}{0.5} = 0.08$.

3. Answer: $Mg(s)$. Pure solids are always excluded from the equilibrium constant expression because their density (and thus concentration) does not change significantly during the reaction.

4. Answer: $K_c = [H_2]^2[O_2]$. Since $H_2O$ is in the liquid state (l), it is excluded from the denominator.

5. Answer: $0.141 ext{ M}$. $K_c = \frac{[HI]^2}{[H_2][I_2]} \Rightarrow 50 = \frac{[HI]^2}{(0.02)(0.02)}$. Thus, $[HI]^2 = 50 \times 0.0004 = 0.02$. Taking the square root gives $[HI] \approx 0.141 ext{ M}$.

6. Answer: $2.5$. $K_c = \frac{[COCl_2]}{[CO][Cl_2]} = \frac{0.15}{(1.2)(0.05)} = \frac{0.15}{0.06} = 2.5$.

7. Answer: False. If you double the coefficients, the new equilibrium constant ($K_c'$) will be the square of the original constant ($K_c^2$).

8. Answer: $K_c = [NH_3][HCl]$. The reactant $NH_4Cl$ is a solid and is therefore omitted from the expression.

9. Answer: Mostly reactants. A very small $K_c$ (much less than 1) indicates that the equilibrium position lies far to the left, favoring the reactants.

10. Answer: $4.0$. $K_c = \frac{[C]^2}{[A][B]} = \frac{(0.8)^2}{(0.4)(0.4)} = \frac{0.64}{0.16} = 4.0$.

Quick Quiz

Frequently Asked Questions

What is the difference between Kc and Kp?

$K_c$ is the equilibrium constant defined by molar concentrations (mol/L), whereas $K_p$ is defined by the partial pressures of gaseous reactants and products. They are related by the equation $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas.

Why are solids and liquids excluded from Kc?

The concentrations of pure solids and pure liquids are considered constant because their density does not change significantly regardless of how much of the substance is present. Since equilibrium constants only track changes in concentration, these constant values are mathematically incorporated into the $K_c$ value itself.

Can Kc be a negative number?

No, $K_c$ cannot be negative because it is calculated using concentrations and coefficients as exponents, all of which result in positive values. A $K_c$ value can be very close to zero, but never less than zero.

Does Kc have units?

In many introductory chemistry courses, $K_c$ is treated as unitless by using "activities" relative to a standard state of 1 M. However, if units are required, they are derived by substituting $(mol/L)$ into the expression, which varies depending on the stoichiometry of the reaction.

How is Kc related to reaction rate?

$K_c$ describes the extent of a reaction at equilibrium, but it provides no information about how fast the reaction reaches that state. A reaction can have a very large $K_c$ but proceed so slowly that it appears not to happen at all without a catalyst.

For more practice with related thermodynamic concepts, check out our guide on easy enthalpy change practice questions.

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