Equilibrium Constants, Expressions, and Le Chatelier’s Principle – Step-by-Step Guidance

Q1. For the reaction below at 298K, given equilibrium concentrations, (i) write the equilibrium expression; (ii) calculate Kc; (iii) does this reaction favor products or reactants? (iv) what is the value of Kp at this temperature? (v) Write an equilibrium expression for Kp.

Background

Topic: Chemical Equilibrium – Equilibrium Constants (Kc and Kp)

This question tests your understanding of how to write equilibrium expressions, calculate equilibrium constants from concentrations, and relate Kc to Kp for reactions involving gases.

Key Terms and Formulas:

• Kc: Equilibrium constant in terms of concentration (mol/L).

• Kp: Equilibrium constant in terms of partial pressure (atm).

• Equilibrium Expression: For a general reaction $aA + bB \rightleftharpoons cC + dD$,

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

• Relationship between Kp and Kc:

$K_p = K_c (RT)^{\Delta n}$

Where $\Delta n =$ (moles of gaseous products) $-$ (moles of gaseous reactants), $R = 0.0821$ L·atm/mol·K, $T$ in Kelvin.

Step-by-Step Guidance

1. Write the balanced chemical equation: $4\ \mathrm{NO} (g) + 6\ \mathrm{H_2O} (g) \rightleftharpoons 4\ \mathrm{NH_3} (g) + 5\ \mathrm{O_2} (g)$

2. Write the equilibrium expression for $K_c$ using the balanced equation. Remember to include only gases and aqueous species (omit pure solids and liquids).

3. Plug the given equilibrium concentrations into your $K_c$ expression. The concentrations are: $[\mathrm{NH_3}] = 0.17$ M, $[\mathrm{O_2}] = 0.39$ M, $[\mathrm{NO}] = 2.36 \times 10^{-2}$ M, $[\mathrm{H_2O}] = 9.98 \times 10^{-3}$ M.

4. Set up the calculation for $K_c$ by substituting the values into the expression you wrote in step 2. Do not calculate the final value yet.

5. To determine if the reaction favors products or reactants, compare the magnitude of $K_c$ (once calculated) to 1. If $K_c \gg 1$, products are favored; if $K_c \ll 1$, reactants are favored.

6. Set up the calculation for $K_p$ using the formula $K_p = K_c (RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas (products minus reactants). Do not solve for $K_p$ yet.

7. Write the equilibrium expression for $K_p$ in terms of partial pressures, analogous to the $K_c$ expression but using $P_{\text{species}}$ instead of concentrations.

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Q2. Using the values of Kc & Kp from (1), determine Kc & Kp if the reaction is: (i) reversed; (ii) multiplied by 9/4; (iii) added to the reaction below: NO2 (g) + N2O (g) ⇌ 3 NO (g), Kc = 7.32×10-2

Background

Topic: Manipulating Equilibrium Constants

This question tests your ability to adjust equilibrium constants when reactions are reversed, multiplied, or added together.

Key Terms and Formulas:

• If a reaction is reversed, $K_{\text{new}} = 1/K_{\text{original}}$

• If a reaction is multiplied by $n$, $K_{\text{new}} = (K_{\text{original}})^n$

• If two reactions are added, $K_{\text{overall}} = K_1 \times K_2$

Step-by-Step Guidance

1. For (i), write the expression for the reversed reaction and recall that the new $K_c$ and $K_p$ are the reciprocals of the original values.

2. For (ii), if the reaction is multiplied by $\frac{9}{4}$, raise both $K_c$ and $K_p$ to the $\frac{9}{4}$ power.

3. For (iii), when adding two reactions, multiply their $K_c$ values to get the new $K_c$ for the sum. Do the same for $K_p$ if both are given.

4. Set up the expressions for each scenario, but do not compute the final values yet.

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Q3. Write an equilibrium expression for the sum of the two reactions above (call it Kc3) and prove that Kc3 is the product of the two Kc values.

Background

Topic: Combining Equilibrium Expressions

This question tests your understanding of how equilibrium constants combine when reactions are added together.

Key Terms and Formulas:

• When two reactions are added, the equilibrium constant for the overall reaction is the product of the individual constants: $K_{c,3} = K_{c,1} \times K_{c,2}$

Step-by-Step Guidance

1. Write the two individual balanced equations and their $K_c$ expressions.

2. Add the two reactions together to get the overall reaction.

3. Write the equilibrium expression for the overall reaction ($K_{c,3}$) using the concentrations of all species involved.

4. Show algebraically that multiplying the two individual $K_c$ expressions yields the overall $K_{c,3}$ expression.

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Q4. Write an equilibrium expression (for Kc) for the following heterogeneous reactions:

• i. SO3 (g) + H2O (l) ⇌ H2SO4 (aq)

• ii. Ru3+ (aq) + 3 Br- (aq) ⇌ RuBr3 (s)

• iii. 2 H2O2 (aq) ⇌ 2 H2O (l) + O2 (g)

Background

Topic: Heterogeneous Equilibria

This question tests your ability to write equilibrium expressions for reactions involving solids, liquids, gases, and aqueous species, and to recognize which species are included in the expression.

Key Terms and Formulas:

• Only aqueous and gaseous species appear in the equilibrium expression; pure solids and pure liquids are omitted.

• General form: $K_c = \frac{\text{[products]}}{\text{[reactants]}}$ (excluding solids and liquids)

Step-by-Step Guidance

1. For each reaction, identify which species are gases, aqueous, solids, or liquids.

2. Write the $K_c$ expression for each, including only aqueous and gaseous species.

3. Set up the expressions, but do not simplify or calculate any values yet.

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Q5. For the reaction NO2 (g) + N2O (g) ⇌ 3 NO (g), if the initial concentrations of NO2 and N2O are 1.38M and 2.24M, and [NO] at equilibrium is 0.489M, (i) what is the equilibrium concentration of NO? (ii) determine Kc under these conditions.

Background

Topic: ICE Tables and Equilibrium Calculations

This question tests your ability to use initial concentrations and changes to determine equilibrium concentrations and calculate $K_c$.

Key Terms and Formulas:

• ICE Table: Initial, Change, Equilibrium

• $K_c = \frac{[NO]^3}{[NO_2][N_2O]}$

Step-by-Step Guidance

1. Set up an ICE table for the reaction, filling in the initial concentrations and the equilibrium concentration of NO.

2. Determine the change in concentration for each species based on the stoichiometry (for every 3 mol NO formed, 1 mol NO2 and 1 mol N2O are consumed).

3. Calculate the equilibrium concentrations of NO2 and N2O using the changes from the ICE table.

4. Set up the $K_c$ expression and substitute the equilibrium concentrations, but do not compute the final value yet.

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Q6. For the reaction H2 (g) + Br2 (g) ⇌ 2 HBr (g), with measured pressures of H2, Br2, and HBr at 3.7 atm, 4.8 atm, and 0.46 atm respectively, calculate Qc and determine if the reaction is progressing to the right, left, or at equilibrium. Kp = 2.1×10^2

Background

Topic: Reaction Quotient (Qc) and Direction of Shift

This question tests your ability to calculate the reaction quotient ($Q_c$) and compare it to $K_p$ to predict the direction the reaction will proceed.

Key Terms and Formulas:

• Reaction Quotient: $Q_c = \frac{[\mathrm{HBr}]^2}{[\mathrm{H_2}][\mathrm{Br_2}]}$ (using concentrations or pressures as appropriate)

• Compare $Q_c$ to $K_p$ (or $K_c$):

  • If $Q < K$, reaction proceeds right (toward products)

  • If $Q > K$, reaction proceeds left (toward reactants)

  • If $Q = K$, system is at equilibrium

Step-by-Step Guidance

1. Write the balanced equation and the expression for $Q_c$ using the given pressures.

2. Plug the given pressures into the $Q_c$ expression.

3. Set up the calculation for $Q_c$ but do not compute the final value yet.

4. Explain how to compare $Q_c$ to $K_p$ to determine the direction of the reaction.

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Q7. For the reaction NO2 (g) + N2O (g) ⇌ 3 NO (g), with starting concentrations of NO2 and N2O at 1.33M and 1.84M, what are the equilibrium concentrations of all three species? Kc = 7.32×10-2

Background

Topic: ICE Tables and Equilibrium Calculations

This question tests your ability to use an ICE table and the equilibrium constant to solve for equilibrium concentrations.

Key Terms and Formulas:

• ICE Table: Initial, Change, Equilibrium

• $K_c = \frac{[NO]^3}{[NO_2][N_2O]}$

Step-by-Step Guidance

1. Set up an ICE table for the reaction, using the initial concentrations and letting the change be $+3x$ for NO, $-x$ for NO2 and N2O.

2. Write the equilibrium concentrations in terms of $x$ for each species.

3. Substitute these expressions into the $K_c$ formula.

4. Set up the equation to solve for $x$, but do not solve for $x$ or the final concentrations yet.

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Q8. For the two reactions below, use Le Chatelier’s principle to predict which direction the equilibrium will shift if the reaction is heated:

• i. H2 (g) + F2 (g) ⇌ 2 HF (g), ΔH = -537 kJ

• ii. 2 C (s) + 2 H2 (g) ⇌ C2H4 (g), ΔH = +52.3 kJ

Background

Topic: Le Chatelier’s Principle and Temperature Effects

This question tests your understanding of how temperature changes affect equilibrium position for exothermic and endothermic reactions.

Key Terms and Concepts:

• Le Chatelier’s Principle: A system at equilibrium will shift to counteract a disturbance.

• For exothermic reactions (ΔH < 0), heat is a product; increasing temperature shifts equilibrium left.

• For endothermic reactions (ΔH > 0), heat is a reactant; increasing temperature shifts equilibrium right.

Step-by-Step Guidance

1. Identify whether each reaction is exothermic or endothermic based on the sign of ΔH.

2. Apply Le Chatelier’s Principle: For each reaction, predict the shift in equilibrium when temperature is increased.

3. Explain the reasoning for each prediction, but do not state the final direction yet.

Try solving on your own before revealing the answer!