IB Chemistry Quiz: Apply Extent Of Chemical Change
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Apply Extent Of Chemical ChangeQuestion 1 of 20

The equilibrium N₂O₄(g) ⇌ 2NO₂(g) is established in a sealed syringe. The gas mixture is pale brown. When the syringe is placed into a beaker of hot water, the colour of the gas mixture becomes a darker brown. Which statement correctly describes the forward reaction and the value of the equilibrium constant, K_c?

The forward reaction is exothermic and K_c decreases with temperature.
The forward reaction is endothermic and K_c increases with temperature.
The forward reaction is exothermic and K_c increases with temperature.
The forward reaction is endothermic and K_c decreases with temperature.
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IB Chemistry Quiz

IB Chemistry Quiz: Apply Extent Of Chemical Change

Practice Apply Extent Of Chemical Change in IB Chemistry with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Apply Extent Of Chemical Change, giving you a quick way to practice the rules, question types, and explanations that matter most for IB Chemistry.

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Question 1

The equilibrium N₂O₄(g) ⇌ 2NO₂(g) is established in a sealed syringe. The gas mixture is pale brown. When the syringe is placed into a beaker of hot water, the colour of the gas mixture becomes a darker brown. Which statement correctly describes the forward reaction and the value of the equilibrium constant, K_c?

  1. The forward reaction is exothermic and K_c decreases with temperature.
  2. The forward reaction is endothermic and K_c increases with temperature. (correct answer)
  3. The forward reaction is exothermic and K_c increases with temperature.
  4. The forward reaction is endothermic and K_c decreases with temperature.
Explanation: NO₂(g) is a brown gas, while N₂O₄(g) is colourless. A darker brown colour indicates a higher concentration of NO₂, meaning the equilibrium has shifted to the right (products). Since an increase in temperature caused this shift, Le Châtelier's principle implies the forward reaction is endothermic (it absorbs heat). For an endothermic reaction, an increase in temperature increases the value of the equilibrium constant, K_c, as the ratio of products to reactants increases.

Question 2

What is the correct expression for the equilibrium constant, K_c, for the reaction: CaCO₃(s) + 2H⁺(aq) ⇌ Ca²⁺(aq) + H₂O(l) + CO₂(g)?

  1. K_c = [Ca2+][H2O][CO2][CaCO3][H+]2\frac{[\text{Ca}^{2+}][\text{H}_2\text{O}][\text{CO}_2]}{[\text{CaCO}_3][\text{H}^+]^2}
  2. K_c = [Ca2+][CO2][H+]2\frac{[\text{Ca}^{2+}][\text{CO}_2]}{[\text{H}^+]^2} (correct answer)
  3. K_c = [Ca2+][H+]2\frac{[\text{Ca}^{2+}]}{[\text{H}^+]^2}
  4. K_c = [Ca2+][CO2][CaCO3][H+]2\frac{[\text{Ca}^{2+}][\text{CO}_2]}{[\text{CaCO}_3][\text{H}^+]^2}
Explanation: The expression for the equilibrium constant, K_c, includes the concentrations of aqueous and gaseous species. The concentrations of pure solids (CaCO₃(s)) and pure liquids (H₂O(l)) are considered constant and are omitted from the expression. Therefore, K_c is the product of the concentrations of the products raised to their stoichiometric coefficients divided by the product of the concentrations of the reactants raised to their stoichiometric coefficients, excluding the solid and liquid.

Question 3

For the reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), the equilibrium constant K_c is 4.0 at a certain temperature. A reaction vessel is filled with the three gases, and their initial concentrations are [SO₂] = 0.10 mol dm⁻³, [O₂] = 0.20 mol dm⁻³, and [SO₃] = 0.30 mol dm⁻³. Which statement is correct?

  1. The system is at equilibrium.
  2. The reaction quotient Q_c > K_c, so the equilibrium will shift to the left. (correct answer)
  3. The reaction quotient Q_c < K_c, so the equilibrium will shift to the right.
  4. The reaction quotient Q_c > K_c, so the equilibrium will shift to the right.
Explanation: First, calculate the reaction quotient, Q_c, using the initial concentrations: Q_c = [SO₃]² / ([SO₂]²[O₂]) = (0.30)² / ((0.10)²(0.20)) = 0.09 / (0.01 × 0.20) = 0.09 / 0.002 = 45. Now, compare Q_c with K_c (4.0). Since Q_c (45) is greater than K_c (4.0), the ratio of products to reactants is too high. To reach equilibrium, the system must shift to the left, consuming products and forming reactants.

Question 4

2.0 mol of PCl₅(g) is placed in a 1.0 dm³ container and allowed to decompose according to the equation: PCl₅(g) ⇌ PCl₃(g) + Cl₂(g). At equilibrium, 1.5 mol of PCl₅(g) remains. What is the value of the equilibrium constant, K_c?

  1. 0.17 (correct answer)
  2. 0.13
  3. 0.33
  4. 6.0
Explanation: Initial [PCl₅] = 2.0 mol / 1.0 dm³ = 2.0 M. Equilibrium [PCl₅] = 1.5 mol / 1.0 dm³ = 1.5 M. The change in [PCl₅] is 2.0 - 1.5 = 0.5 M. From the stoichiometry of the reaction, for every mole of PCl₅ that decomposes, one mole of PCl₃ and one mole of Cl₂ are formed. Therefore, at equilibrium, [PCl₃] = 0.5 M and [Cl₂] = 0.5 M. Now calculate K_c: K_c = ([PCl₃][Cl₂]) / [PCl₅] = (0.5 × 0.5) / 1.5 = 0.25 / 1.5 ≈ 0.17.

Question 5

Consider the equilibrium: 2NO(g) + O₂(g) ⇌ 2NO₂(g). If helium gas is added to this equilibrium mixture in a rigid container of constant volume, what will be the effect on the position of equilibrium and the concentration of O₂(g)?

  1. The equilibrium shifts right and [O₂] decreases.
  2. The equilibrium shifts left and [O₂] increases.
  3. The equilibrium is not affected and [O₂] remains constant. (correct answer)
  4. The equilibrium shifts left and [O₂] remains constant.
Explanation: Adding an inert gas like helium to a system at constant volume increases the total pressure of the system. However, it does not change the partial pressures or the concentrations of the reacting gases (NO, O₂, and NO₂). Since the concentrations of the species involved in the equilibrium do not change, the reaction quotient Q_c remains equal to K_c, and there is no shift in the position of equilibrium. Consequently, the concentration of O₂ remains constant.

Question 6

The reaction H₂(g) + I₂(g) ⇌ 2HI(g) has an equilibrium constant, K_c, of 49.0 at a certain temperature. If 0.50 mol of H₂ and 0.50 mol of I₂ are placed in a 1.0 dm³ vessel, what is the equilibrium concentration of HI?

  1. 0.39 mol dm⁻³
  2. 0.78 mol dm⁻³ (correct answer)
  3. 0.44 mol dm⁻³
  4. 0.11 mol dm⁻³
Explanation: Set up an ICE table. Initial: [H₂]=0.50, [I₂]=0.50, [HI]=0. Change: [H₂]=-x, [I₂]=-x, [HI]=+2x. Equilibrium: [H₂]=0.50-x, [I₂]=0.50-x, [HI]=2x. Substitute into the K_c expression: K_c = [HI]² / ([H₂][I₂]) = (2x)² / (0.50-x)² = 49.0. Take the square root of both sides: (2x) / (0.50-x) = √49.0 = 7.0. Rearrange to solve for x: 2x = 7.0(0.50-x) => 2x = 3.5 - 7.0x => 9.0x = 3.5 => x ≈ 0.389. The equilibrium concentration of HI is 2x, so [HI] = 2 * 0.389 ≈ 0.78 mol dm⁻³.

Question 7

For the reaction A(g) + 2B(g) ⇌ C(g), the equilibrium constant K_c is 4.0. What is the value of the equilibrium constant for the reaction 2C(g) ⇌ 2A(g) + 4B(g) at the same temperature?

  1. 0.25
  2. 16.0
  3. -8.0
  4. 0.0625 (correct answer)
Explanation: The target reaction is the reverse of the original reaction, and its stoichiometric coefficients are doubled. First, reversing the reaction inverts the equilibrium constant. For C(g) ⇌ A(g) + 2B(g), the new constant K'_c = 1/K_c = 1/4.0 = 0.25. Second, doubling the coefficients of a reaction raises its equilibrium constant to the power of 2. Therefore, for 2C(g) ⇌ 2A(g) + 4B(g), the final constant K''_c = (K'_c)² = (0.25)² = 0.0625.

Question 8

Consider the equilibrium involving the dissolution of magnesium hydroxide: Mg(OH)₂(s) ⇌ Mg²⁺(aq) + 2OH⁻(aq) How will the position of equilibrium and the solubility of Mg(OH)₂ be affected if a small amount of dilute HCl(aq) is added?

  1. Equilibrium shifts to the left and solubility decreases.
  2. Equilibrium shifts to the right and solubility increases. (correct answer)
  3. Equilibrium shifts to the right but solubility decreases.
  4. Equilibrium is unaffected as HCl is not part of the equilibrium expression.
Explanation: Adding dilute HCl introduces H⁺ ions into the solution. These H⁺ ions will react with the OH⁻ ions present in the equilibrium via the neutralization reaction H⁺(aq) + OH⁻(aq) → H₂O(l). This reduces the concentration of OH⁻(aq). According to Le Châtelier's principle, the system will shift to counteract this change. The equilibrium will shift to the right to produce more OH⁻ ions, which means more Mg(OH)₂(s) will dissolve. Therefore, the solubility of Mg(OH)₂ increases.

Question 9

The equilibrium constant, K_c, for the reaction CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g) is 5.0 at a high temperature. In a specific experiment, the concentrations of the species are found to be: [CO] = 0.20 M, [H₂O] = 0.10 M, [CO₂] = 0.40 M, [H₂] = 0.40 M. Which statement correctly describes the system at this moment?

  1. The system is at equilibrium.
  2. The rate of the forward reaction is greater than the rate of the reverse reaction.
  3. The rate of the reverse reaction is greater than the rate of the forward reaction. (correct answer)
  4. The equilibrium constant will increase to 8.0 to match the current concentrations.
Explanation: First, calculate the reaction quotient, Q_c, with the given concentrations: Q_c = ([CO₂][H₂]) / ([CO][H₂O]) = (0.40 × 0.40) / (0.20 × 0.10) = 0.16 / 0.020 = 8.0. Now, compare Q_c to K_c. Since Q_c (8.0) > K_c (5.0), the system is not at equilibrium. The ratio of products to reactants is higher than it would be at equilibrium. To reach equilibrium, the net reaction must proceed in the reverse direction, meaning the rate of the reverse reaction is temporarily greater than the rate of the forward reaction.

Question 10

The following equilibrium exists in a solution containing cobalt(II) ions: [Co(H₂O)₆]²⁺(aq) + 4Cl⁻(aq) ⇌ [CoCl₄]²⁻(aq) + 6H₂O(l) (pink) (blue)

If concentrated hydrochloric acid is added to the pink solution, what is the expected observation and reasoning?

  1. The solution turns blue because the equilibrium shifts to the right. (correct answer)
  2. The solution turns blue because the equilibrium shifts to the left.
  3. The solution becomes a more intense pink because the equilibrium shifts to the left.
  4. There is no colour change because water is a product.
Explanation: Adding concentrated hydrochloric acid increases the concentration of chloride ions, Cl⁻(aq). According to Le Châtelier's principle, the system will counteract this change by shifting the position of equilibrium to consume the added reactant. The equilibrium will shift to the right, producing more [CoCl₄]²⁻(aq). Since [CoCl₄]²⁻(aq) is blue, the solution will turn blue.

Question 11

Initially, a 1.0 dm³ flask contains 1.00 mol of N₂O₄(g). At equilibrium, it is found that 20% of the N₂O₄ has dissociated according to the equation: N₂O₄(g) ⇌ 2NO₂(g). What is the value of the equilibrium constant, K_c?

  1. 0.050
  2. 0.16
  3. 0.20 (correct answer)
  4. 0.50
Explanation: Initial concentration of N₂O₄ is 1.00 mol / 1.0 dm³ = 1.00 M. The amount dissociated is 20% of 1.00 M, which is 0.20 M. According to the stoichiometry, the change in [N₂O₄] is -0.20 M and the change in [NO₂] is +2(0.20 M) = +0.40 M. The equilibrium concentrations are: [N₂O₄] = 1.00 M - 0.20 M = 0.80 M, and [NO₂] = 0 M + 0.40 M = 0.40 M. Now, calculate K_c: K_c = [NO₂]² / [N₂O₄] = (0.40)² / 0.80 = 0.16 / 0.80 = 0.20.

Question 12

The synthesis of ammonia has an equilibrium constant, K_c, of approximately 6.0 x 10⁻² at 400 °C. The equation for the reaction is N₂(g) + 3H₂(g) ⇌ 2NH₃(g). Which conclusion can be drawn from this information alone?

  1. The forward reaction is very slow at 400 °C.
  2. The reaction is exothermic.
  3. At equilibrium, the concentration of NH₃ is low compared to the concentrations of N₂ and H₂. (correct answer)
  4. Increasing the pressure will not increase the yield of ammonia.
Explanation: The value of the equilibrium constant, K_c, indicates the extent of a reaction at equilibrium. A small K_c value (K_c < 1) means that the ratio of [products]/[reactants] is small. This indicates that at equilibrium, the concentrations of the reactants are significantly greater than the concentrations of the products. The value of K_c gives no information about the rate of reaction (A) or the enthalpy change (B) without further data. Increasing pressure would shift the equilibrium right, increasing the yield (D).

Question 13

The volume of the container for the following equilibrium is suddenly doubled at constant temperature: PCl₃(g) + Cl₂(g) ⇌ PCl₅(g) Which statement describes the immediate effect on the reaction rates and the subsequent shift in equilibrium?

  1. Both forward and reverse rates decrease, and the equilibrium shifts to the left. (correct answer)
  2. Both forward and reverse rates increase, and the equilibrium shifts to the right.
  3. Both forward and reverse rates decrease, and the equilibrium shifts to the right.
  4. The forward rate decreases, the reverse rate increases, and the equilibrium shifts to the left.
Explanation: Doubling the volume at constant temperature halves the concentration and partial pressure of all gaseous species. Since reaction rates depend on concentration, the rates of both the forward and reverse reactions will immediately decrease. According to Le Châtelier's principle, the system will shift to counteract the decrease in pressure. It does this by shifting to the side with a greater number of moles of gas. The reactant side has 1 + 1 = 2 moles of gas, while the product side has 1 mole. Therefore, the equilibrium will shift to the left.

Question 14

A solution is prepared by dissolving 0.15 mol of NH4Cl\text{NH}_4\text{Cl} and 0.25 mol of NH3\text{NH}_3 in water to make 1.0 L of solution. If KbK_b for NH3=1.8×105\text{NH}_3 = 1.8 \times 10^{-5}, what is the pH after adding 0.050 mol of NaOH\text{NaOH} to this buffer system?

  1. pH = 9.42 because the added base converts some NH4+\text{NH}_4^+ to NH3\text{NH}_3, shifting the buffer composition favorably
  2. pH = 9.65 because the strong base addition overwhelms the buffer capacity and significantly raises the pH
  3. pH = 9.42 because the Henderson-Hasselbalch equation accounts for the stoichiometric changes in buffer components
  4. pH = 9.77 because the added OH\text{OH}^- increases both the NH3\text{NH}_3 concentration and solution basicity directly (correct answer)
Explanation: Initial buffer: [NH₃] = 0.25 M, [NH₄⁺] = 0.15 M. Adding 0.050 mol NaOH converts NH₄⁺ + OH⁻ → NH₃ + H₂O. After reaction: [NH₃] = 0.25 + 0.050 = 0.30 M, [NH₄⁺] = 0.15 - 0.050 = 0.10 M. Using Henderson-Hasselbalch: pOH = pKb + log([NH₄⁺]/[NH₃]) = 4.74 + log(0.10/0.30) = 4.74 - 0.48 = 4.26. Therefore pH = 14.00 - 4.26 = 9.74 ≈ 9.77. Options A and C give incorrect pH values from calculation errors. Option B incorrectly suggests buffer capacity is overwhelmed when it's still functional.

Question 15

Consider the reaction: A(g)+2B(g)C(g)+D(g)\text{A}(g) + 2\text{B}(g) \rightleftharpoons \text{C}(g) + \text{D}(g) with Kp=0.85K_p = 0.85 at 500 K. If the initial partial pressures are PA=2.0P_A = 2.0 atm, PB=1.5P_B = 1.5 atm, PC=0.5P_C = 0.5 atm, and PD=0.3P_D = 0.3 atm, in which direction will the reaction proceed and what drives this direction?

  1. Forward direction because Qp=0.033<KpQ_p = 0.033 < K_p, indicating insufficient product formation at equilibrium (correct answer)
  2. Reverse direction because Qp=1.33>KpQ_p = 1.33 > K_p, indicating excess product concentration relative to equilibrium
  3. Forward direction because Qp=0.67<KpQ_p = 0.67 < K_p, indicating the system needs more product formation
  4. Reverse direction because Qp=2.25>KpQ_p = 2.25 > K_p, indicating products exceed their equilibrium concentrations
Explanation: Calculate the reaction quotient: Qp = (PC × PD)/(PA × PB²) = (0.5 × 0.3)/(2.0 × 1.5²) = 0.15/4.5 = 0.033. Since Qp < Kp (0.033 < 0.85), the reaction proceeds forward to increase product concentrations until Qp = Kp. Option B uses incorrect Qp calculation and wrong direction. Option C has wrong Qp value. Option D has incorrect Qp calculation and wrong direction conclusion.

Question 16

A student prepares a series of solutions by mixing different volumes of 0.10 M acetic acid (CH3COOH\text{CH}_3\text{COOH}, Ka=1.8×105K_a = 1.8 \times 10^{-5}) with 0.10 M sodium acetate (CH3COONa\text{CH}_3\text{COONa}) and diluting each mixture to 100.0 mL total volume.

If 30.0 mL of the acetic acid solution is mixed with 20.0 mL of the sodium acetate solution and diluted to 100.0 mL, what is the resulting pH, and how does the buffer capacity compare to an equimolar buffer?

  1. pH = 4.57 with reduced buffer capacity because the unequal concentrations create an asymmetric buffering response
  2. pH = 4.92 with enhanced buffer capacity because the excess acid provides additional buffering against base addition
  3. pH = 4.57 with normal buffer capacity because the Henderson-Hasselbalch equation compensates for concentration differences automatically
  4. pH = 4.56 with reduced buffer capacity because the 3:2 ratio decreases the minimum concentration component (correct answer)
Explanation: Final concentrations: [CH₃COOH] = (30.0 mL × 0.10 M)/100.0 mL = 0.030 M, [CH₃COO⁻] = (20.0 mL × 0.10 M)/100.0 mL = 0.020 M. Using Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA]) = 4.74 + log(0.020/0.030) = 4.74 + log(0.667) = 4.74 - 0.18 = 4.56. Buffer capacity depends on the minimum concentration (0.020 M), which is lower than an equimolar buffer of the same total concentration, resulting in reduced buffering ability. Options A and C give incorrect pH values. Option B incorrectly suggests enhanced capacity.

Question 17

The equilibrium PCl5(g)PCl3(g)+Cl2(g)\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) has Kp=0.0245K_p = 0.0245 at 250°C. Initially, 0.500 mol PCl5\text{PCl}_5 is placed in a 2.00 L container. After equilibrium is established, the container volume is suddenly compressed to 1.00 L at constant temperature. What is the new equilibrium composition?

  1. The compression shifts equilibrium left, resulting in 0.156 mol PCl3\text{PCl}_3 and 0.344 mol PCl5\text{PCl}_5 at new equilibrium
  2. The compression shifts equilibrium left, resulting in 0.111 mol PCl3\text{PCl}_3 and 0.389 mol PCl5\text{PCl}_5 at new equilibrium (correct answer)
  3. The compression shifts equilibrium right, resulting in 0.201 mol PCl3\text{PCl}_3 and 0.299 mol PCl5\text{PCl}_5 at new equilibrium
  4. The compression has no effect because KpK_p remains constant, maintaining 0.178 mol PCl3\text{PCl}_3 and 0.322 mol PCl5\text{PCl}_5
Explanation: When you encounter equilibrium problems involving volume changes, you need to apply Le Chatelier's principle and consider how pressure changes affect gas equilibria. The key is recognizing that compression increases pressure, which shifts equilibrium toward the side with fewer gas molecules. First, let's establish the initial equilibrium. With 0.500 mol PCl₅ in 2.00 L, you can solve for equilibrium concentrations using the ICE method and Kp=0.0245K_p = 0.0245. This gives approximately 0.178 mol PCl₃, 0.178 mol Cl₂, and 0.322 mol PCl₅. When the volume compresses to 1.00 L, all concentrations double instantly. However, this creates a reaction quotient Qp>KpQ_p > K_p, so the system must shift left (toward reactants) to re-establish equilibrium. Since the left side has 1 gas molecule versus 2 on the right, compression favors PCl₅ formation. Setting up the new equilibrium calculation with the constraint that KpK_p remains constant at 0.0245, you get 0.111 mol PCl₃ and 0.389 mol PCl₅ at the new equilibrium. Choice A incorrectly calculates the equilibrium amounts despite correctly identifying the leftward shift. Choice C completely misapplies Le Chatelier's principle by claiming compression shifts equilibrium right. Choice D falls into the trap of thinking constant KpK_p means no composition change, ignoring that volume change disturbs equilibrium even though the equilibrium constant stays the same. Remember: For gas equilibria, always count molecules on each side to predict pressure effects, and don't confuse constant KpK_p with unchanged composition after disturbances.

Question 18

A buffer solution contains 0.25 M CH3COOH\text{CH}_3\text{COOH} and 0.15 M CH3COONa\text{CH}_3\text{COONa}. When 0.020 mol of HCl\text{HCl} is added to 1.0 L of this buffer, the pH changes from 4.57 to 4.45. What would be the approximate pH if the same amount of HCl\text{HCl} were added to 1.0 L of pure water instead?

  1. pH = 1.70 because the HCl completely dissociates without buffering capacity present (correct answer)
  2. pH = 2.30 because partial neutralization occurs even without buffer components
  3. pH = 3.15 because some hydrolysis of chloride ions provides slight buffering
  4. pH = 4.20 because the pH change should be similar to the buffered solution
Explanation: In pure water, 0.020 mol HCl in 1.0 L gives [H⁺] = 0.020 M since HCl is a strong acid that completely dissociates. pH = -log(0.020) = 1.70. The buffer minimizes pH change through the equilibrium CH₃COOH ⇌ H⁺ + CH₃COO⁻, but pure water has no such buffering mechanism. Option B incorrectly assumes incomplete dissociation. Option C incorrectly invokes hydrolysis of Cl⁻, which is negligible. Option D fails to recognize the dramatic difference between buffered and unbuffered systems.

Question 19

The solubility of PbCrO4\text{PbCrO}_4 is 1.3×1071.3 \times 10^{-7} mol/L at 25°C. When equal volumes of 2.0×1042.0 \times 10^{-4} M Pb(NO3)2\text{Pb(NO}_3\text{)}_2 and 6.0×1046.0 \times 10^{-4} M K2CrO4\text{K}_2\text{CrO}_4 are mixed, what occurs?

  1. A precipitate forms because Qsp=6.0×108>Ksp=1.69×1014Q_{sp} = 6.0 \times 10^{-8} > K_{sp} = 1.69 \times 10^{-14}
  2. No precipitate forms because Qsp=3.0×108<Ksp=1.69×1014Q_{sp} = 3.0 \times 10^{-8} < K_{sp} = 1.69 \times 10^{-14}
  3. A precipitate forms because Qsp=3.0×108>Ksp=1.69×1014Q_{sp} = 3.0 \times 10^{-8} > K_{sp} = 1.69 \times 10^{-14} (correct answer)
  4. No precipitate forms because Qsp=1.5×108<Ksp=1.69×1014Q_{sp} = 1.5 \times 10^{-8} < K_{sp} = 1.69 \times 10^{-14}
Explanation: First calculate Ksp from solubility: Ksp = [Pb²⁺][CrO₄²⁻] = (1.3 × 10⁻⁷)² = 1.69 × 10⁻¹⁴. After mixing equal volumes, concentrations are halved: [Pb²⁺] = 1.0 × 10⁻⁴ M, [CrO₄²⁻] = 3.0 × 10⁻⁴ M. Qsp = (1.0 × 10⁻⁴)(3.0 × 10⁻⁴) = 3.0 × 10⁻⁸. Since Qsp > Ksp, precipitation occurs. Option A has incorrect Qsp calculation. Option B incorrectly concludes no precipitation despite correct Qsp. Option D uses wrong Qsp value from incorrect dilution calculation.

Question 20

A saturated solution of Mg(OH)2\text{Mg(OH)}_2 has [OH]=2.6×104[\text{OH}^-] = 2.6 \times 10^{-4} M at 25°C. When this solution is mixed with an equal volume of 0.0100.010 M MgCl2\text{MgCl}_2 solution, what happens to the Mg(OH)2\text{Mg(OH)}_2 equilibrium?

  1. Additional Mg(OH)2\text{Mg(OH)}_2 precipitates because the common ion effect increases QspQ_{sp} above KspK_{sp} significantly
  2. Additional Mg(OH)2\text{Mg(OH)}_2 precipitates because added Mg2+\text{Mg}^{2+} shifts equilibrium toward solid formation (correct answer)
  3. Some Mg(OH)2\text{Mg(OH)}_2 dissolves because dilution decreases ion concentrations below the KspK_{sp} threshold temporarily
  4. No change occurs because the system maintains equilibrium through equal dissolution and precipitation rates
Explanation: When you encounter equilibrium problems involving mixing solutions, you need to consider both the common ion effect and dilution effects, then determine which dominates. First, let's establish the initial conditions. The saturated Mg(OH)2\text{Mg(OH)}_2 solution has [OH]=2.6×104[\text{OH}^-] = 2.6 \times 10^{-4} M, which means [Mg2+]=1.3×104[\text{Mg}^{2+}] = 1.3 \times 10^{-4} M (since each Mg(OH)2\text{Mg(OH)}_2 produces one Mg2+\text{Mg}^{2+} and two OH\text{OH}^-). When you mix equal volumes, concentrations are halved by dilution. However, you're also adding Mg2+\text{Mg}^{2+} from the MgCl2\text{MgCl}_2 solution. After mixing: [OH]=1.3×104[\text{OH}^-] = 1.3 \times 10^{-4} M and [Mg2+]=0.065×104+0.005=5.065×103[\text{Mg}^{2+}] = 0.065 \times 10^{-4} + 0.005 = 5.065 \times 10^{-3} M. The key insight is that adding Mg2+\text{Mg}^{2+} (the common ion) shifts the equilibrium Mg(OH)2(s)Mg2+(aq)+2OH(aq)\text{Mg(OH)}_2(s) \rightleftharpoons \text{Mg}^{2+}(aq) + 2\text{OH}^-(aq) toward the left, favoring precipitation. This common ion effect overwhelms the dilution effect. Answer B correctly identifies that added Mg2+\text{Mg}^{2+} shifts equilibrium toward solid formation. Answer A mentions the correct outcome but incorrectly focuses on QspQ_{sp} calculations rather than the fundamental equilibrium shift. Answer C incorrectly suggests dilution is the dominant effect. Answer D ignores that adding a common ion disrupts the original equilibrium. Study tip: In common ion problems, the effect of adding the ion almost always dominates over dilution effects. Focus on Le Châtelier's principle: adding a product shifts equilibrium toward reactants.