Chemistry Objective Questions and Answers: Equilibrium
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Multiple Choice Questions
(a) forward favoured if \( \Delta n \) is negative
(b) backward favoured if \( \Delta n = 0 \)
(c) forward favoured if \( \Delta n \) is positive
(d) no effect, whatever the value of \( \Delta n \)
Show Answer & Explanation
Answer: (d) no effect, whatever the value of \( \Delta n \)
Explanation:
1. At constant volume the concentrations (partial pressures) of the reacting gases are unchanged.
2. So there is no effect for any \( \Delta n \).
Teacher's Note:
1. Le Chatelier's principle: the system shifts to oppose the change applied.
2. An inert gas shifts the equilibrium only when it changes the partial pressures, that is at constant total pressure with a change in gas moles.
(a) 0.25 atm
(b) 0.5 atm
(c) 2.5 atm
(d) 1.0 atm
Show Answer & Explanation
Answer: (b) 0.5 atm
Explanation:
1. \( \ce{PCl3} \) and \( \ce{Cl2} \) form in equal amounts, so the mole fraction of \( \ce{Cl2} \) is also 0.25.
2. \( p_{Cl_2} = 0.25\times2.0 = 0.5 \) atm.
Teacher's Note:
1. Write the moles of each species at equilibrium in terms of the degree of dissociation, then find the total moles.
2. Partial pressure equals mole fraction times total pressure.
(a) \( e^{-3} \)
(b) \( 10^{-6} \)
(c) \( e^{-6} \)
(d) \( e^{6} \)
Show Answer & Explanation
Answer: (c) \( e^{-6} \)
Explanation:
1. \( \ln K_c = -\Delta G^\circ/RT = -15000/(8.314\times300) = -6.0 \).
2. \( K_c = e^{-6} \).
Teacher's Note:
1. The van't Hoff relation shows that K increases with temperature for an endothermic reaction and decreases for an exothermic one.
2. Use the standard free energy relation to connect K with energy changes.
(a) \( \Delta G = -2.30\,RT\log K \)
(b) \( \Delta G^\circ = 2.30\,RT\log K \)
(c) \( \Delta G = 2.30\,RT\log K \)
(d) \( \Delta G^\circ = -2.30\,RT\log K \)
Show Answer & Explanation
Answer: (d) \( \Delta G^\circ = -2.30\,RT\log K \)
Explanation:
1. At equilibrium \( \Delta G = 0 \) and \( \Delta G^\circ = -RT\ln K = -2.30\,RT\log K \).
Teacher's Note:
1. The van't Hoff relation shows that K increases with temperature for an endothermic reaction and decreases for an exothermic one.
2. Use the standard free energy relation to connect K with energy changes.
(a) addition of \( \ce{NH4Cl} \) crystals
(b) a decrease in temperature
(c) an increase in temperature
(d) addition of \( \ce{NH4OH} \) solution
Show Answer & Explanation
Answer: (c) an increase in temperature
Explanation:
1. The dissolution is endothermic, so a higher temperature shifts it to the right.
2. Adding more solid does not change the equilibrium.
Teacher's Note:
1. Le Chatelier's principle: the system shifts to oppose the change applied.
2. An inert gas shifts the equilibrium only when it changes the partial pressures, that is at constant total pressure with a change in gas moles.
(a) introducing \( \ce{Cl2} \) at constant volume
(b) introducing \( \ce{PCl5} \) at constant volume
(c) increasing the volume of the container
(d) introducing an inert gas at constant pressure
Show Answer & Explanation
Answer: (a) introducing \( \ce{Cl2} \) at constant volume
Explanation:
1. Added product \( \ce{Cl2} \) shifts the equilibrium backward.
2. The other three changes shift it forward.
Teacher's Note:
1. Le Chatelier's principle: the system shifts to oppose the change applied.
2. An inert gas shifts the equilibrium only when it changes the partial pressures, that is at constant total pressure with a change in gas moles.
(a) 8
(b) 6
(c) 0.25
(d) 0.125
Show Answer & Explanation
Answer: (a) 8
Explanation:
1. The second reaction is the reverse of the first, so \( K' = 1/0.125 = 8 \).
Teacher's Note:
1. Reverse the reaction and K becomes 1/K; multiply the equation by n and K is raised to the power n; add equations and multiply the K values.
2. Combine the given equilibria so that the unwanted species cancel.
(a) \( K_p \) does not change significantly with pressure
(b) the concentration of ammonia does not change with pressure
(c) the concentration of hydrogen is less than that of nitrogen
(d) the degree of dissociation does not change with pressure
Show Answer & Explanation
Answer: (a) \( K_p \) does not change significantly with pressure
Explanation:
1. \( K_p \) depends only on temperature.
2. The degree of dissociation decreases with pressure for \( \ce{2NH3 <=> N2 + 3H2} \), and \( [\ce{H2}] = 3[\ce{N2}] \).
Teacher's Note:
1. Write the moles of each species at equilibrium in terms of the degree of dissociation, then find the total moles.
2. Partial pressure equals mole fraction times total pressure.
(a) 4
(b) 1
(c) 3
(d) 2
Show Answer & Explanation
Answer: (a) 4
Explanation:
1. Ester = water = 2/3, alcohol = acid = 1/3 (volume cancels).
2. \( K = (2/3)^2/(1/3)^2 = 4 \).
Teacher's Note:
1. Write the equilibrium expression from the balanced equation and leave out pure solids and liquids.
2. Always substitute equilibrium concentrations, never initial ones.
(a) dm\(^3\) mol\(^{-1}\)
(b) mol dm\(^{-3}\)
(c) dm\(^6\) mol\(^{-2}\)
(d) mol\(^2\) dm\(^{-3}\)
Show Answer & Explanation
Answer: (a) dm\(^3\) mol\(^{-1}\)
Explanation:
1. \( K_c = [\ce{C2H6}]/([\ce{C2H4}][\ce{H2}]) \), with units (mol/dm\(^3\))\(^{1-2}\).
2. The unit is dm\(^3\) mol\(^{-1}\).
Teacher's Note:
1. Write the equilibrium expression from the balanced equation and leave out pure solids and liquids.
2. Always substitute equilibrium concentrations, never initial ones.
(a) \( \dfrac{[2C][D]}{[A][2B]} \)
(b) \( \dfrac{[C][D]}{[A][B]} \)
(c) \( \dfrac{[C]^2[D]}{[A][2B]} \)
(d) \( \dfrac{[C]^2[D]}{[A][B]^2} \)
Show Answer & Explanation
Answer: (d) \( \dfrac{[C]^2[D]}{[A][B]^2} \)
Explanation:
1. Each concentration is raised to the power of its stoichiometric coefficient.
Teacher's Note:
1. Write the equilibrium expression from the balanced equation and leave out pure solids and liquids.
2. Always substitute equilibrium concentrations, never initial ones.
(a) 0.022
(b) 45.45
(c) 2.20
(d) 0.4545
Show Answer & Explanation
Answer: (b) 45.45
Explanation:
1. \( K = k_f/k_r = 1.25\times10^{-3}/2.75\times10^{-5} = 45.45 \).
Teacher's Note:
1. Write the equilibrium expression from the balanced equation and leave out pure solids and liquids.
2. Always substitute equilibrium concentrations, never initial ones.
(a) \( K = [H_2][Cl_2]/(2[HCl]) \)
(b) \( K = 2[HCl]/([H_2][Cl_2]) \)
(c) \( K = [HCl]^2/([H_2][Cl_2]) \)
(d) \( K = [H_2][Cl_2]/[HCl]^2 \)
Show Answer & Explanation
Answer: (c) \( K = [HCl]^2/([H_2][Cl_2]) \)
Explanation:
1. Products over reactants, each raised to its stoichiometric coefficient.
Teacher's Note:
1. Write the equilibrium expression from the balanced equation and leave out pure solids and liquids.
2. Always substitute equilibrium concentrations, never initial ones.
(a) mol\(^{-1}\) L\(^{-1}\) and bar\(^{-1}\)
(b) mol\(^{-2}\) L\(^2\) and bar\(^{-2}\)
(c) mol\(^{-1}\) L and bar\(^{-2}\)
(d) mol\(^{-2}\) L\(^2\) and bar\(^{-1}\)
Show Answer & Explanation
Answer: (b) mol\(^{-2}\) L\(^2\) and bar\(^{-2}\)
Explanation:
1. \( \Delta n = -2 \), so \( K_c \) has (mol/L)\(^{-2}\), i.e. mol\(^{-2}\) L\(^2\).
2. \( K_p \) has bar\(^{-2}\).
Teacher's Note:
1. Write the equilibrium expression from the balanced equation and leave out pure solids and liquids.
2. Always substitute equilibrium concentrations, never initial ones.
(a) \( 1.4\times10^{-2} \)
(b) \( 2.9\times10^{-2} \)
(c) \( 1.2\times10^{-1} \)
(d) \( 2.0\times10^{-4} \)
Show Answer & Explanation
Answer: (c) \( 1.2\times10^{-1} \)
Explanation:
1. The required reaction is the reverse of half the given one.
2. \( K' = (1/70)^{1/2} = 0.12 \).
Teacher's Note:
1. Reverse the reaction and K becomes 1/K; multiply the equation by n and K is raised to the power n; add equations and multiply the K values.
2. Combine the given equilibria so that the unwanted species cancel.
(a) \( K_p = K_c \)
(b) \( K_p = K_c(RT)^3 \)
(c) \( K_p = K_c(RT) \)
(d) \( K_p = K_c(RT)^{-1} \)
Show Answer & Explanation
Answer: (d) \( K_p = K_c(RT)^{-1} \)
Explanation:
1. \( \Delta n = (4+6) - (4+7) = -1 \).
2. \( K_p = K_c(RT)^{-1} \).
Teacher's Note:
1. Use Kp = Kc(RT)^(change in gas moles) and take R in units that match the pressure and concentration units.
2. Count only gaseous species when finding the change in moles.
(a) equilibrium is achieved slowly
(b) equilibrium is achieved rapidly
(c) product concentrations are much greater than reactant concentrations at equilibrium
(d) reactant concentrations are much greater than product concentrations
Show Answer & Explanation
Answer: (c) product concentrations are much greater than reactant concentrations at equilibrium
Explanation:
1. A large K means products dominate at equilibrium.
2. K says nothing about how fast equilibrium is reached.
Teacher's Note:
1. Write the equilibrium expression from the balanced equation and leave out pure solids and liquids.
2. Always substitute equilibrium concentrations, never initial ones.
(a) \( \ce{3O2(g) <=> 2O3(g)} \)
(b) \( \ce{C(s) + H2O(g) <=> CO(g) + H2(g)} \)
(c) \( \ce{H2(g) + I2(g) <=> 2HI(g)} \)
(d) \( \ce{4NH3(g) + 5O2(g) <=> 4NO(g) + 6H2O(l)} \)
Show Answer & Explanation
Answer: (b) \( \ce{C(s) + H2O(g) <=> CO(g) + H2(g)} \)
Explanation:
1. A volume increase favours the side with more gas moles.
2. The first reaction has 1 mole of gas on the left and 2 on the right.
Teacher's Note:
1. Le Chatelier's principle: the system shifts to oppose the change applied.
2. An inert gas shifts the equilibrium only when it changes the partial pressures, that is at constant total pressure with a change in gas moles.
(a) decreasing the volume of the container
(b) increasing the temperature
(c) adding a catalyst
(d) removing the gaseous water by absorbing it
Show Answer & Explanation
Answer: (d) removing the gaseous water by absorbing it
Explanation:
1. Removing a product shifts the equilibrium to the right.
2. A higher temperature (exothermic) and a smaller volume (7 moles to 8 moles) shift it left; a catalyst does not shift it.
Teacher's Note:
1. Le Chatelier's principle: the system shifts to oppose the change applied.
2. An inert gas shifts the equilibrium only when it changes the partial pressures, that is at constant total pressure with a change in gas moles.
(a) \( K_1 = \sqrt{K_2} \)
(b) \( K_1 = 1/\sqrt{K_2} \)
(c) \( K_1 = 2K_2 \)
(d) \( K_1 = 1/K_2 \)
Show Answer & Explanation
Answer: (b) \( K_1 = 1/\sqrt{K_2} \)
Explanation:
1. The second reaction is the reverse of twice the first.
2. \( K_2 = 1/K_1^2 \), so \( K_1 = 1/\sqrt{K_2} \).
Teacher's Note:
1. Reverse the reaction and K becomes 1/K; multiply the equation by n and K is raised to the power n; add equations and multiply the K values.
2. Combine the given equilibria so that the unwanted species cancel.
(a) \( K_2 = 1/\sqrt{K_1} \)
(b) \( K_2 = \sqrt{K_1} \)
(c) \( K_2 = 1/K_1 \)
(d) \( K_2 = K_1 \)
Show Answer & Explanation
Answer: (a) \( K_2 = 1/\sqrt{K_1} \)
Explanation:
1. The second reaction is the reverse of half the first.
2. \( K_2 = K_1^{-1/2} \).
Teacher's Note:
1. Reverse the reaction and K becomes 1/K; multiply the equation by n and K is raised to the power n; add equations and multiply the K values.
2. Combine the given equilibria so that the unwanted species cancel.
(a) A and B
(b) B only
(c) A only
(d) C and D
Show Answer & Explanation
Answer: (d) C and D
Explanation:
1. Equation (b) = (2/3) \(\times\) equation (a), so \( K_2 = K_1^{2/3} \).
2. Hence \( K_1 = K_2^{3/2} \), and \( K_1^2 = K_2^3 \) (not \( K_1^3 = K_2^2 \)).
Teacher's Note:
1. Reverse the reaction and K becomes 1/K; multiply the equation by n and K is raised to the power n; add equations and multiply the K values.
2. Combine the given equilibria so that the unwanted species cancel.
(a) \( Q_c < K_c \); more HI will be produced
(b) \( Q_c = K_c \); the system is at equilibrium
(c) \( Q_c > K_c \); more \( \ce{H2} \) and \( \ce{I2} \) will be produced
(d) \( Q_c < K_c \); more \( \ce{H2} \) and \( \ce{I2} \) will be produced
Show Answer & Explanation
Answer: (d) \( Q_c < K_c \); more \( \ce{H2} \) and \( \ce{I2} \) will be produced
Explanation:
1. \( Q_c = (0.50\times0.10)/2.0^2 = 0.0125 \).
2. \( Q_c < K_c = 0.020 \), so the reaction goes forward and produces more \( \ce{H2} \) and \( \ce{I2} \).
Teacher's Note:
1. Compare the reaction quotient Q with K: Q < K means the net reaction goes forward and Q > K means it goes backward.
2. Q has the same form as K but uses the concentrations present at that moment.
(a) \( \ce{H2 + I2 <=> 2HI} \)
(b) \( \ce{PCl3 + Cl2 <=> PCl5} \)
(c) \( \ce{2SO3 <=> 2SO2 + O2} \)
(d) \( \ce{N2 + 3H2 <=> 2NH3} \)
Show Answer & Explanation
Answer: (c) \( \ce{2SO3 <=> 2SO2 + O2} \)
Explanation:
1. \( K_p > K_c \) when \( \Delta n > 0 \).
2. \( \ce{2SO3 -> 2SO2 + O2} \) has \( \Delta n = +1 \).
Teacher's Note:
1. Use Kp = Kc(RT)^(change in gas moles) and take R in units that match the pressure and concentration units.
2. Count only gaseous species when finding the change in moles.
(a) 0.0301
(b) 1.0001
(c) 0.0831
(d) 33.26
Show Answer & Explanation
Answer: (d) 33.26
Explanation:
1. \( \Delta n = 10 - 9 = +1 \).
2. \( K_p/K_c = RT = 0.08314\times400 = 33.26 \).
Teacher's Note:
1. Use Kp = Kc(RT)^(change in gas moles) and take R in units that match the pressure and concentration units.
2. Count only gaseous species when finding the change in moles.
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