NUMS — Medical & Dental Entry Test
Take the NUMS Chemistry — Kinetics, Acids and Bases, Electrochemistry (Set 6): 30 multiple-choice questions (40 minutes) with instant scoring and a full…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A first-order reaction has a half-life of 12 min. How long does it take for 99% of the reactant to react? (log₂100 = 6.64)
Answer: C. 79.7 min
Explanation: Remaining fraction = 0.01, so t = t½ × log₂(100) = 12 × 6.64 = 79.7 min. (Six half-lives, 72 min, leave 1.6% unreacted.)
Q2. Spoilage of milk has an apparent activation energy of 60 kJ mol⁻¹. By what factor is the spoilage rate changed when milk is moved from a kitchen at 298 K to a refrigerator at 277 K? (Arrhenius equation, R = 8.314 J K⁻¹ mol⁻¹)
Answer: D. 6.3 times slower
Explanation: ln(k₂₉₈/k₂₇₇) = (Eₐ/R)(1/277 − 1/298) = (60000/8.314)(2.544 × 10⁻⁴) = 1.836, so the ratio is e^1.836 = 6.3. The rate in the refrigerator is 6.3 times slower.
Q3. A proposed mechanism for 2NO + O₂ → 2NO₂ is: step 1 (fast, reversible) NO + NO ⇌ N₂O₂; step 2 (slow) N₂O₂ + O₂ → 2NO₂. What rate law and overall order follow from this mechanism?
Answer: A. Rate = k[NO]²[O₂]; third order
Explanation: The slow step sets the rate: rate = k₂[N₂O₂][O₂]. N₂O₂ is an intermediate in fast equilibrium with NO, so [N₂O₂] = K[NO]². Substituting, rate = k₂K[NO]²[O₂], third order overall.
Q4. The hydrolysis of ethyl ethanoate in a large excess of dilute aqueous acid has rate = k[ester][H₂O] but is found to be first order in ester. Why does the rate appear independent of [H₂O]?
Answer: D. Water is in such large excess that its concentration is effectively constant
Explanation: Because water is present in great excess, its concentration hardly changes during the reaction and merges into the rate constant: rate = k′[ester] with k′ = k[H₂O]. This is a pseudo-first-order reaction.
Q5. An enzyme-catalysed reaction is studied with a fixed small amount of enzyme and increasing substrate concentration. At very high substrate concentration the rate stops increasing. What does this indicate?
Answer: D. All active sites are occupied, so the rate is zero order in substrate
Explanation: When every enzyme active site is saturated, adding more substrate cannot raise the rate; the reaction is zero order in substrate and its rate is limited by enzyme concentration (and turnover rate).
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Q6. Two gas-phase reactions have the same activation energy and the same collision frequency at a given temperature, yet one is a thousand times slower. Which factor of collision theory most likely accounts for this?
Q7. For a reaction, a plot of ln[A] against time (in minutes) is a straight line with a slope of −0.035 min⁻¹. What is the half-life of the reaction?
Q8. For a reaction of a single reactant A, the half-life is 20 min when [A]₀ = 0.80 M and 40 min when [A]₀ = 0.40 M. What is the order of the reaction in A?
Q9. The gas-phase reaction A + B → products is first order in A and first order in B. The mixture is compressed isothermally to half its volume with no change in the number of moles. By what factor does the rate change?
Q10. What is the pH of a solution that is 0.10 M in HCl and 0.10 M in ethanoic acid (Kₐ = 1.8 × 10⁻⁵)?
Q11. 50 cm³ of 0.20 M acetic acid is mixed with 20 cm³ of 0.20 M NaOH. What is the pH of the resulting solution? (Kₐ of CH₃COOH = 1.8 × 10⁻⁵; log 1.8 = 0.255)
Q12. What is the pH of 0.10 M hydrocyanic acid, HCN (Kₐ = 4.9 × 10⁻¹⁰)? (Ignore ionisation of water.)
Q13. What is the pH of 0.10 M sodium ethanoate (CH₃COONa) at 25 °C? (Kₐ of ethanoic acid = 1.8 × 10⁻⁵, K_w = 1.0 × 10⁻¹⁴)
Q14. Carbonic acid has pKₐ₁ = 6.35 and pKₐ₂ = 10.33. Taking the pH of an amphiprotic salt solution as ½(pKₐ₁ + pKₐ₂), what is the approximate pH of a sodium hydrogencarbonate (NaHCO₃) solution?
Q15. An indicator HIn has pKₐ = 5.0. In a solution of pH 4.0, what is the ratio [In⁻]/[HIn]?
Q16. Magnesium hydroxide (Ksp = 1.8 × 10⁻¹¹ mol³ dm⁻⁹) is shaken with a buffer solution held at pH 10.00. What is the equilibrium concentration of Mg²⁺ in the solution?
Q17. 40.0 cm³ of 0.100 M ethanoic acid is mixed with 30.0 cm³ of 0.100 M sodium hydroxide (Kₐ = 1.8 × 10⁻⁵). What is the pH of the mixture?
Q18. What is the average oxidation number of nitrogen in hydrazoic acid, HN₃?
Q19. In acid solution: 2MnO₄⁻ + 5C₂O₄²⁻ + 16H⁺ → 2Mn²⁺ + 10CO₂ + 8H₂O. What volume of 0.0250 M KMnO₄ is needed to oxidise 25.0 cm³ of 0.0500 M sodium oxalate?
Q20. Which of these reactions is a disproportionation?
Q21. An aluminium–copper cell Al | Al³⁺ ‖ Cu²⁺ | Cu has E°(Al³⁺/Al) = −1.66 V and E°(Cu²⁺/Cu) = +0.34 V. What is ΔG° for 2Al + 3Cu²⁺ → 2Al³⁺ + 3Cu? (F = 96 485 C mol⁻¹)
Q22. Molten sodium chloride is electrolysed with a steady current of 5.0 A for 965 s. What volume of chlorine gas is released at the anode, measured at STP (22.4 dm³ mol⁻¹)? (F = 96 500 C mol⁻¹)
Q23. A spoon with a surface area of 50 cm² is silver-plated using a current of 2.0 A for 600 s from a silver nitrate solution. Assuming the current is 100% efficient and the silver deposits evenly, what is the thickness of the layer? (Ag = 108 g mol⁻¹, density of silver = 10.5 g cm⁻³, F = 96 500 C mol⁻¹)
Q24. A conductivity cell with cell constant (l/A) of 1.25 cm⁻¹ filled with 0.100 mol dm⁻³ KCl solution has a resistance of 250 Ω. What is the molar conductivity of the solution? (Λ = κ × 1000/c, with c in mol dm⁻³ and κ in S cm⁻¹)
Q25. A buried steel pipeline is connected by a wire to blocks of magnesium. Why does this slow the corrosion of the pipeline?
Q26. Standard electrode potentials: Ag⁺/Ag +0.80 V, Cu²⁺/Cu +0.34 V, Fe²⁺/Fe −0.44 V, Zn²⁺/Zn −0.76 V. Which reaction is spontaneous under standard conditions?
Q27. In neutral solution permanganate is reduced to MnO₂ (MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻). What is the equivalent mass of KMnO₄ (M = 158 g mol⁻¹) in this reaction?
Q28. How long must a steady current of 9.65 A be passed through molten aluminium oxide (Al³⁺) to deposit 0.90 g of aluminium? (Al = 27 g mol⁻¹, F = 96500 C mol⁻¹)
Q29. Aqueous copper(II) sulphate is electrolysed between inert platinum electrodes until most of the copper is deposited. What happens to the pH of the solution?
Q30. In an iodometric titration, 25.0 cm³ of an iodine solution requires 20.0 cm³ of 0.100 M sodium thiosulphate: I₂ + 2S₂O₃²⁻ → 2I⁻ + S₄O₆²⁻. What is the concentration of the iodine solution?