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NUMS — Medical & Dental Entry Test

NUMS Chemistry — States of Matter, Energetics and Equilibria (Set 4)

Take the NUMS Chemistry — States of Matter, Energetics and Equilibria (Set 4): 30 multiple-choice questions (40 minutes) with instant scoring and a full…

What this test covers

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

  1. Q1. In gaseous diffusion for enriching uranium, the rate of effusion of ²³⁵UF₆ is compared with that of ²³⁸UF₆. What is the ratio rate(²³⁵UF₆) : rate(²³⁸UF₆)? (F = 19; U = 235 or 238)

    • A. 1.0086
    • B. 1.0043 ✓
    • C. 0.9957
    • D. 1.0129

    Answer: B. 1.0043

    Explanation: Molar masses are 349 and 352. Graham: ratio = √(352/349) = 1.0043. The tiny difference is why thousands of stages are needed (note it is the square root, not 352/349 = 1.0086).

  2. Q2. A container holds 2.0 g of H₂, 8.0 g of He and 16 g of CH₄ at a total pressure of 8.0 atm. What is the partial pressure of helium? (H = 1, He = 4, C = 12)

    • A. 4.0 atm ✓
    • B. 3.2 atm
    • C. 2.0 atm
    • D. 6.0 atm

    Answer: A. 4.0 atm

    Explanation: Moles: H₂ = 1.0, He = 2.0, CH₄ = 1.0; total 4.0. P(He) = (2/4) × 8.0 = 4.0 atm. Mass fractions are not mole fractions.

  3. Q3. A weather balloon of volume 2.0 L is filled at 27 °C and 1.0 atm. At altitude the pressure is 0.50 atm and the temperature is −33 °C. What is the new volume, assuming ideal behaviour?

    • A. 1.6 L
    • B. 4.8 L
    • C. 3.2 L ✓
    • D. 2.5 L

    Answer: C. 3.2 L

    Explanation: V₂ = V₁P₁T₂/(P₂T₁) = 2.0 × 1.0 × 240/(0.50 × 300) = 3.2 L (temperatures must be in kelvin).

  4. Q4. 3.2 g of a gas occupies 1.642 L at 2.00 atm and 127 °C. What is its molar mass? (R = 0.0821 L atm K⁻¹ mol⁻¹)

    • A. 64 g mol⁻¹
    • B. 16 g mol⁻¹
    • C. 32 g mol⁻¹ ✓
    • D. 44 g mol⁻¹

    Answer: C. 32 g mol⁻¹

    Explanation: n = PV/RT = (2.00 × 1.642)/(0.0821 × 400) = 0.100 mol, so M = 3.2/0.100 = 32 g mol⁻¹ (T = 127 + 273 = 400 K).

  5. Q5. At the same temperature, what is the ratio of the root-mean-square speed of helium atoms to that of methane molecules? (He = 4.0, CH₄ = 16.0 g mol⁻¹)

    • A. 0.5
    • B. 1.4
    • C. 2.0 ✓
    • D. 4.0

    Answer: C. 2.0

    Explanation: v_rms = √(3RT/M), so the ratio = √(M(CH₄)/M(He)) = √(16/4) = 2.0. The lighter gas is faster, and it is the square root of the mass ratio.

The other 25 questions

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  1. Q6. The compressibility factor Z = PV/nRT of CO₂ at 200 K and moderate pressure is less than 1. What is the reason?

    • A. Intermolecular attractions dominate, lowering the volume below ideal
    • B. The gas follows Boyle’s law exactly at that temperature
    • C. The molecular volume of CO₂ is negligible compared with the container
    • D. CO₂ molecules have no intermolecular attractions at that pressure

  2. Q7. The enthalpy of vaporisation of water is 40.7 kJ mol⁻¹ and its vapour pressure is 760 torr at 100 °C. Using the Clausius–Clapeyron equation, what is its approximate vapour pressure at 90 °C? (R = 8.314 J K⁻¹ mol⁻¹)

    • A. 460 torr
    • B. 530 torr
    • C. 700 torr
    • D. 650 torr

  3. Q8. Water forms a concave meniscus in a glass tube, while mercury forms a convex one. What explains this difference?

    • A. Mercury wets glass better than water does under the same conditions
    • B. Water’s adhesion to glass exceeds its cohesion; for mercury cohesion wins
    • C. Water has a larger surface tension than mercury does
    • D. Water has a higher density than mercury does

  4. Q9. Iron crystallises in a body-centred cubic lattice with edge length 287 pm. What is its density? (Fe = 55.85 g mol⁻¹; Nₐ = 6.022 × 10²³ mol⁻¹)

    • A. 5.24 g cm⁻³
    • B. 7.85 g cm⁻³
    • C. 15.7 g cm⁻³
    • D. 3.93 g cm⁻³

  5. Q10. What fraction of the volume of a body-centred cubic unit cell is occupied by atoms, assuming touching spheres along the body diagonal?

    • A. 52% (0.52)
    • B. 74% (0.74)
    • C. 60% (0.60)
    • D. 68% (0.68)

  6. Q11. How many NaCl formula units are present in one face-centred cubic unit cell of rock salt?

    • A. 8
    • B. 1
    • C. 2
    • D. 4

  7. Q12. The radius of Mg²⁺ is 72 pm and that of O²⁻ is 140 pm. Using radius ratio ranges (0.225–0.414 tetrahedral, 0.414–0.732 octahedral, 0.732–1.0 cubic), what coordination geometry is predicted for Mg²⁺ in MgO?

    • A. Cubic (r⁺/r⁻ = 0.51)
    • B. Tetrahedral (r⁺/r⁻ = 0.51)
    • C. Octahedral (r⁺/r⁻ = 1.94)
    • D. Octahedral (r⁺/r⁻ = 0.51)

  8. Q13. X-rays of wavelength 154 pm give a first-order Bragg reflection at θ = 15° from a set of planes. What is the spacing between the planes? (sin 15° = 0.259)

    • A. 298 pm
    • B. 149 pm
    • C. 595 pm
    • D. 77 pm

  9. Q14. How much heat is needed to convert 18 g of ice at 0 °C into steam at 100 °C? (ΔHfus = 6.01 kJ mol⁻¹, ΔHvap = 40.7 kJ mol⁻¹, specific heat of water 4.18 J g⁻¹ K⁻¹; take 18 g = 1 mol)

    • A. 46.7 kJ
    • B. 40.7 kJ
    • C. 48.2 kJ
    • D. 54.2 kJ

  10. Q15. Two moles of an ideal gas expand against a constant external pressure of 1.0 atm from 10 L to 30 L. How much work is done on the gas? (1 L atm = 101.3 J)

    • A. −0.20 kJ
    • B. −2.03 kJ
    • C. −4.05 kJ
    • D. +2.03 kJ

  11. Q16. Standard enthalpies of combustion are: C(graphite) −393.5, H₂(g) −285.8 and C₂H₂(g) −1299.6 kJ mol⁻¹. What is the standard enthalpy of formation of C₂H₂(g)?

    • A. +226.8 kJ mol⁻¹
    • B. −620.1 kJ mol⁻¹
    • C. −226.8 kJ mol⁻¹
    • D. +1,979 kJ mol⁻¹

  12. Q17. A reaction has ΔH = +30.0 kJ mol⁻¹ and ΔS = +100 J K⁻¹ mol⁻¹, both independent of temperature. Above what temperature does it become spontaneous?

    • A. 0.3 K
    • B. 300 K
    • C. 30 K
    • D. 3000 K

  13. Q18. A reaction has ΔG° = −11.4 kJ mol⁻¹ at 298 K. What is its equilibrium constant? (R = 8.314 J K⁻¹ mol⁻¹)

    • A. ≈ 4.6
    • B. ≈ 10
    • C. ≈ 100
    • D. ≈ 1000

  14. Q19. The enthalpy of fusion of ice is 6.01 kJ mol⁻¹ at its melting point of 273.15 K. What is the entropy change when 1 mol of ice melts at this temperature?

    • A. +22.0 J K⁻¹ mol⁻¹
    • B. +6.01 J K⁻¹ mol⁻¹
    • C. −22.0 J K⁻¹ mol⁻¹
    • D. +0.022 J K⁻¹ mol⁻¹

  15. Q20. Using mean bond enthalpies (kJ mol⁻¹) N≡N 945, H–H 436, N–H 391, estimate ΔH for N₂ + 3H₂ → 2NH₃.

    • A. −1,038 kJ
    • B. −93 kJ
    • C. +93 kJ
    • D. −351 kJ

  16. Q21. 1.0 mol each of H₂ and I₂ are heated in a 1.0 L vessel at a temperature where Kc = 64 for H₂ + I₂ ⇌ 2HI. What is the equilibrium concentration of HI?

    • A. 0.8 mol L⁻¹
    • B. 0.2 mol L⁻¹
    • C. 1.6 mol L⁻¹
    • D. 1.0 mol L⁻¹

  17. Q22. For PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), Kp = 0.50 atm at a certain temperature. What fraction of PCl₅ is dissociated at an equilibrium total pressure of 3.0 atm? (Kp = α²P/(1 − α²))

    • A. 0.17
    • B. 0.50
    • C. 0.38
    • D. 0.41

  18. Q23. For a reaction at 300 K, K = 100 but the reaction quotient is Q = 10. What is ΔG for the mixture? (R = 8.314 J K⁻¹ mol⁻¹)

    • A. −5.74 kJ mol⁻¹
    • B. +5.74 kJ mol⁻¹
    • C. −11.5 kJ mol⁻¹
    • D. 0 kJ mol⁻¹

  19. Q24. For an endothermic reaction with ΔH° = +50.0 kJ mol⁻¹, by what factor does K change when the temperature rises from 300 K to 310 K? (R = 8.314 J K⁻¹ mol⁻¹)

    • A. Stays the same
    • B. Increases by a factor of about 5
    • C. Decreases by a factor of about 1.9
    • D. Increases by a factor of about 1.9

  20. Q25. The solubility product of Ca(OH)₂ is 3.2 × 10⁻¹¹ at 25 °C (units mol³ L⁻³). What is its molar solubility in pure water?

    • A. 2.0 × 10⁻⁴ mol L⁻¹
    • B. 4.0 × 10⁻⁴ mol L⁻¹
    • C. 8.0 × 10⁻⁶ mol L⁻¹
    • D. 5.7 × 10⁻⁶ mol L⁻¹

  21. Q26. The Ksp of AgCl is 1.8 × 10⁻¹⁰. What is the solubility of AgCl in 0.10 mol L⁻¹ NaCl solution (assume Cl⁻ from AgCl is negligible)?

    • A. 1.8 × 10⁻⁸ mol L⁻¹
    • B. 1.8 × 10⁻⁹ mol L⁻¹
    • C. 1.8 × 10⁻¹¹ mol L⁻¹
    • D. 1.3 × 10⁻⁵ mol L⁻¹

  22. Q27. 50 mL of 2.0 × 10⁻³ M Pb(NO₃)₂ is mixed with 50 mL of 4.0 × 10⁻³ M KI. Ksp of PbI₂ = 7.1 × 10⁻⁹. What happens?

    • A. PbI₂ precipitates, since Q = 4.0 × 10⁻⁹ exceeds Ksp
    • B. No precipitate forms, since Q = 4.0 × 10⁻⁹ is below Ksp
    • C. No precipitate forms, since Q = 8.0 × 10⁻⁹ is below Ksp
    • D. PbI₂ precipitates, since Q = 1.6 × 10⁻⁸ exceeds Ksp

  23. Q28. The Haber equilibrium N₂(g) + 3H₂(g) ⇌ 2NH₃(g) is established in a rigid closed vessel. Argon is now added at constant volume and the same temperature. What happens to the equilibrium yield of NH₃?

    • A. No change, because the partial pressures of the reacting gases are unchanged
    • B. It increases, because the total pressure rises and favours the side with fewer moles
    • C. It increases, because Kp increases when an inert gas is added to the vessel
    • D. It decreases, because argon dilutes the reacting gases and shifts the equilibrium left

  24. Q29. For an elementary reversible reaction A ⇌ B, the forward rate constant is 2.0 × 10⁻³ s⁻¹ and the reverse rate constant is 5.0 × 10⁻⁴ s⁻¹. What is the equilibrium constant K?

    • A. 2.5 × 10⁻⁶
    • B. 4.0
    • C. 0.25
    • D. 1.5 × 10⁻³

  25. Q30. At 1000 K, C(s) + CO₂(g) ⇌ 2CO(g) has Kp = 2.0 atm. At equilibrium the partial pressure of CO₂ is 0.50 atm. What is the total gas pressure?

    • A. 1.5 atm
    • B. 1.0 atm
    • C. 2.5 atm
    • D. 0.5 atm