NUMS — Medical & Dental Entry Test
Take the NUMS Chemistry — States of Matter, Energetics and Equilibria (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. Taking air as an ideal gas of mean molar mass 29 g mol⁻¹, what is its density at 0.90 atm and 27 °C? (R = 0.0821 dm³ atm K⁻¹ mol⁻¹)
Answer: B. 1.06 g dm⁻³
Explanation: d = PM/RT = (0.90 × 29)/(0.0821 × 300) = 1.06 g dm⁻³. (1.18 g dm⁻³ is the density at 1 atm and 27 °C; 1.29 g dm⁻³ is the value at STP.)
Q2. Air is 21% oxygen by volume at every altitude. On a mountain summit the total pressure is 0.33 atm. What is the partial pressure of oxygen there?
Answer: A. 0.069 atm
Explanation: By Dalton's law, partial pressure = mole fraction × total pressure = 0.21 × 0.33 = 0.069 atm, about one third of the sea-level value of 0.21 atm.
Q3. What is the total translational kinetic energy of one mole of any ideal gas at 27 °C? (R = 8.314 J K⁻¹ mol⁻¹; use KE = (3/2)RT per mole)
Answer: B. 3.74 kJ mol⁻¹
Explanation: KE = (3/2)RT = 1.5 × 8.314 × 300 = 3741 J = 3.74 kJ mol⁻¹. It is the same for every ideal gas at a given temperature; 2.49 kJ is RT.
Q4. A rigid vessel at 27 °C holds a gas mixture of 2.0 g of H₂, 28 g of N₂ and 8.0 g of He (H = 1, N = 14, He = 4). If the total pressure is 4.0 atm, what is the partial pressure of helium?
Answer: D. 2.0 atm
Explanation: Moles: H₂ = 1.0, N₂ = 1.0, He = 2.0, total 4.0. By Dalton's law, p(He) = mole fraction × total pressure = (2.0/4.0) × 4.0 = 2.0 atm.
Q5. One mole of oxygen is held in a 1.00 dm³ vessel at 300 K. Using the van der Waals equation (a = 1.36 dm⁶ atm mol⁻², b = 0.0318 dm³ mol⁻¹, R = 0.0821 dm³ atm K⁻¹ mol⁻¹), what is the pressure?
Answer: A. 24.1 atm
Explanation: P = RT/(V − b) − a/V² = (0.0821 × 300)/(1.00 − 0.0318) − 1.36/1.00² = 25.44 − 1.36 = 24.1 atm. The ideal-gas value is 24.6 atm; ignoring the attraction term gives 25.4 atm.
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Q6. A liquid boils at 80 °C under 1.00 atm and has a molar enthalpy of vaporisation of 30.0 kJ mol⁻¹ (assume constant). Using ln(P₂/P₁) = −(ΔH/R)(1/T₂ − 1/T₁), what is its vapour pressure at 60 °C? (R = 8.314 J K⁻¹ mol⁻¹)
Q7. Polonium (M = 209 g mol⁻¹) crystallises in a simple cubic lattice with edge length 336 pm. What is its density? (Nₐ = 6.022 × 10²³ mol⁻¹)
Q8. Atoms of element Y form a cubic close-packed (face-centred cubic) lattice, and atoms of element X occupy half of the octahedral holes. What is the formula of the compound?
Q9. Cotton plugs soaked in concentrated ammonia and concentrated hydrochloric acid are placed at opposite ends of a horizontal glass tube 100 cm long. A white ring of NH₄Cl forms where the gases meet. How far from the ammonia end does it form? (NH₃ = 17, HCl = 36.5)
Q10. For CaCO₃(s) ⇌ CaO(s) + CO₂(g), Kp = 0.50 atm at 900 K. If 0.20 mol of CaCO₃ is placed in an evacuated 10.0 dm³ vessel at 900 K and allowed to reach equilibrium, how many moles of CaCO₃ remain? (R = 0.0821 dm³ atm K⁻¹ mol⁻¹)
Q11. A white solid is soft, melts at 80 °C, does not conduct electricity either as a solid or when molten, and dissolves in benzene. What type of solid is it?
Q12. The triple point of water is at 0.006 atm and 0.01 °C. A sample of ice at −10 °C is held at a constant pressure of 0.004 atm and slowly heated. What happens?
Q13. Standard enthalpies of combustion (kJ mol⁻¹): C₂H₄(g) −1411, H₂(g) −286, C₂H₆(g) −1560. What is ΔH° for C₂H₄(g) + H₂(g) → C₂H₆(g)?
Q14. For the combustion C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(l) at 298 K, the bomb-calorimeter value is ΔU = −1364.2 kJ mol⁻¹. What is ΔH at 298 K? (R = 8.314 J K⁻¹ mol⁻¹; ΔH = ΔU + ΔnRT)
Q15. A reaction has ΔH = −10.0 kJ mol⁻¹ and ΔS = −50.0 J K⁻¹ mol⁻¹, both independent of temperature. Below what temperature is it spontaneous?
Q16. Using mean bond enthalpies (kJ mol⁻¹): C=C 614, C–C 348, C–H 413, H–H 436, estimate ΔH for C₂H₄ + H₂ → C₂H₆.
Q17. A 50 g iron block at 100 °C is dropped into 100 g of water at 20 °C in an insulated container. Specific heat capacities: iron 0.45 J g⁻¹ K⁻¹, water 4.18 J g⁻¹ K⁻¹. What is the final temperature, ignoring heat loss to the container?
Q18. Enthalpies of combustion to SO₂(g) are −296.8 kJ mol⁻¹ for rhombic sulphur and −297.2 kJ mol⁻¹ for monoclinic sulphur. What is ΔH for S(rhombic) → S(monoclinic)?
Q19. For H₂(g) + I₂(g) ⇌ 2HI(g), Kc = 49 at a certain temperature. Pure HI at 1.00 mol dm⁻³ is allowed to decompose to equilibrium at that temperature. What is the equilibrium concentration of H₂?
Q20. For 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), Kc = 280 dm³ mol⁻¹ at 1000 K. What is Kp at this temperature? (R = 0.0821 dm³ atm K⁻¹ mol⁻¹; Kp = Kc(RT)^Δn)
Q21. The equilibrium N₂O₄(g) ⇌ 2NO₂(g) is established in a cylinder with a movable piston at constant temperature and constant total pressure. Argon, which takes no part in the reaction, is now added at constant total pressure. What happens?
Q22. N₂O₄(g) ⇌ 2NO₂(g). At a certain temperature and pressure the equilibrium mixture has an average molar mass of 73.6 g mol⁻¹ (N₂O₄ = 92 g mol⁻¹). What percentage of N₂O₄ has dissociated?
Q23. The Ksp of lead(II) iodide, PbI₂, is 7.1 × 10⁻⁹ mol³ dm⁻⁹. What is its solubility in 0.10 M KI solution? (Neglect the iodide contributed by PbI₂.)
Q24. The solubility of silver chromate, Ag₂CrO₄, in water at 25 °C is 6.5 × 10⁻⁵ mol dm⁻³. What is its solubility product?
Q25. At a certain temperature, X ⇌ Y has K₁ = 4.0 and Y + Z ⇌ W has K₂ = 0.50. What is the equilibrium constant for 2W ⇌ 2X + 2Z at the same temperature?
Q26. How do the viscosities of a liquid and of a gas change when each is heated?
Q27. A Maxwell–Boltzmann distribution of molecular speeds for a gas is drawn at 300 K and again at 600 K. Which description of the 600 K curve is correct?
Q28. The enthalpy of fusion of iodine is 15.5 kJ mol⁻¹ and its enthalpy of vaporisation is 41.6 kJ mol⁻¹ (both near the triple point). What is its enthalpy of sublimation?
Q29. The reaction N₂(g) + 3H₂(g) → 2NH₃(g) has ΔH = −92.2 kJ at 298 K and constant pressure. Taking ΔS(surroundings) = −ΔH/T, what is the entropy change of the surroundings per mole of reaction as written?
Q30. Ethanoic acid reacts with ethanol: CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ + H₂O, Kc = 4.0 at a certain temperature. If 1.0 mol of acid is mixed with 2.0 mol of ethanol, how many moles of ester are present at equilibrium?