NUMS — Medical & Dental Entry Test
Take the NUMS Chemistry — States of Matter, Energetics and Equilibria (Set 5): 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. Hydrogen is collected over water at 25 °C. The gas occupies 250 mL at a total pressure of 750 mmHg; the vapour pressure of water at 25 °C is 23.8 mmHg. How many moles of H₂ are present? (R = 0.08206 L atm mol⁻¹ K⁻¹; 760 mmHg = 1 atm; T = 298.15 K)
Answer: B. 9.76 × 10⁻³ mol
Explanation: P(H₂) = 750 − 23.8 = 726.2 mmHg = 0.9555 atm. n = PV/RT = 0.9555 × 0.250/(0.08206 × 298.15) = 9.76 × 10⁻³ mol. Ignoring water vapour gives 1.01 × 10⁻².
Q2. What is the root-mean-square speed of N₂ molecules (M = 28.0 g mol⁻¹) at 300 K? (u_rms = √(3RT/M), R = 8.314 J mol⁻¹ K⁻¹)
Answer: B. 517 m s⁻¹
Explanation: u = √(3 × 8.314 × 300/0.0280) = √(2.67 × 10⁵) = 517 m s⁻¹. (Using M in g mol⁻¹ would be wrong by √1000.)
Q3. One mole of a gas at 200 K and 10.0 atm occupies 1.50 L. Using the compressibility factor Z = PV/nRT (R = 0.08206 L atm mol⁻¹ K⁻¹), what is Z and what does it imply?
Answer: D. Z = 0.914; attractive forces dominate
Explanation: Z = (10.0 × 1.50)/(0.08206 × 200) = 15.0/16.41 = 0.914. Z < 1 means the gas is more compressible than ideal, which occurs when attractions dominate.
Q4. The molar enthalpy of vaporisation of water is 40.7 kJ mol⁻¹. If it boils at 373.15 K under 101.3 kPa, what is the approximate vapour pressure at 363.15 K from the Clausius–Clapeyron equation ln(P₂/P₁) = −(ΔH/R)(1/T₂ − 1/T₁)? (R = 8.314 J mol⁻¹ K⁻¹)
Answer: A. 70.6 kPa
Explanation: ln(P₂/P₁) = −(40700/8.314)(1/363.15 − 1/373.15) = −4896 × 7.38 × 10⁻⁵ = −0.361. P₂ = 101.3 × e^(−0.361) = 70.6 kPa.
Q5. How much heat is needed to convert 36 g of ice at 0 °C to steam at 100 °C? (ΔH_fus = 6.01 kJ mol⁻¹; specific heat of water 4.18 J g⁻¹ K⁻¹; ΔH_vap = 40.7 kJ mol⁻¹; M(H₂O) = 18 g mol⁻¹)
Answer: A. 108 kJ
Explanation: n = 2 mol. Melting 2 × 6.01 = 12.0 kJ; heating 36 × 4.18 × 100 = 15.05 kJ; vaporising 2 × 40.7 = 81.4 kJ. Total = 108.5 kJ.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. Copper crystallises in a face-centred cubic lattice with cell edge a = 361 pm. What is its density? (Cu = 63.55 g mol⁻¹; N_A = 6.022 × 10²³ mol⁻¹)
Q7. Iron has a body-centred cubic structure with cell edge 287 pm. What is the radius of an iron atom, if atoms touch along the body diagonal?
Q8. For CaCO₃(s) → CaO(s) + CO₂(g), ΔH_f° values are CaCO₃ −1207.0, CaO −635.1 and CO₂ −393.5 kJ mol⁻¹, and ΔS° = +160.5 J mol⁻¹ K⁻¹. Neglecting temperature dependence of ΔH and ΔS, above what temperature does decomposition become spontaneous?
Q9. For N₂(g) + 3H₂(g) → 2NH₃(g), S° values are N₂ 191.6, H₂ 130.7 and NH₃ 192.5 J mol⁻¹ K⁻¹, and ΔH° = −92.2 kJ. What is ΔG° at 298 K?
Q10. Benzene burns with ΔH_c = −3267.6 kJ mol⁻¹ (to CO₂(g) and H₂O(l)). Given ΔH_f° of CO₂(g) = −393.5 and H₂O(l) = −285.8 kJ mol⁻¹, what is the standard enthalpy of formation of liquid benzene, C₆H₆(l)?
Q11. For CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g), Kc = 9.0 at a certain temperature. If 1.00 mol CO and 3.00 mol H₂O are placed in a 1.00 L vessel, how many moles of CO₂ form at equilibrium?
Q12. For N₂ + 3H₂ ⇌ 2NH₃ at 500 K, Kc = 36. What is Kc for NH₃ ⇌ ½N₂ + 3/2 H₂ at the same temperature?
Q13. Solid Mg(OH)₂ (Ksp = 1.8 × 10⁻¹¹) is shaken with pure water until saturated at 25 °C. What is the approximate pH of the solution? (Ignore water's own ionisation.)
Q14. A solution contains 0.010 M Cl⁻ and 0.010 M CrO₄²⁻. AgNO₃ is added slowly. Ksp(AgCl) = 1.8 × 10⁻¹⁰ and Ksp(Ag₂CrO₄) = 1.1 × 10⁻¹². Which solid appears first, and at what [Ag⁺]?
Q15. Argon is pumped into a rigid sealed vessel containing N₂, H₂ and NH₃ at equilibrium (N₂ + 3H₂ ⇌ 2NH₃). What happens to the equilibrium composition?
Q16. Which change alters the numerical value of the equilibrium constant of a reaction?
Q17. For a one-step 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?
Q18. A 2.0 L flask holds N₂ at 3.0 atm and a 3.0 L flask holds O₂ at 2.0 atm, both at the same temperature. The flasks are joined by a tap and the gases mix without reacting. What is the final total pressure?
Q19. Water (γ = 0.072 N m⁻¹, density 1000 kg m⁻³, contact angle 0°) rises in a glass capillary of radius 0.50 mm. Using h = 2γ cosθ/(ρgr) with g = 9.8 m s⁻², what is the height of rise?
Q20. Solid carbon dioxide (dry ice) sublimes at normal atmospheric pressure. Which statement best explains this?
Q21. Which substance has a standard enthalpy of formation of exactly zero at 298 K?
Q22. Equal numbers of moles of H₂ and O₂ are held at 300 K. Which statement about them is correct?
Q23. A gas mixture contains 4.0 g of H₂ and 32.0 g of O₂ (H = 1.0, O = 16.0) at a total pressure of 3.0 atm. What is the partial pressure of H₂?
Q24. 20 mL of ethene (C₂H₄) is exploded with 100 mL of oxygen in a closed vessel, and the products are cooled to the original temperature, when water is liquid. The remaining gas is then shaken with excess KOH solution. What volume of gas remains?
Q25. The molar enthalpy of combustion of ethanol is −1367 kJ mol⁻¹ (M = 46.07 g mol⁻¹). If the heat from burning 1.00 g is absorbed entirely by 200 g of water (c = 4.184 J g⁻¹ K⁻¹), what is the temperature rise?
Q26. Which of the following has the highest standard molar entropy at 298 K?
Q27. A bubble of volume 1.00 cm³ is released at a depth of 20.0 m in a lake and rises to the surface at constant temperature. Taking atmospheric pressure as 101.3 kPa, water density 1000 kg m⁻³ and g = 9.8 m s⁻², what is the bubble volume at the surface?
Q28. A liquid obeys Trouton's rule (ΔS_vap ≈ 85 J mol⁻¹ K⁻¹) and has a molar enthalpy of vaporisation of 29.7 kJ mol⁻¹. What is its approximate normal boiling point?
Q29. For 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), the equilibrium partial pressures are SO₃ 0.40 atm, SO₂ 0.20 atm and O₂ 0.10 atm. What is Kp?
Q30. A sealed syringe contains the equilibrium mixture N₂O₄(g) (colourless) ⇌ 2NO₂(g) (brown) at constant temperature. The plunger is suddenly pushed in to halve the volume. What is observed?