States of Matter and Thermodynamics — Practice

Question 1

A gas at 2 atm occupies 3 L. At constant temperature, its volume at 6 atm is:
(a) 1 L (b) 9 L (c) 4 L (d) 0.5 L

Accepted Answer

(a) 1 L.

Boyle's law P₁V₁ = P₂V₂: 2 × 3 = 6 × V₂ ⇒ V₂ = 6/6 = 1 L.

Question 2

The number of moles of an ideal gas occupying 22.4 L at 273 K and 1 atm is:
(a) 1 (b) 2 (c) 0.5 (d) 22.4

Accepted Answer

(a) 1.

At STP (273 K, 1 atm) one mole occupies 22.4 L, so n = 1. (Check: n = PV/RT = 1×22.4/(0.0821×273) ≈ 1.)

Question 3

The rms speed of a gas at 300 K becomes what factor at 1200 K?
(a) 2× (b) 4× (c) √2× (d) 16×

Accepted Answer

(a) 2×.

u_rms ∝ √T, so the factor is √(1200/300) = √4 = 2.

Question 4

At the same temperature and pressure, the ratio of the rate of effusion of H₂ to O₂ is:
(a) 4 : 1 (b) 1 : 4 (c) 1 : 1 (d) 16 : 1

Accepted Answer

(a) 4 : 1.

Rate ∝ 1/√M, so r(H₂)/r(O₂) = √(32/2) = √16 = 4. Hydrogen effuses four times faster.

Question 5

The correct order of molecular speeds for a gas is:
(a) u_mp < u_avg < u_rms (b) u_rms < u_avg < u_mp (c) u_avg < u_mp < u_rms (d) all equal

Accepted Answer

(a) u_mp < u_avg < u_rms.

The fixed ratio is √2 : √(8/π) : √3 ≈ 1 : 1.13 : 1.22, so most probable < average < root-mean-square.

Question 6

For a real gas showing Z < 1, the dominant effect is:
(a) intermolecular attraction (b) finite molecular volume (c) high temperature (d) zero pressure

Accepted Answer

(a) intermolecular attraction.

Z = PV/nRT < 1 means the gas is more compressible than ideal, which happens when intermolecular attractions (the 'a' term) pull the molecules together.

Question 7

Which of the following is NOT a state function?
(a) work (b) enthalpy (c) internal energy (d) entropy

Accepted Answer

(a) work.

Work (like heat) is a path function — it depends on how the change is carried out. Enthalpy, internal energy and entropy depend only on the state.

Question 8

A system absorbs 300 J of heat and does 100 J of work on the surroundings. The change in internal energy is:
(a) +200 J (b) +400 J (c) −200 J (d) −400 J

Accepted Answer

(a) +200 J.

ΔU = q + w = +300 + (−100) = +200 J. Work done by the system is negative w.

Question 9

For an ideal gas, C_P − C_V equals:
(a) R (b) 0 (c) 2R (d) R/2

Accepted Answer

(a) R.

For one mole of an ideal gas, C_P − C_V = R (the gas constant), and C_P is always greater than C_V.

Question 10

Given Δ_fH: CO₂ = −393.5, H₂O = −285.8, CH₄ = −74.8 kJ/mol, the enthalpy of combustion of CH₄ (CH₄ + 2O₂ → CO₂ + 2H₂O) is:
(a) −890.3 kJ/mol (b) −604.5 kJ/mol (c) −965.1 kJ/mol (d) +890.3 kJ/mol

Accepted Answer

(a) −890.3 kJ/mol.

Δ_rH = [(−393.5) + 2(−285.8)] − [(−74.8) + 0] = −965.1 + 74.8 = −890.3 kJ/mol (O₂ has Δ_fH = 0).

Question 11

For the reaction N₂(g) + 3H₂(g) → 2NH₃(g), Δn_g equals:
(a) −2 (b) +2 (c) 0 (d) −1

Accepted Answer

(a) −2.

Gaseous moles: products 2, reactants 4, so Δn_g = 2 − 4 = −2. Then ΔH = ΔU + Δn_g RT = ΔU − 2RT.

Question 12

For which process is ΔS positive?
(a) melting of ice (b) 2NO₂(g) → N₂O₄(g) (c) freezing of water (d) condensation of steam

Accepted Answer

(a) melting of ice.

Solid → liquid increases disorder, so ΔS > 0. The other three reduce disorder (fewer gas molecules, gas→liquid, liquid→solid), giving ΔS < 0.

Question 13

A reaction has ΔH = +30 kJ/mol and ΔS = +100 J K⁻¹ mol⁻¹. It becomes spontaneous above:
(a) 300 K (b) 30 K (c) 3000 K (d) 273 K

Accepted Answer

(a) 300 K.

Spontaneous when ΔG = ΔH − TΔS < 0 ⇒ T > ΔH/ΔS = 30000/100 = 300 K.

Question 14

For a reaction at equilibrium at constant T and P, ΔG is:
(a) 0 (b) negative (c) positive (d) equal to ΔH

Accepted Answer

(a) 0.

At equilibrium the free energy is at a minimum and does not change, so ΔG = 0 (and ΔG° = −RT ln K).

Question 15

A reaction with ΔH < 0 and ΔS > 0 is:
(a) spontaneous at all temperatures (b) spontaneous only at high T (c) spontaneous only at low T (d) never spontaneous

Accepted Answer

(a) spontaneous at all temperatures.

ΔG = ΔH − TΔS is negative for all T when ΔH is negative and ΔS is positive (both terms favour spontaneity).

Practice — States of Matter and Thermodynamics

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