CUET Chemistry Set-1: Physical Chemistry Basics
Question 1
The value of $R$ in SI units is
(1) 8.314 J mol⁻¹ K⁻¹
(2) 0.0821 L atm mol⁻¹ K⁻¹
(3) 2 cal mol⁻¹ K⁻¹
(4) 1.987 L atm mol⁻¹ K⁻¹
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Answer: (1)
Solution: The universal gas constant $R$ in SI is 8.314 J mol⁻¹ K⁻¹.
Question 2
If 5 g of a gas at 1 bar pressure occupies 5 L at 300 K, its molar mass (g mol⁻¹) is approximately
(1) 30
(2) 25
(3) 20
(4) 15
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Answer: (3)
Solution: $PV = nRT \Rightarrow n = \frac{1 \times 5}{0.083 \times 300} \approx 0.2$ mol; $M = \frac{5}{0.2} = 25$ g mol⁻¹, closest 20.
Question 3
The root-mean-square speed of $O_2$ at 300 K is closest to (in m s⁻¹)
(1) 483
(2) 680
(3) 390
(4) 240
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Answer: (1)
Solution: $v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3 \times 8.314 \times 300}{0.032}} \approx 483$ m s⁻¹.
Question 4
Which of the following gases will have the highest average speed at 400 K?
(1) $H_2$
(2) $He$
(3) $N_2$
(4) $CO_2$
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Answer: (1)
Solution: $v_{avg} \propto \frac{1}{\sqrt{M}}$; $H_2$ has lowest $M$, hence highest speed.
Question 5
The compressibility factor $Z$ of a real gas is less than 1 at low pressure because
(1) attractive forces dominate
(2) repulsive forces dominate
(3) $V_{real} > V_{ideal}$
(4) $PV = nRT$ always
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Answer: (1)
Solution: $Z < 1$ implies gas is more compressible than ideal; attractive forces reduce effective volume.
Question 6
The van der Waals constant $a$ (in L² atm mol⁻²) is largest for
(1) $H_2$
(2) $N_2$
(3) $NH_3$
(4) $CH_4$
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Answer: (3)
Solution: $a$ measures intermolecular attraction; $NH_3$ exhibits hydrogen bonding hence largest $a$.
Question 7
The ratio $\frac{C_p}{C_v}$ for a monoatomic ideal gas is
(1) 1.40
(2) 1.67
(3) 1.33
(4) 1.50
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Answer: (2)
Solution: $\gamma = \frac{C_p}{C_v} = \frac{5/2 R}{3/2 R} = \frac{5}{3} \approx 1.67$.
Question 8
For 1 mole of an ideal gas undergoing reversible adiabatic expansion, which relation holds?
(1) $PV^\gamma = constant$
(2) $PV = constant$
(3) $TV^{\gamma-1} = constant$
(4) both (1) and (3)
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Answer: (4)
Solution: Both $PV^\gamma = constant$ and $TV^{\gamma-1} = constant$ are valid for adiabatic process.
Question 9
The work done (in J) when 2 mol of an ideal gas expands isothermally and reversibly from 10 atm to 1 atm at 300 K is
(1) –11.49
(2) –11490
(3) –5745
(4) 5745
Show Answer
Answer: (2)
Solution: $w = –nRT \ln\frac{P_1}{P_2} = –2 \times 8.314 \times 300 \times \ln 10 \approx –11490$ J.
Question 10
The enthalpy change for the reaction $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$ at 298 K is –572 kJ. The internal energy change $\Delta U$ (in kJ) is approximately
(1) –570
(2) –574
(3) –569
(4) –575
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Answer: (3)
Solution: $\Delta H = \Delta U + \Delta n_g RT \Rightarrow \Delta U = –572 – (–3) \times 8.314 \times 298 / 1000 \approx –569$ kJ.
Question 11
The standard enthalpy of formation of $CO_2(g)$ is –393 kJ mol⁻¹ and that of $H_2O(l)$ is –286 kJ mol⁻¹. The enthalpy of combustion of $CH_4(g)$ to $CO_2(g)$ and $H_2O(l)$ is –890 kJ mol⁻¹. The standard enthalpy of formation of $CH_4(g)$ (in kJ mol⁻¹) is
(1) –75
(2) +75
(3) –211
(4) +211
Show Answer
Answer: (1)
Solution: $\Delta H_c = \sum \Delta H_f$(products) – $\Delta H_f$(reactant) ⇒ –890 = [–393×1 + –286×2] – $\Delta H_f(CH_4)$ ⇒ $\Delta H_f(CH_4) = –75$ kJ mol⁻¹.
Question 12
For which process is $\Delta S_{system}$ negative?
(1) Melting of ice
(2) Vaporisation of water
(3) Sublimation of $CO_2$
(4) Freezing of water
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Answer: (4)
Solution: Freezing decreases disorder, hence $\Delta S < 0$.
Question 13
The spontaneity criterion for a process at constant $T$ and $P$ is
(1) $\Delta H < 0$
(2) $\Delta S > 0$
(3) $\Delta G < 0$
(4) $\Delta U < 0$
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Answer: (3)
Solution: $\Delta G < 0$ guarantees spontaneity at constant $T,P$.
Question 14
The equilibrium constant $K_p$ for the reaction $N_2O_4(g) \rightleftharpoons 2NO_2(g)$ is 0.25 at 300 K. If $P_{N_2O_4} = 1$ bar at equilibrium, $P_{NO_2}$ (in bar) is
(1) 0.25
(2) 0.50
(3) 0.75
(4) 1.0
Show Answer
Answer: (2)
Solution: $K_p = \frac{P_{NO_2}^2}{P_{N_2O_4}} \Rightarrow 0.25 = \frac{P_{NO_2}^2}{1} \Rightarrow P_{NO_2} = 0.5$ bar.
Question 15
The degree of dissociation of $PCl_5$ at 1 atm is 0.2. The equilibrium constant $K_p$ is
(1) 0.05
(2) 0.20
(3) 0.50
(4) 0.02
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Answer: (1)
Solution: $K_p = \frac{\alpha^2 P}{1 – \alpha^2} \approx \frac{0.04 \times 1}{0.8} = 0.05$ atm.
Question 16
The pH of 0.01 M HCl solution at 25 °C is
(1) 1
(2) 2
(3) 3
(4) 0
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Answer: (2)
Solution: $[H^+] = 10^{-2}$ M ⇒ pH = 2.
Question 17
The conjugate base of $HCO_3^-$ is
(1) $CO_3^{2-}$
(2) $H_2CO_3$
(3) $OH^-$
(4) $H_3O^+$
Show Answer
Answer: (1)
Solution: $HCO_3^- \rightarrow CO_3^{2-} + H^+$; $CO_3^{2-}$ is conjugate base.
Question 18
For a buffer solution containing 0.1 M $CH_3COOH$ and 0.1 M $CH_3COONa$, the pH (p$K_a$ = 4.76) is approximately
(1) 4.76
(2) 9.24
(3) 2.38
(4) 7.00
Show Answer
Answer: (1)
Solution: $pH = pK_a + \log\frac{[salt]}{[acid]} = 4.76 + \log 1 = 4.76$.
Question 19
The solubility product $K_{sp}$ of $BaSO_4$ is $1 \times 10^{-10}$. Its solubility (in mol L⁻¹) in pure water is
(1) $10^{-5}$
(2) $10^{-10}$
(3) $10^{-3}$
(4) $10^{-7}$
Show Answer
Answer: (1)
Solution: $s^2 = K_{sp} \Rightarrow s = \sqrt{10^{-10}} = 10^{-5}$ mol L⁻¹.
Question 20
In a 0.01 M $NH_4OH$ solution with $K_b = 1.8 \times 10^{-5}$, the degree of ionisation is approximately
(1) 0.042
(2) 0.42
(3) 0.0042
(4) 0.84
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Answer: (1)
Solution: $\alpha = \sqrt{\frac{K_b}{c}} = \sqrt{\frac{1.8 \times 10^{-5}}{0.01}} \approx 0.042$.
Question 21
The standard electrode potential $E^\circ$ for the cell $Zn|Zn^{2+}(1 M)||Cu^{2+}(1 M)|Cu$ is 1.10 V. The standard free energy change $\Delta G^\circ$ (in kJ mol⁻¹) for the reaction is
(1) –212
(2) –106
(3) +212
(4) +106
Show Answer
Answer: (1)
Solution: $\Delta G^\circ = –nFE^\circ = –2 \times 96485 \times 1.10 / 1000 \approx –212$ kJ mol⁻¹.
Question 22
The molar conductivity at infinite dilution for $NH_4Cl$ is 150 S cm² mol⁻¹. If $\lambda^\circ$ for $NH_4^+$ is 75, that for $Cl^-$ (in S cm² mol⁻¹) is
(1) 75
(2) 150
(3) 225
(4) 50
Show Answer
Answer: (1)
Solution: $\Lambda^\circ = \lambda_+^\circ + \lambda_-^\circ \Rightarrow 150 = 75 + \lambda_-^\circ \Rightarrow \lambda_-^\circ = 75$.
Question 23
For a first-order reaction, the half-life is 100 s. The rate constant (in s⁻¹) is
(1) 6.93 × 10⁻³
(2) 1.0 × 10⁻²
(3) 0.693 × 10⁻²
(4) 0.693 × 10⁻¹
Show Answer
Answer: (1)
Solution: $k = \frac{0.693}{t_{1/2}} = \frac{0.693}{100} = 6.93 \times 10^{-3}$ s⁻¹.
Question 24
The unit of rate constant for a zero-order reaction is
(1) mol L⁻¹ s⁻¹
(2) s⁻¹
(3) L mol⁻¹ s⁻¹
(4) mol⁻¹ L s⁻¹
Show Answer
Answer: (1)
Solution: Zero-order: rate = k, hence unit same as rate: mol L⁻¹ s⁻¹.
Question 25
The activation energy for a reaction is 50 kJ mol⁻¹. The ratio of rate constants at 310 K to 300 K is approximately (use $R = 8.314$ J mol⁻¹ K⁻¹)
(1) 1.5
(2) 2.0
(3) 2.5
(4) 3.0
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Answer: (2)
Solution: $\ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{300} – \frac{1}{310}\right) \approx \frac{50000}{8.314} \times 1.08 \times 10^{-4} \approx 0.65 \Rightarrow \frac{k_2}{k_1} \approx e^{0.65} \approx 1.9 \approx 2$.
BETA
