CUET Chemistry Set-2: Electrochemistry & Kinetics
Question 1
The molar conductivity of $0.04~\text{M}$ $\text{BaCl}_2$ solution is $200~\text{S cm}^2~\text{mol}^{-1}$. The limiting molar conductivity of $\text{BaCl}_2$ is $280~\text{S cm}^2~\text{mol}^{-1}$. The degree of dissociation $(\alpha)$ of $\text{BaCl}_2$ is
(1) 0.60 (2) 0.71 (3) 0.80 (4) 0.90
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Answer: (2)
Solution: $\alpha = \frac{\Lambda}{\Lambda^\circ} = \frac{200}{280} \approx 0.714$
Question 2
For a first-order reaction, the half-life is 30 min. The time required for 75% completion is
(1) 30 min (2) 45 min (3) 60 min (4) 90 min
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Answer: (3)
Solution: $t_{75%}=2\times t_{1/2}=2\times30=60$ min
Question 3
The standard reduction potentials of $\text{Ag}^+/\text{Ag}$ and $\text{Cu}^{2+}/\text{Cu}$ are $+0.80~\text{V}$ and $+0.34~\text{V}$ respectively. The emf of the cell $\text{Cu}|\text{Cu}^{2+}(1~\text{M})||\text{Ag}^+(1~\text{M})|\text{Ag}$ is
(1) 0.46 V (2) 1.14 V (3) –0.46 V (4) 0.23 V
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Answer: (1)
Solution: $E^\circ_{\text{cell}}=0.80-0.34=0.46$ V
Question 4
The rate law for the reaction $2\text{A}+\text{B}\to \text{Products}$ is $\text{Rate}=k[\text{A}][\text{B}]^2$. If $[\text{A}]$ is doubled and $[\text{B}]$ is halved, the rate changes by a factor of
(1) 2 (2) 4 (3) 1 (4) 0.5
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Answer: (4)
Solution: New rate $\propto 2\times (0.5)^2=0.5$ times
Question 5
Which of the following increases the conductivity of a strong electrolyte solution?
(1) Dilution (2) Increasing ion size (3) Lowering temperature (4) Adding non-polar solvent
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Answer: (1)
Solution: Dilution increases ion mobility $\Rightarrow$ conductivity increases.
Question 6
For the reaction $\text{2N}_2\text{O}_5\to 4\text{NO}_2+\text{O}_2$, the rate of formation of $\text{O}_2$ is $2\times10^{-4}~\text{mol L}^{-1}\text{s}^{-1}$. The rate of disappearance of $\text{N}_2\text{O}_5$ is
(1) $4\times10^{-4}$ (2) $2\times10^{-4}$ (3) $1\times10^{-4}$ (4) $0.5\times10^{-4}$
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Answer: (1)
Solution: $-\frac{1}{2}\frac{d[\text{N}_2\text{O}_5]}{dt}=\frac{d[\text{O}_2]}{dt}\Rightarrow -\frac{d[\text{N}_2\text{O}_5]}{dt}=4\times10^{-4}$
Question 7
The Kohlrausch law is obeyed when
(1) Concentration approaches zero (2) Temperature approaches zero (3) Pressure approaches zero (4) Ionic strength is maximum
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Answer: (1)
Solution: At infinite dilution (c→0) molar conductivity becomes additive.
Question 8
The activation energy of a reaction is 50 kJ mol$^{-1}$. The ratio of rate constants at 310 K and 300 K is approximately ($R=8.3~\text{J mol}^{-1}\text{K}^{-1}$)
(1) 1.1 (2) 1.9 (3) 2.2 (4) 3.0
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Answer: (2)
Solution: $\ln\frac{k_2}{k_1}=\frac{50000}{8.3}\left(\frac{10}{300\times310}\right)\approx 0.65\Rightarrow \frac{k_2}{k_1}\approx 1.9$
Question 9
The electrolysis of aqueous $\text{Na}_2\text{SO}_4$ using inert electrodes produces at anode
(1) $\text{Na}$ (2) $\text{H}_2$ (3) $\text{O}_2$ (4) $\text{SO}_2$
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Answer: (3)
Solution: Over anode water is oxidised: $2\text{H}_2\text{O}\to \text{O}_2+4\text{H}^++4e^-$
Question 10
A fuel cell uses the reaction $\text{H}_2+\tfrac12\text{O}_2\to \text{H}_2\text{O}(l)$. If $\Delta G^\circ=-237~\text{kJ mol}^{-1}$, the standard emf is
(1) 1.23 V (2) 2.46 V (3) 0.80 V (4) 1.10 V
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Answer: (1)
Solution: $E^\circ=-\frac{\Delta G^\circ}{nF}=\frac{237000}{2\times96500}\approx 1.23$ V
Question 11
The unit of rate constant for a zero-order reaction is
(1) $\text{s}^{-1}$ (2) $\text{mol L}^{-1}\text{s}^{-1}$ (3) $\text{L mol}^{-1}\text{s}^{-1}$ (4) $\text{L}^2\text{mol}^{-2}\text{s}^{-1}$
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Answer: (2)
Solution: Zero-order: $\text{mol L}^{-1}\text{s}^{-1}$
Question 12
The time for 90% completion of a first-order reaction is 20 min. The rate constant is
(1) $0.115~\text{min}^{-1}$ (2) $0.069~\text{min}^{-1}$ (3) $0.046~\text{min}^{-1}$ (4) $0.023~\text{min}^{-1}$
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Answer: (1)
Solution: $k=\frac{2.303}{t}\log\frac{100}{10}=\frac{2.303}{20}=0.115~\text{min}^{-1}$
Question 13
The equivalent conductance of $\text{CH}3\text{COOH}$ at infinite dilution is $390.7~\text{S cm}^2~\text{equiv}^{-1}$. If $\lambda^\circ{\text{H}^+}=349.6$ and $\lambda^\circ_{\text{CH}_3\text{COO}^-}=40.9$, the value verifies
(1) Faraday’s law (2) Kohlrausch law (3) Ostwald dilution law (4) Nernst equation
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Answer: (2)
Solution: $\Lambda^\circ=\lambda^\circ_++\lambda^\circ_-$ is Kohlrausch law.
Question 14
A current of 2 A is passed for 30 min through molten $\text{Al}_2\text{O}_3$. The mass of Al deposited is (Al = 27, 1 F = 96500 C)
(1) 0.54 g (2) 0.27 g (3) 1.08 g (4) 2.16 g
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Answer: (3)
Solution: $Q=2\times1800=3600~\text{C};\ \text{mol Al}=\frac{3600}{3\times96500}\Rightarrow \text{mass}=1.08~\text{g}$
Question 15
For a reaction, a plot of $\ln k$ vs $1/T$ gives a straight line with slope $-5\times10^3~\text{K}$. The activation energy is
(1) 41.6 kJ mol$^{-1}$ (2) 83.2 kJ mol$^{-1}$ (3) 125 kJ mol$^{-1}$ (4) 166 kJ mol$^{-1}$
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Answer: (1)
Solution: $E_a=-R\times\text{slope}=8.3\times5\times10^3=41.5~\text{kJ mol}^{-1}$
Question 16
In a concentration cell of Ag electrodes with $0.1~\text{M}$ $\text{AgNO}_3$ and $1.0~\text{M}$ $\text{AgNO}_3$, the emf at 298 K is
(1) 0.059 V (2) 0.0295 V (3) 0.118 V (4) 0.030 V
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Answer: (1)
Solution: $E_{\text{cell}}=0.0591\log\frac{1.0}{0.1}=0.059~\text{V}$
Question 17
The rate-determining step of a reaction has molecularity 2. The overall order is
(1) always 2 (2) always 1 (3) at least 2 (4) cannot be predicted
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Answer: (4)
Solution: Molecularity of RDS ≠ overall order; intermediates may change rate law.
Question 18
Which statement is incorrect for a second-order reaction?
(1) $t_{1/2}\propto [\text{A}]_0^{-1}$ (2) Unit of $k$ is $\text{L mol}^{-1}\text{s}^{-1}$ (3) Plot of $1/[\text{A}]$ vs $t$ is linear (4) Half-life is independent of initial concentration
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Answer: (4)
Solution: $t_{1/2}=\frac{1}{k[\text{A}]_0}$ depends on $[\text{A}]_0$.
Question 19
The limiting molar conductivity of $\text{Ba(OH)}_2$ is $x$. The limiting molar conductivity of $\text{BaCl}_2$ is $y$ and of $\text{NaOH}$ is $z$. Then $\Lambda^\circ$ of NaCl is
(1) $z+y-x$ (2) $x+y-z$ (3) $x+z-y$ (4) $y+z-x$
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Answer: (1)
Solution: $\Lambda^\circ_{\text{NaCl}}=\Lambda^\circ_{\text{NaOH}}+\Lambda^\circ_{\text{BaCl}2}-\Lambda^\circ{\text{Ba(OH)}_2}=z+y-x$
Question 20
A first-order gaseous reaction $\text{A}\to 2\text{B}$ is carried out in a closed vessel. After 10 min the total pressure changes from 0.5 atm to 0.6 atm. The rate constant is
(1) $0.069~\text{min}^{-1}$ (2) $0.023~\text{min}^{-1}$ (3) $0.046~\text{min}^{-1}$ (4) $0.115~\text{min}^{-1}$
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Answer: (3)
Solution: $p_\text{A}=0.5-0.1=0.4~\text{atm};\ k=\frac{2.303}{10}\log\frac{0.5}{0.4}=0.0223\approx0.023~\text{min}^{-1}$ (nearest option 3)
Question 21
The number of electrons exchanged when 1 mol of $\text{K}_2\text{Cr}_2\text{O}_7$ acts as oxidant in acid medium is
(1) 3 (2) 5 (3) 6 (4) 4
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Answer: (3)
Solution: $\text{Cr}_2\text{O}_7^{2-}+14\text{H}^++6e^-\to 2\text{Cr}^{3+}+7\text{H}_2\text{O}$
Question 22
For a reaction, the rate constant doubles on increasing temperature from 300 K to 310 K. The activation energy is approximately
(1) 51 kJ mol$^{-1}$ (2) 60 kJ mol$^{-1}$ (3) 71 kJ mol$^{-1}$ (4) 83 kJ mol$^{-1}$
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Answer: (1)
Solution: $\ln 2=\frac{E_a}{8.3}\left(\frac{10}{300\times310}\right)\Rightarrow E_a\approx 51~\text{kJ mol}^{-1}$
Question 23
The product obtained at cathode during electrolysis of dilute $\text{H}_2\text{SO}_4$ with Pt electrodes is
(1) $\text{H}_2$ (2) $\text{O}_2$ (3) $\text{SO}_2$ (4) $\text{S}$
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Answer: (1)
Solution: Reduction of water: $2\text{H}_2\text{O}+2e^-\to \text{H}_2+2\text{OH}^-$
Question 24
The charge required to deposit 0.5 mol of Ni from $\text{Ni}^{2+}$ solution is
(1) 48250 C (2) 96500 C (3) 193000 C (4) 289500 C
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Answer: (2)
Solution: $Q=0.5\times2\times96500=96500~\text{C}$
Question 25
A reaction has enthalpy of activation $80~\text{kJ mol}^{-1}$ and entropy of activation $20~\text{J mol}^{-1}\text{K}^{-1}$ at 300 K. The Gibbs energy of activation is
(1) 74 kJ mol$^{-1}$ (2) 80 kJ mol$^{-1}$ (3) 86 kJ mol$^{-1}$ (4) 92 kJ mol$^{-1}$
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Answer: (1)
Solution: $\Delta G^\ddagger=\Delta H^\ddagger-T\Delta S^\ddagger=80-300\times0.020=74~\text{kJ mol}^{-1}$
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