Chapter 5: Electrochemistry Mock Test
Time: 1 Hour | Maximum Marks: 25
- All questions are compulsory.
- Section A contains Q1 (Multiple Choice) and Q2 (Very Short Answer).
- Section B contains Short Answer Type I questions (2 marks each). Attempt any 4.
- Section C contains Short Answer Type II questions (3 marks each). Attempt any 2.
- Section D contains Long Answer questions (4 marks each). Attempt any 1.
- Use of logarithmic tables is allowed. Calculators are not permitted.
SECTION A
Q1. Select and write the most appropriate answer from the given alternatives: [4 Marks]
-
The SI unit of conductivity ($\kappa$) is:
(A) $\Omega^{-1} \text{ m}^2 \text{ mol}^{-1}$(B) $\text{S m}^{-1}$(C) $\text{S m}^2 \text{ mol}^{-1}$(D) $\text{S cm}^2$
-
In a Galvanic cell, oxidation takes place at the:
(A) Anode(B) Cathode(C) Salt bridge(D) Electrolyte
-
The reference electrode chosen by convention, which has a standard potential of exactly 0.00 V at all temperatures, is:
(A) Calomel electrode(B) Standard Hydrogen Electrode(C) Glass electrode(D) Silver-Silver chloride electrode
-
The quantity of electricity required to deposit 1 mole of Copper from a $Cu^{2+}$ solution is:
(A) 1 Faraday(B) 2 Faradays(C) 3 Faradays(D) 4 Faradays
Q2. Answer the following questions in one sentence: [3 Marks]
- Define: Cell constant.
- State Kohlrausch's law of independent migration of ions.
- Write the mathematical relationship between molar conductivity ($\Lambda_m$) and conductivity ($\kappa$).
SECTION B
Attempt any FOUR of the following: [8 Marks]
- Distinguish between a Galvanic cell and an Electrolytic cell.
- State Faraday's first law of electrolysis and write its mathematical equation.
- Write any two functions of a salt bridge.
- The resistance of a conductivity cell filled with 0.1 M KCl solution is 100 $\Omega$. If the conductivity of 0.1 M KCl is 0.0129 S/cm, calculate the cell constant.
- Write the cell reactions that occur during the discharging of a Lead Storage battery at the anode and cathode.
SECTION C
Attempt any TWO of the following: [6 Marks]
- Describe the construction of the Standard Hydrogen Electrode (SHE) with the help of a labeled diagram (or description). Write its half-cell reaction.
- Calculate the EMF of the following cell at 298 K:
$Mg(s) | Mg^{2+}(0.1 \text{ M}) || Cu^{2+}(0.001 \text{ M}) | Cu(s)$
Given: $E^\circ_{Mg} = -2.37 \text{ V}$ and $E^\circ_{Cu} = +0.34 \text{ V}$. - Calculate the molar conductivity of acetic acid ($CH_3COOH$) at infinite dilution.
Given: $\Lambda^\circ_m(HCl) = 426 \text{ S cm}^2 \text{ mol}^{-1}$, $\Lambda^\circ_m(NaCl) = 126 \text{ S cm}^2 \text{ mol}^{-1}$, and $\Lambda^\circ_m(CH_3COONa) = 91 \text{ S cm}^2 \text{ mol}^{-1}$.
SECTION D
Attempt any ONE of the following: [4 Marks]
- (a) A solution of $CuSO_4$ is electrolyzed for 10 minutes with a current of 1.5 Amperes. Calculate the mass of copper deposited at the cathode. (Molar mass of Cu = 63.5 g/mol, $F = 96500 \text{ C mol}^{-1}$). [3 Marks]
(b) What are primary voltaic cells? [1 Mark] - (a) Derive the relationship between Standard Gibbs Free Energy change ($\Delta G^\circ$) and Standard Cell Potential ($E^\circ_{cell}$). [2 Marks]
(b) Calculate the standard Gibbs free energy change for the Daniell cell. Given $E^\circ_{cell} = 1.1 \text{ V}$ and $F = 96500 \text{ C mol}^{-1}$. [2 Marks]
Solutions & Marking Scheme
SECTION A [7 Marks]
Q1. Multiple Choice Answers:
1. (B) $\text{S m}^{-1}$ [1 Mark for correct option]
2. (A) Anode [1 Mark for correct option]
3. (B) Standard Hydrogen Electrode [1 Mark for correct option]
4. (B) 2 Faradays [1 Mark. $Cu^{2+} + 2e^- \rightarrow Cu$, requires 2 moles of electrons]
Q2. Very Short Answers:
1. Cell Constant:
It is the ratio of the distance between the electrodes ($l$) to the area of cross-section of the electrodes ($a$). Formula: $b = l/a$. [1 Mark for correct definition/formula]
2. Kohlrausch's Law:
It states that at infinite dilution, each ion migrates independently of its co-ion and makes its own definite contribution to the total molar conductivity of the electrolyte. [1 Mark for correct statement]
3. Molar Conductivity Formula:
$\Lambda_m = \frac{1000 \times \kappa}{C}$ (where $\kappa$ is conductivity and $C$ is concentration in mol/L). [1 Mark for correct formula]
SECTION B [8 Marks]
Q3. Galvanic vs Electrolytic Cell:
| Galvanic (Voltaic) Cell | Electrolytic Cell |
|---|---|
| Converts chemical energy into electrical energy. | Converts electrical energy into chemical energy. |
| Reactions are spontaneous ($\Delta G < 0$). | Reactions are non-spontaneous ($\Delta G > 0$). |
| Anode is negative, Cathode is positive. | Anode is positive, Cathode is negative. |
[1 Mark for each point of distinction. Total 2 Marks]
Q4. Faraday's First Law:
Statement: The mass of any substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. [1 Mark]
Equation: $W = Z \cdot Q$ OR $W = Z \cdot I \cdot t$ (where $Z$ is electrochemical equivalent, $I$ is current, $t$ is time). [1 Mark]
Q5. Functions of Salt Bridge:
- It completes the inner electrical circuit by connecting the two half-cells. [1 Mark]
- It maintains electrical neutrality in both half-cell solutions by allowing the flow of oppositely charged ions. [1 Mark]
- It prevents the mechanical mixing of the two electrolytes.
Q6. Cell Constant Numerical:
Given: $R = 100 \text{ }\Omega$, $\kappa = 0.0129 \text{ S cm}^{-1}$. [1/2 Mark]
Formula: Cell Constant ($b$) $= \kappa \times R$ [1/2 Mark]
Calculation: $b = 0.0129 \times 100$ [1/2 Mark]
Answer: $b = 1.29 \text{ cm}^{-1}$ [1/2 Mark for correct answer with units]
Q7. Lead Storage Battery Discharging Reactions:
At Anode (Oxidation):
$Pb(s) + SO_4^{2-}(aq) \rightarrow PbSO_4(s) + 2e^-$ [1 Mark]
At Cathode (Reduction):
$PbO_2(s) + 4H^+(aq) + SO_4^{2-}(aq) + 2e^- \rightarrow PbSO_4(s) + 2H_2O(l)$ [1 Mark]
SECTION C [6 Marks]
Q8. Standard Hydrogen Electrode (SHE):
Construction: It consists of a pure platinum wire sealed in a glass tube. The lower end is attached to a platinum foil coated with finely divided platinum black. The foil is immersed in an acidic solution having $H^+$ ion concentration of exactly $1 \text{ M}$ (e.g., $1 \text{ M } HCl$). Pure hydrogen gas at 1 atm pressure is continuously bubbled through the solution over the platinum foil at 298 K. [2 Marks for description/diagram]
Half-cell Reaction: $2H^+(aq) + 2e^- \rightleftharpoons H_2(g)$ [1 Mark]
Q9. Nernst Equation Numerical:
1. Calculate $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} = 0.34 - (-2.37) = 2.71 \text{ V}$. [1 Mark]
2. Reaction: $Mg + Cu^{2+} \rightarrow Mg^{2+} + Cu$. Here $n = 2$. [1/2 Mark]
3. Nernst Eq: $E_{cell} = E^\circ_{cell} - \frac{0.0592}{n} \log_{10} \frac{[Mg^{2+}]}{[Cu^{2+}]}$ [1/2 Mark]
$E_{cell} = 2.71 - \frac{0.0592}{2} \log_{10} \left( \frac{0.1}{0.001} \right) = 2.71 - 0.0296 \log_{10}(100)$
$E_{cell} = 2.71 - 0.0296(2) = 2.71 - 0.0592$
Answer: $E_{cell} = 2.6508 \text{ V}$. [1 Mark]
Q10. Kohlrausch's Law Numerical:
According to Kohlrausch's law, to find $\Lambda^\circ_m(CH_3COOH)$, we combine the strong electrolytes to yield the ions of the weak acid.
$\Lambda^\circ_m(CH_3COOH) = \Lambda^\circ_m(CH_3COONa) + \Lambda^\circ_m(HCl) - \Lambda^\circ_m(NaCl)$ [1.5 Marks for correct setup]
$\Lambda^\circ_m = 91 + 426 - 126$ [1/2 Mark]
$\Lambda^\circ_m = 517 - 126 = 391$
Answer: $\Lambda^\circ_m(CH_3COOH) = 391 \text{ S cm}^2 \text{ mol}^{-1}$ [1 Mark for correct answer]
SECTION D [4 Marks]
Q11. (a) Faraday Numerical [3 Marks] (b) Primary Cell [1 Mark]
(a) Mass Calculation:
Given: $I = 1.5 \text{ A}$, $t = 10 \text{ min} = 600 \text{ s}$.
$Q = I \times t = 1.5 \times 600 = 900 \text{ C}$. [1 Mark]
Reaction: $Cu^{2+} + 2e^- \rightarrow Cu$. So $n = 2$. [1/2 Mark]
$W = \frac{M \times Q}{n \times F} = \frac{63.5 \times 900}{2 \times 96500}$ [1 Mark for substitution]
Answer: $W = \frac{57150}{193000} \approx 0.296 \text{ g}$ [1/2 Mark for answer]
(b) Primary Voltaic Cells: These are cells that cannot be recharged once they are exhausted because the cell reaction is not completely reversible. (e.g., Dry cell). [1 Mark]
Q12. (a) $\Delta G^\circ$ Derivation [2 Marks] (b) Daniell Cell Numerical [2 Marks]
(a) Derivation:
The maximum electrical work done by a galvanic cell equals the decrease in its Gibbs free energy: $-\Delta G^\circ = W_{\text{electrical}}$. [1/2 Mark]
Electrical work = Total charge $\times$ Cell potential = $nF \times E^\circ_{cell}$. [1 Mark]
Equating both: $-\Delta G^\circ = nF E^\circ_{cell} \implies \Delta G^\circ = -nF E^\circ_{cell}$. [1/2 Mark]
(b) Numerical:
For Daniell cell ($Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu$), $n = 2$. [1/2 Mark]
$\Delta G^\circ = -nF E^\circ_{cell} = -2 \times 96500 \times 1.1$ [1 Mark]
$\Delta G^\circ = -212,300 \text{ J mol}^{-1}$
Answer: $\Delta G^\circ = -212.3 \text{ kJ mol}^{-1}$ [1/2 Mark]
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