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1. A 1.0 M solution of Cd²⁺ is mixed with excess iron, and the system is allowed to reach equilibrium.
The reaction is as follows:
\(\mathrm{Cd}^{2+}_{(a q)}+\mathrm{Fe}_{(s)} \longrightarrow \mathrm{Cd}_{(s)}+\mathrm{Fe}^{2+}_{(a q)}~~ ; \quad E^{\circ}=0.037~V \)
What is the concentration of Cd²⁺ at equilibrium?
1. \(0.195\)
2. \(0.097\)
3. \(0.053\)
4. \(0.145\)

2. Given below are two statements:

Assertion (A):	In the equation, \(\Delta_{\mathrm{r}} \mathrm{G}=-\mathrm{nFE} _{\text {cell }}, \) value of \(\mathrm{\Delta_rG }\) depends on n.
Reason (R):	\(\mathrm{E_{cell} }\) is an intensive property and  \(\mathrm{\Delta_rG }\)  is an extensive property.

 

1.	(A) is False but (R) is True.
2.	Both (A) and (R) are True and (R) is the correct explanation of (A).
3.	Both (A) and (R) are True and (R) is not the correct explanation of (A).
4.	(A) is True but (R) is False.

3. Electrolysis of Fe₂(SO₄)₃ solution is carried out for 'x' minutes with a current of 1.5 A, depositing 0.3482 g of Fe. What is the value of x to the nearest integer?
[Given: \(1 ~\text{F}=96500 ~\text{C} ~\text{mol}^{-1}\)
Atomic mass of \(\text{Fe}=56~ \text{g}~ \text{mol}^{-1}\)]
1. 20
2. 25
3. 18
4. 17

4. How many of the given statements are true for a fuel cell?

(a)	It is a type of Galvanic cell.
(b)	It is used for providing electrical power in space programs.
(c)	Hydrogen and oxygen are bubbled through porous carbon electrodes into concentrated \(NaOH ~\)solution.
(d)	It produces electricity with an efficiency of \(40\%\)
(e)	It is a pollution-free cell.

1. (a), (b), (c), and (e) 
2. (a), (b), and (e) 
3. (a), (c), (d), and (e) 
4. (a), (b), (d), and (e)

5. \({ 1 \over \wedge_M}\) is plotted against \(C\times \wedge_M\) for an aq. solution of caproic acid. It results into a straight line having slope = \(\alpha _1\) and intercept on Y-axis = \(\alpha_2\). Find \({ 1 \over \alpha_1 } \times { 1 \over \alpha_2}\):
[Where : \(\wedge_M\)= Molar conductivity
\(\wedge^\circ _M\) = Limiting molar conductivity
C= molar concentration
\(K_a\) = Acid dissociation constant of caproic acid]
Choose the correct option:

1.	\(K_a \times (\wedge^\circ _M )^2\)	2.	\(K_a \times {1 \over (\wedge^\circ _M )^3}\)
3.	\(K_a \times {1 \over (\wedge^\circ _M )^2}\)	4.	\(K_a\times (\wedge^\circ _M )^3 \)