$$K = {1 \over R} \times {l \over A} = \left( {\left( {{1 \over {1500}}} \right) \times 1.14} \right)$$ S cm^$$-$$1

$$ \Rightarrow { \wedge _m} = 1000 \times {{\left( {{{1.14} \over {1500}}} \right)} \over {0.001}}$$ S cm² mol^$$-$$1

= 760 S cm² mol^$$-$$1

$$\Rightarrow$$ 760

Galvanic cell :

$$Z{n_{(s)}} + \mathop {Cu_{(aq.)}^{ + 2}}\limits_{0.02\,M} \to \mathop {Zn_{}^{ + 2}}\limits_{0.04\,M} + Cu(s)$$

Nernst equation = $${F_{cell}} = E_{cell}^o - {{0.059} \over 2}\log {{[2{n^{ + 2}}]} \over {[C{u^{ + 2}}]}}$$

$$ \Rightarrow {E_{cell}}\left[ {E_{cell}^o - E_{Z{n^{ + 2}}/Zn}^o} \right] - {{0.059} \over 2}\log {{0.04} \over {0.02}}$$

$$ \Rightarrow {E_{cell}}[0.34 - ( - 0.76)] - {{0.059} \over 2}{\log ^2}$$

$$ \Rightarrow {E_{cell}}1 - 1 - {{0.059} \over 2} \times 0.3010$$

= 1.0911 = 109.11 $$\times$$ 10^$$-$$2

= 109

Cell reaction is :

$$Cu(s) + 2A{g^ + }(aq) \to C{u^{2 + }}(aq) + 2Ag(s)$$

Now, $${E_{cell}} = E_{cell}^o - {{0.059} \over 2}\log {{[C{u^{2 + }}]} \over {{{[A{g^ + }]}^2}}}$$ .... (1)

$$\therefore$$ $${E_1} = 0.3095 = E_{cell}^o - {{0.059} \over 2}.\log {{0.01} \over {{{(0.001)}^2}}}$$ ....(2)

From (1) and (2), E₂ = 0.28 V = 28 $$\times$$ 10^$$-$$2 V

$$\Lambda _m^{} = 1000 \times {\kappa \over M}$$

$$ = 1000 \times {{2 \times {{10}^{ - 5}}} \over {0.001}} = 20$$ S cm² mol^$$-$$1

$$ \Rightarrow \alpha = {{\Lambda _m^{}} \over {\Lambda _m^\infty }} = {{20} \over {190}} = \left( {{2 \over {19}}} \right)$$

HA $$\rightleftharpoons$$ H⁺ + A^$$-$$

$$0.001(1 - \alpha )0.001\alpha 0.001\alpha $$

$$ \Rightarrow {k_a} = 0.001\left( {{{{\alpha ^2}} \over {1 - \alpha }}} \right) = {{0.001 \times {{\left( {{2 \over {19}}} \right)}^2}} \over {1 - \left( {{2 \over {19}}} \right)}}$$

$$ = 12.3 \times {10^{ - 6}}$$