For the electrochemical cell,

$$\left. {Mg\left( s \right)} \right|M{g^{2 + }}\left( {aq,1\,M} \right)\left\| {C{u^{2 + }}} \right.\left( {aq,1M} \right)\left| {Cu\left( s \right)} \right.$$

the standard $$emf$$ of the cell is $$2.70$$ $$V$$ at $$300$$ $$K.$$ When the concentration of $$M{g^{2 + }}$$ is changed to $$x$$ $$M,$$ the cell potential changes to $$2.67$$ $$V$$ at $$300$$ $$K.$$ The value of $$x$$ is ___________.

(given, $${F \over R} = 11500\,K{V^{ - 1}},$$ where $$F$$ is the Faraday constant and $$R$$ is the gas constant, In $$(10=2.30)$$

Treatment of benzene with $$CO/HCl$$ in the presence of anhydrous $$AlC{l_3}/CuCl$$ followed by reaction with $$A{c_2}O/NaOAc$$ gives compound $$X$$ as the major product. Compound $$X$$ upon reaction with $$B{r_2}/N{a_2}C{O_3},$$ followed by heating at $$473$$ $$K$$ with moist $$KOH$$ furnishes $$Y$$ as the, major product. Reaction of $$X$$ with $${H_2}/Pd$$-$$C,$$ followed by $${H_3}P{O_4}$$ treatment gives $$Z$$ as the major product.

The compound $$Z$$ is

In the following reaction sequence, the correct structure(s) of $$X$$ is (are)

The solubility of a salt of weak acid $$(AB)$$ at $$pH\,$$ $$3$$ is $$Y \times {10^{ - 3}}$$ $$mol\,{L^{ - 1}}.$$ The value of $$Y$$ is ________________.

(Given that the value of solubility product of $$AB$$ $$\left( {{K_{sp}}} \right) = 2 \times {10^{ - 10}}$$ and the value of ionization constant of $$HB$$ $$\left( {{K_a}} \right) = 1 \times {10^{ - 8}}$$)