Question

A metal is regarded as an assembly of metal ions and free electrons.An electrode represents an electronic conductor partially dipped in an electrolytic conductor. The potential difference set up at the surface of separation of electronic and electrolytic conductors in contact with each other is called electrode potential. When the metal is in contact with an electrolytic solution,some metal ions enter into the liquid due to a tendency in the metal,called by Nernst as ‘Electrolytic solution tension’.Thus $M \rightarrow M^{n+} +e^-$.The potential difference set up at equilibrium is called oxidation electrode potential.An alloy of 1.45g Ag and Pb was dissolved in the desired amount of $HNO_3$ and volume made up to 500ml. An Ag electrode was dipped in solution and $E_{cell}$ of the cell
$PtH_2 |H^+||Ag^+|Ag$ was 0.503V at 298K.
$[E^o_{Ag^+|Ag}=0.80V$
Find $$ mass of $Pb$ metal in below alloy sample is:
a.$99.23$
b.$89.95$
c.$99.96$
d.$82.30$

Answer 1

Hint : We know that a mixture that contains equal proportions of the components throughout any sample of the mixture is called a homogeneous mixture, whereas in a heterogeneous mixture the composition of the components varies for any given sample taken.

Complete Step By Step Answer:
An alloy is a mixture of two or more metals, or a metal and a nonmetal, in which the composition of each element used is uniform throughout the volume. Brass(copper and zinc),bronze(copper and tin) and steel(iron and carbon) are a few examples of alloys. Since the composition of substances in the alloy remains uniform throughout any given sample, it can be considered as a homogeneous mixture. Too much carbon makes the steel brittle and unusable and less carbon makes the steel soft and ductile. Alloys are preferred over regular metal due to their lower reactivity and higher versatility, due to its homogeneity.
According to Nernst equation: $E=Eo-\dfrac{0.0591}{n}\times logQ$
So for the cell: $Pt,{{H}_{2}}|{{H}^{+}}||A{{g}^{+}}|Ag$
Thus, ${{E}_{cell}}={{E}_{O{{P}_{{{H}_{2}}/2{{H}^{+}}}}}}+{{E}_{R{{P}_{A{{g}^{+}}/Ag}}}}$ which is relative to hydrogen electrode.
$0.503=0+0.80+\dfrac{1}{0.059}log\left[ A{{g}^{+}} \right]$
Therefore, $[A{{g}^{+}}]=9.25\times {{10}^{-6}}M$, So the mass of silver ion in solution is
$A{{g}^{+}}=\dfrac{9.25\times 10-6\times 108\times 500g}{1000}=4.995\times {{10}^{-4}}g$
Similarly, $\therefore Pb=1.45-4.995\times {{10}^{-4}}g$, thus $$mass of $Pb$ metal in below alloy sample is given by:
$\%Pb=\left[ \dfrac{1.45-4.995\times {{10}^{-4}}}{1.45} \right]\times 100$
$\Rightarrow \%Pb=99.96\%$
Therefore, the correct answer is option C.

Note :
Remember that Alloys are made in such a way that the resulting alloy has the desirable properties of the components used. For this to happen, the right amount of components should be used to achieve a desirable constitution, else it will produce a defective batch of alloys which might even be useless. For example, steel is generally a mixture of iron and carbon, with carbon content in between $0.002$ and $2.14$ by weight.