Copper in an alloy is estimated by dissolving in conc. nitric acid. In this process,copper is converted to cupric nitrate with the evolution of nitric oxide $(NO)$. The mixture when treated with potassium iodide forms cupric iodide,which is unstable and decomposes to cuprous iodide and iodine. The amount of copper in the alloy is estimated by titrating the liberated iodine with sodium thiosulphate. The reactions are:
$a \,Cu + b \,HNO_3 \rightarrow c \,Cu(NO_3)_2 + d \,NO + e \,H_2O$
$f \,CuI_2 \rightarrow g \,Cu_2I_2 + h \,I_2$
$i \,Na_2S_2O_3 + j \,I_2 \rightarrow k \,Na_2S_4O_6 + l \,NaI$
(Fill in the blanks)
$(a)$ The coefficients are: $a=\ldots, b=\ldots, c=\ldots, d=\ldots$ and $e=\ldots$.
$(b)$ The coefficients are: $f=\ldots, g=\ldots$ and $h=\ldots$.
$(c)$ The coefficients are: $i=\ldots, j=\ldots, k=\ldots$ and $l=\ldots$.
$(d)$ If $2.54 \,g$ of $I_2$ is evolved from a $2.0 \,g$ sample of the alloy,what is the percentage of copper in the alloy? (Atomic weights of iodine and copper are $127$ and $63.5$,respectively).