The standard reduction potentials at $$298 \mathrm{~K}$$ for the following half cells are given below:

$$\mathrm{NO}_{3}^{-}+4 \mathrm{H}^{+}+3 \mathrm{e}^{-} \rightarrow \mathrm{NO}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O} \quad \mathrm{E}^{\theta}=0.97 \mathrm{~V}$$

$$\mathrm{V}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{V} \quad\quad\quad \mathrm{E}^{\theta}=-1.19 \mathrm{~V}$$

$$\mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Fe} \quad\quad\quad \mathrm{E}^{\theta}=-0.04 \mathrm{~V}$$

$$\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Ag}(\mathrm{s}) \quad\quad\quad \mathrm{E}^{\theta}=0.80 \mathrm{~V}$$

$$\mathrm{Au}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Au}(\mathrm{s}) \quad\quad\quad \mathrm{E}^{\theta}=1.40 \mathrm{~V}$$

The number of metal(s) which will be oxidized by $$\mathrm{NO}_{3}^{-}$$ in aqueous solution is __________.

$$1 \times 10^{-5} ~\mathrm{M} ~\mathrm{AgNO}_{3}$$ is added to $$1 \mathrm{~L}$$ of saturated solution of $$\mathrm{AgBr}$$. The conductivity of this solution at $$298 \mathrm{~K}$$ is _____________ $$\times 10^{-8} \mathrm{~S} \mathrm{~m}^{-1}$$.

[Given : $$\mathrm{K}_{\mathrm{SP}}(\mathrm{AgBr})=4.9 \times 10^{-13}$$ at $$298 \mathrm{~K}$$

$$ \begin{aligned} & \lambda_{\mathrm{Ag}^{+}}^{0}=6 \times 10^{-3} \mathrm{~S} \mathrm{~m}^{2} \mathrm{~mol}^{-1} \\ & \lambda_{\mathrm{Br}^{-}}^{0}=8 \times 10^{-3} \mathrm{~S} \mathrm{~m}^{2} \mathrm{~mol}^{-1} \\ & \left.\lambda_{\mathrm{NO}_{3}^{-}}^{0}=7 \times 10^{-3} \mathrm{~S} \mathrm{~m}^{2} \mathrm{~mol}^{-1}\right] \end{aligned} $$

At what pH, given half cell $$\mathrm{MnO_{4}^{-}(0.1~M)~|~Mn^{2+}(0.001~M)}$$ will have electrode potential of 1.282 V? ___________ (Nearest Integer)

Given $$\mathrm{E_{MnO_4^ - |M{n^{2 + }}}^o}=1.54~\mathrm{V},\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059\mathrm{V}$$

Its molar conductivity is _________ $\times 10^{4}~ \Omega^{-1} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$. (Nearest integer)