Consider the strong electrolytes $Z_{m} X_{n}, U_{m} Y_{p}$ and $V_{m} X_{n}$. Limiting molar conductivity ( $\Lambda^{0}$ ) of $\mathrm{U}_{\mathrm{m}} \mathrm{Y}_{\mathrm{p}}$ and $\mathrm{V}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}}$ are 250 and $440 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$, respectively. The value of $(\mathrm{m}+\mathrm{n}+\mathrm{p})$ is

Given:

Ion	$\mathrm{Z}^{\mathrm{n}+}$	$\mathrm{U}^{\mathrm{p}+}$	$\mathrm{V}^{\mathrm{n}+}$	$\mathrm{X}^{\mathrm{m}-}$	$\mathrm{Y}^{\mathrm{m}-}$
$\lambda^{0}\left(\mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\right)$	$50.0$	$25.0$	$100.0$	$80.0$	$100.0$

$\lambda^{0}$ is the limiting molar conductivity of ions

The plot of molar conductivity ( $\Lambda$ ) of $\mathrm{Z}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}} v s\, \mathrm{c}^{1 / 2}$ is given below.

The reduction potential $\left(E^{0}\right.$, in $\left.\mathrm{V}\right)$ of $\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})$ is __________.

[Given: $E_{\left(\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{MnO}_{2}(\mathrm{~s})\right)}^{0}=1.68 \mathrm{~V} ; E_{\left(\mathrm{MnO}_{2}(\mathrm{~s}) / \mathrm{Mn}^{2+}(\mathrm{aq})\right)}^{0}=1.21 \mathrm{~V} ; E_{\left(\mathrm{Mn}^{2+}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})\right)}^{0}=-1.03 \mathrm{~V}$ ]

At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, for an aqueous solution of the acid the degree of dissociation is $$\alpha$$ and the molar conductivity is y $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y $$\times$$ 10² S cm² mol^$$-$$1.

The value of $$\alpha$$ is __________.

At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, for an aqueous solution of the acid the degree of dissociation is $$\alpha$$ and the molar conductivity is y $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y $$\times$$ 10² S cm² mol^$$-$$1.

The value of y is __________.