Consider the strong electrolytes $\mathrm{Z}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}}$, $\mathrm{U}_{\mathrm{m}} \mathrm{Y}_{\mathrm{p}}$ and $\mathrm{V}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}}$. Limiting molar conductivity ( $\Lambda^{o}$ ) 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 $\mathrm{Z}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}}$ vs $\mathrm{c}^{1 / 2}$ is given below.

JEE Advanced · 2022 · 28 Aug 2022 · Paper 2 · Redox Reactions and Electrochemistry

Consider the strong electrolytes

Z_{m} X_{n}

U_{m} Y_{p}

and

V_{m} X_{n}

. Limiting molar conductivity (

Λ^{o}

) of

U_{m} Y_{p}

and

V_{m} X_{n}

are 250 and

440 S cm^{2} mol^{- 1}

, respectively. The value of (

m + n + p

) is ____.
Given:

Ion	$Z^{n +}$	$U^{p +}$	$V^{n +}$	$X^{m -}$	$Y^{m -}$
$λ^{0} (S cm^{2} mol^{- 1})$	50.0	25.0	100.0	80.0	100.0

λ^{0}

is the limiting molar conductivity of ions
The plot of molar conductivity (

Λ

) of

Z_{m} X_{n}

c^{1/2}

is given below.

Answer: 7

From the given limiting molar conductivities:

For

U_{m} Y_{p}

25 m + 100 p = 250 \Rightarrow m + 4 p = 10

... (1)

For

V_{m} X_{n}

100 m + 80 n = 440 \Rightarrow 5 m + 4 n = 22

... (2)

From the graph extrapolation,

Λ^{\circ} (Z_{m} X_{n}) = 340

50 m + 80 n = 340 \Rightarrow 5 m + 8 n = 34

... (3)

Subtracting (2) from (3):

4 n = 12 \Rightarrow n = 3

Substituting in (2):

5 m + 12 = 22 \Rightarrow m = 2

Substituting in (1):

2 + 4 p = 10 \Rightarrow p = 2

Therefore,

m + n + p = 2 + 3 + 2 = 7

JEE Advanced · 2022 · 28 Aug 2022 · Paper 2 · Integer answer