Question

Consider the strong electrolytes $Z_m{X}_n,U_m{Y}_p$ and $V_m{X}_n$. Limiting molar conductivity $\left({\Lambda }^0\right)$ of $U_m{Y}_p$ and $V_m{X}_n$ are $250$ and $440Sc{m}^{2}mo{l}^{-1}$, respectively. The value of $(m+n+p)$ is ______.
Given:

Ion	$Z^{n+}$	$U^{p+}$	$V^{n+}$	$X^{m-}$	$Y^{m-}$
${\lambda }^0(Sc{m}^{2}mo{l}^{-1})$	50.0	25.0	100.0	80.0	100.0

${\lambda }^0$ is the limiting molar conductivity of ions
The plot of molar conductivity (A) of $Z_m{X}_{n}vs{c}^{1/2}$ is given below.

Answer 1

Answer: 7

${\Lambda }^{\circ }\left(U_m{Y}_p\right)=m\times {\lambda }_{u^p}^0+p\times {\lambda }_{Y^{+-}}^0=250$
$25m+100p=250$
$m+4p=\mathrm{10....}$(1)
${\Lambda }^{\circ }\left(V_m{X}_n\right)=m\times {\lambda }_{v^{2+}}+n\times {\lambda }_{x^{m-}}^0=440$
$100m+80n=440$
$5m+4n=\mathrm{22....}$(2)

From the extrapolation of curve
${\Lambda }^{\circ }\left(Z_m{X}_n\right)=340$
$m\times {\lambda }_{z^{n+}}^{\circ }+n{\lambda }_{x^{m-}}^{\circ }=340$
$50m+80n=340$
$5m+8n=\mathrm{34.....}$(3)
(3) - (2) $\Rightarrow 4n=12\Rightarrow n=3$
Putting in (2) we get $m=2$
Putting in (1) we get $p=2$
$m+n+p=2+3+2=7$