Given,  ${\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{H}}_2{\mathrm{SO}}_4\right)=\mathrm{x}{\mathrm{Scm}}^2{\mathrm{mole}}^{-1};$

$$\begin{gathered} {\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{K}}_2{\mathrm{SO}}_4\right)=\mathrm{y}{\mathrm{Scm}}^2{\mathrm{mole}}^{-1}; \\ {\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{CH}}_3\mathrm{COOK}\right)=\mathrm{z}{\mathrm{Scm}}^2{\mathrm{mole}}^{-1} \end{gathered}$$

${\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{CH}}_3\mathrm{COOH}\right)\text{will be \_\_\_\_\_\_\_\_ }{\mathrm{Scm}}^2{\mathrm{mole}}^{-1}$

 

$$\begin{gathered} {\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{H}}_2{\mathrm{SO}}_4\right)=2{\mathrm{\Lambda }}_{{\mathrm{H}}^{+}}^{\mathrm{m}}+{\mathrm{\Lambda }}_{{\mathrm{SO}}_4^{-2}}^{\mathrm{m}}............ \left(1\right) \\ {\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{K}}_2{\mathrm{SO}}_4\right)=2{\mathrm{\Lambda }}_{{\mathrm{K}}^{+}}^{\mathrm{m}}+{\mathrm{\Lambda }}_{{\mathrm{SO}}_4^{-2}}^{\mathrm{m}}..............\left(2\right) \\ {\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{CH}}_3\mathrm{COOK}\right)={\mathrm{\Lambda }}_{{\mathrm{CH}}_3{\mathrm{COO}}^{-}}^{\mathrm{m}}+{\mathrm{\Lambda }}_{{\mathrm{K}}^{+}}^{\mathrm{m}}.....\left(3\right) \end{gathered}$$

$$\begin{gathered} \frac{\mathrm{Eq}\left(1\right)}{2}+\mathrm{Eq}\left(3\right)-\frac{\mathrm{Eq}\left(2\right)}{2} \\ {\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{CH}}_3\mathrm{COOH}\right)=\frac{2{\mathrm{\Lambda }}_{{\mathrm{H}}^{+}}^{\mathrm{m}}}{2}+\frac{{\mathrm{\Lambda }}_{{\mathrm{SO}}_4^{-2}}^{\mathrm{m}}}{2}+{\mathrm{\Lambda }}_{{\mathrm{CH}}_3{\mathrm{COO}}_{ }^{-}}^{\mathrm{m}}+{\mathrm{\Lambda }}_{{\mathrm{K}}^{+}}^{\mathrm{m}}-\frac{2{\mathrm{\Lambda }}_{{\mathrm{K}}_{ }^{+}}^{\mathrm{m}}}{2}-\frac{{\mathrm{\Lambda }}_{{\mathrm{SO}}_4^{-2}}^{\mathrm{m}}}{2} \\ ={\mathrm{\Lambda }}_{{\mathrm{H}}^{+}}^{\mathrm{m}}+{\mathrm{\Lambda }}_{{\mathrm{CH}}_3{\mathrm{COO}}^{-}}^{\mathrm{m}} \\ \therefore {\mathrm{\Lambda }}_{\mathrm{m}}^{\mathrm{o}}{}_{\left({\mathrm{CH}}_3\mathrm{COOH}\right)}=\frac{\mathrm{x}}{2}+\mathrm{z}-\frac{\mathrm{y}}{2} \\ =\frac{\mathrm{x}-\mathrm{y}}{2}+\mathrm{z} \end{gathered}$$