At 298 K , the molar conductivity of $x \%(\mathrm{w} / \mathrm{w}) \mathrm{MX}$ solution (aqueous) is $123.5 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$. The conductance of same solution is $1.9 \times 10^{-3} \mathrm{~S}$. The value of $x$ is $\_\_\_\_$ $\times 10^{-2}$.
(Given: cell constant $=1.3 \mathrm{~cm}^{-1}$; molar mass of MX is $75 \mathrm{~g} \mathrm{~mol}^{-1}$, density of aqueous solution of MX at 298 K is $1.0 \mathrm{~g} \mathrm{~mL}^{-1}$ )
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Solution
Let molarity of MX solution $=\mathrm{y} \mathrm{M}$
$$
\begin{aligned}
& \Rightarrow \Lambda_{\mathrm{m}}=\mathrm{c}(\ell / \mathrm{A}) \times \frac{1000}{\mathrm{y}} \\
& \Rightarrow 123.5=1.9 \times 10^{-3} \times 1.3 \times \frac{1000}{\mathrm{y}} \\
& \Rightarrow \mathrm{y}=0.02 \mathrm{M}
\end{aligned}
$$
Let molar mass of $\mathrm{MX}=\mathrm{Mgmol}^{-1} 0.02 \mathrm{~mol} \mathrm{MX}$ is dissolve in 1 L solution $(0.02 \times 75) \mathrm{gm} \mathrm{MX}$ is dissolved in 1000 g solution
$$
\begin{aligned}
& \% \mathrm{w} / \mathrm{w}=\mathrm{x} \%=\frac{0.02 \times 75}{1000} \times 100 \\
& =0.15 \% \\
& \text { Ans }=15
\end{aligned}
$$
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