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A 5% solution of cane sugar (mol. wt. = 342) is isotonic with 1% solution of a substance X. The molecular weight of , X is

(a) 68.4 (b) 171.2 (c) 34.2 (d) 136.8

1 Answer

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by (90.1k points)
Correct option (a) \(68.4\)
Explanation:
$$
\begin{array}{ll}
\text { 'Cane Sugar' } & ' X \text { ' } \\
W_{1}=5 \mathrm{~g} & W_{2}=1 \mathrm{~g} \\
V_{1}=100 \mathrm{~mL} & V_{2}=100 \mathrm{~mL} \\
=0.1 \mathrm{~L} & =0.1 \mathrm{~L} \\
M_{1}=342 & M_{2}=?
\end{array}
$$
For isotonic solutions, \(C_{1}=C_{2}\)
$$
\begin{aligned}
&\frac{W_{1}}{M_{1} V_{1}}=\frac{W_{2}}{M_{2} V_{2}} \Rightarrow \frac{5}{342 \times 0.1}=\frac{1}{M_{2} \times 0.1} \\
&\Rightarrow M_{2}=\frac{342}{5}=68.4
\end{aligned}
$$
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