Mole fraction of the solute in a $1.00$ molal aqueous solution is

1.7700

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0.1770

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0.0177

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0.0344

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Solution

The correct option is C $0.0177$
Mole fraction of solute $(χ_{s o l u t e})$ $= \frac{n_{s o l u t e}}{n_{s o l u t e} + n_{s o l v e n t}}$

Molality $(m)$ $= \frac{χ_{s o l u t e}}{χ_{s o l v e n t}} \times \frac{1000}{M_{s o l v e n t}}$

$⟹$ $χ_{s o l u t e} = m \times χ_{s o l v e n t} \times \frac{M_{s o l v e n t}}{1000}$

putting values;
$χ_{s o l u t e} = 1 \times (1 - χ_{s o l u t e}) \times \frac{18}{1000}$

$⟹$ $χ_{s o l u t e} = \frac{18}{1000} - χ_{s o l u t e} \times \frac{18}{1000}$

$⟹$ $χ_{s o l u t e} = \frac{18}{1000} \times \frac{1000}{1018} = \frac{18}{1018} = 0.0177$

Hence the correct answer is option (c).

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