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Section: Chemistry

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Question : 13 of 29

Marks: +1, -0

A solution containing 7.5 g of urea (molar mass

=60\ \mathrm{g}\ \mathrm{mol}^{-1}

) in 1 kg of water freezes at the same temperature as another solution containing 15 g of solute X , in the same amount of water. The molar mass of

X(\ \mathrm{g}\ \mathrm{mol}^{-1})

[AP EAPCET 21 May 2025 S1]

$60$
$180$
$120$
$240$

Solution:

Moles of urea

\frac{\;\text{ Mass }\;}{\;\text{ Molar mass }\;}\;=\;\frac{7.5}{60}=0.125\ \text{mol}

\;\text{ Molality of urea }\;\;=\;\frac{\;\text{ Moles of urea }\;}{\;\text{ Mass of water in }\; \text{kg}}

\;=\;\frac{0.125}{1}=0.125\ \text{mol/kg}

Since both solution freezes at the same temperature, their molalities are equal.

\;\text{ Molality of }\; x\;=\;\text{ Molality of urea }\; \\\;=0.125\ \text{mol/kg}

Moles of

x=

Molality

\times

mass of water

\;=0.125 \times 1

\;\Rightarrow\;\; 0.125\ \text{mol}

\;\text{ Molar mass of }\; x\;=\;\frac{\;\text{ Mass }\;}{\;\text{ Moles }\;}=\;\frac{15}{0.125} \\\;=120\ \text{g/mol}

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