Mass of Urea $\left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right)$ required to be dissolved in $1000 \mathrm{~g}$ of water in order to reduce the vapour pressure of water by $25 \%$ is _________ g. (Nearest integer)
Given: Molar mass of N, C, O and H are $14,12,16$ and $1 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively
Answer (integer)
1111
Solution
<p>Given:</p>
<ul>
<li>Vapor pressure reduction: $25\%$ ($0.75$ times the vapor pressure of pure water)</li><br/>
<li>Molar mass of water ($\text{H}_2\text{O}$): $18 \, \text{g/mol}$</li><br/>
<li>Mass of solvent (water): $1000 \, \text{g}$</li>
</ul>
<p>Using Raoult's law:<br/><br/>
$$\frac{P^0 - P_s}{P_s} = \frac{n_{\text{solute}}}{n_{\text{solvent}}} = \frac{\frac{x}{M_{\text{urea}}}}{\frac{1000}{M_{\text{water}}}} = \frac{P^0 - 0.75P^0}{0.75P^0}$$</p>
<p>Solving for (x):<br/><br/>
$\frac{x}{60} = \frac{10000}{9}$
$x = 1111.11111 \approx 1111 \, \text{g}$</p>
<p>So, the mass of urea required to be dissolved in $1000 \, \text{g}$ of water is $1111 \, \text{g}$.</p>
About this question
Subject: Chemistry · Chapter: States of Matter · Topic: Gas Laws
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