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Using Raoult's law explain how the total vapour pressure over the solution is related to mole fraction of components in the following solutions.
(a) $\mathrm{CHCl}_3(l)$ and $\mathrm{CH}_2 \mathrm{Cl}_2(l)$
(b) $\quad \mathrm{NaCl}(s)$ and $\mathrm{H}_2 \mathrm{O}^2(l)$
(a) $\mathrm{CHCl}_3(l)$ and $\mathrm{CH}_2 \mathrm{Cl}_2(l)$
(b) $\quad \mathrm{NaCl}(s)$ and $\mathrm{H}_2 \mathrm{O}^2(l)$
Solution:
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Verified Answer
Raoult's law states that for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.
$$
p_1=p_1^{\circ} x_1
$$
(a) $\mathrm{CHCl}_3(l)$ and $\mathrm{CH}_2 \mathrm{Cl}_2$ (l) both are volatile components. A binary solution which has both components as volatile liquids, the total pressure will be given as
$$
\begin{aligned}
p &=p_1+p_2=x_1 p_1^{\circ}+x_2 p_2^{\circ} \\
&=x_1 p_1^{\circ}+\left(1-x_1\right) p_2^{\circ}=\left(p_1^{\circ}-p_2^{\circ}\right) x_1+p_2^{\circ}
\end{aligned}
$$
where, $p=$ total vapour pressure
$p_1=$ partial vapour pressure of component 1
$p_2=$ partial vapour pressure of component 2
(b) $\mathrm{NaCl}(s)$ and $\mathrm{H}_2 \mathrm{O}(l)$ both are non-volatile components. When a solution has non-volatile solute, the Raoult's law is applicable only to vaporisable component, therefore, total vapour pressure can be written as
$$
p=p_1=x_1 p_1^{\circ}
$$
$$
p_1=p_1^{\circ} x_1
$$
(a) $\mathrm{CHCl}_3(l)$ and $\mathrm{CH}_2 \mathrm{Cl}_2$ (l) both are volatile components. A binary solution which has both components as volatile liquids, the total pressure will be given as
$$
\begin{aligned}
p &=p_1+p_2=x_1 p_1^{\circ}+x_2 p_2^{\circ} \\
&=x_1 p_1^{\circ}+\left(1-x_1\right) p_2^{\circ}=\left(p_1^{\circ}-p_2^{\circ}\right) x_1+p_2^{\circ}
\end{aligned}
$$
where, $p=$ total vapour pressure
$p_1=$ partial vapour pressure of component 1
$p_2=$ partial vapour pressure of component 2
(b) $\mathrm{NaCl}(s)$ and $\mathrm{H}_2 \mathrm{O}(l)$ both are non-volatile components. When a solution has non-volatile solute, the Raoult's law is applicable only to vaporisable component, therefore, total vapour pressure can be written as
$$
p=p_1=x_1 p_1^{\circ}
$$
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