What is the expected value of $\Delta T_f$ for $1.25 \mathrm{~m} \mathrm{CaCl}_2$ solution if 1.25 m sucrose…
What is the expected value of $\Delta T_f$ for $1.25 \mathrm{~m} \mathrm{CaCl}_2$ solution if 1.25 m sucrose solution has $\Delta \mathrm{T}_{\mathrm{f}}$ value $\mathrm{x} K$ ?
$x$ K
$\frac{x}{2} \mathrm{~K}$
$2 x \mathrm{K}$
$3 x$ K
Solution
For sucrose solution, $\left(\Delta T_f\right)_1=K_f m_1 \ldots$. (i)
For $\mathrm{CaCl}_2$ solution, $\left(\Delta \mathrm{T}_{\mathrm{f}}\right)_2=\mathrm{iK}_{\mathrm{f}} \mathrm{m}_2 \quad \ldots$ (ii),
From equation (i) and (ii),
$\begin{aligned}
\frac{\left(\Delta T_f\right)_1}{\left(\Delta T_f\right)_2} & =\frac{m_1}{i_2} \\
\therefore \quad\left(\Delta T_f\right)_2 & =\frac{\left(\Delta T_f\right)_1 \times i \times m_2}{m_1} \\
& =\frac{x K \times 3 \times 1.25 \mathrm{~m}}{1.25 \mathrm{~m}} \quad\left(\because \text { i for } \mathrm{CaCl}_2=3\right) \\
& =3 x \mathrm{K}
\end{aligned}$