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Which of the following aqueous solution has the highest freezing point?
- A \( 0.1 M \) Sucrose
- B \( 0.01 \mathrm{MNaCl} \)
- C \( 0.1 \mathrm{MN} \mathrm{ACl} \)
- D \( 0.01 \mathrm{MN} a_{2} \mathrm{SO}_{4} \)
Answer & Solution
Correct Answer
(B) \( 0.01 \mathrm{MNaCl} \)
Step-by-step Solution
Detailed explanation
Depression in freezing point, \( \Delta T_{f}=i K_{f} m \)
\(\Delta T_{f} \) will depends on van't Hoff factor.
\(\begin{array}{|l|l|l|l|}
\hline \text{Compounds} & \text{Concentration} & \text{van't Hoff factor (i)} & \boldsymbol{\Delta} T_boldsymbol{f} \\
\hline \text{Sucrose} & 0.1 \mathrm{M} & 1 & 0.1 K_{f} \\
\hline \mathrm{NaCl} & 0.01 \mathrm{M} & 2 & 0.02 K_{f} \\
\hline \mathrm{NaCl} & 0.1 \mathrm{M} & 2 & 0.2 K_{f} \\
\hline \mathrm{Na}_{2} \mathrm{SO}_{4} & 0.01 \mathrm{M} & 3 & 0.03 K_{f} \\
\hline
\end{array}\)
Therefore, depression in freezing point follow the order:
\(0.1 \mathrm{MNaCl}_{i=2}>0.1 \mathrm{M} \text { Glucose }>0.01 \mathrm{MN}_{i=1} \underset{i=3}{\mathrm{~N}} \mathbf{S O}_{4}>0.01 \mathrm{MNaCl}_{i=2}\)
Depression in freezing point is minimum in case of \( 0.01 \mathrm{M} \mathrm{NaCl} \) solution, hence, it will have maximum freezing point.
\(\Delta T_{f} \) will depends on van't Hoff factor.
\(\begin{array}{|l|l|l|l|}
\hline \text{Compounds} & \text{Concentration} & \text{van't Hoff factor (i)} & \boldsymbol{\Delta} T_boldsymbol{f} \\
\hline \text{Sucrose} & 0.1 \mathrm{M} & 1 & 0.1 K_{f} \\
\hline \mathrm{NaCl} & 0.01 \mathrm{M} & 2 & 0.02 K_{f} \\
\hline \mathrm{NaCl} & 0.1 \mathrm{M} & 2 & 0.2 K_{f} \\
\hline \mathrm{Na}_{2} \mathrm{SO}_{4} & 0.01 \mathrm{M} & 3 & 0.03 K_{f} \\
\hline
\end{array}\)
Therefore, depression in freezing point follow the order:
\(0.1 \mathrm{MNaCl}_{i=2}>0.1 \mathrm{M} \text { Glucose }>0.01 \mathrm{MN}_{i=1} \underset{i=3}{\mathrm{~N}} \mathbf{S O}_{4}>0.01 \mathrm{MNaCl}_{i=2}\)
Depression in freezing point is minimum in case of \( 0.01 \mathrm{M} \mathrm{NaCl} \) solution, hence, it will have maximum freezing point.
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