MHT CET · Chemistry · Solutions
If \(0.15 \mathrm{~m}\) aqueous solution of \(\mathrm{KCI}\) freezes at \(-0.51^{\circ} \mathrm{C}\), calculate van't Hoff factor of \(\mathrm{KCI}\) (cryoscopic constant of water is \(1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) )
- A \(1.45\)
- B \(1.26\)
- C \(1.82\)
- D \(3.00\)
Answer & Solution
Correct Answer
(C) \(1.82\)
Step-by-step Solution
Detailed explanation
\(\Delta \mathrm{T}_{\mathrm{f}}=\mathrm{T}_{\mathrm{f}}^0-\mathrm{T}_{\mathrm{f}}=0-\left(-0.51^{\circ} \mathrm{C}\right)=\) \(0.51{ }^{\circ} \mathrm{C}=0.51 \mathrm{~K} \)
\( \therefore \Delta \mathrm{T}_{\mathrm{f}}=\mathrm{iK}_{\mathrm{f}} \mathrm{m} \)
\( \therefore \mathrm{i}=\frac{\Delta \mathrm{T}}{\mathrm{K}_{\mathrm{f}} \mathrm{m}}=\frac{0.51 \mathrm{~K}}{1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 0.15 \mathrm{~mol} \mathrm{~kg}^{-1}}=1.82\)
\( \therefore \Delta \mathrm{T}_{\mathrm{f}}=\mathrm{iK}_{\mathrm{f}} \mathrm{m} \)
\( \therefore \mathrm{i}=\frac{\Delta \mathrm{T}}{\mathrm{K}_{\mathrm{f}} \mathrm{m}}=\frac{0.51 \mathrm{~K}}{1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 0.15 \mathrm{~mol} \mathrm{~kg}^{-1}}=1.82\)
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