MHT CET · Chemistry · Solutions
Calculate the depression in freezing point of solution when \(4 \mathrm{~g}\) nonvolatile solute of molar mass \(126 \mathrm{~g} \mathrm{~mol}^{-1}\) dissolved in \(80 \mathrm{~mL}\) water. \(\left[\right.\) Cryoscopic constant of water \(\left.=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]\)
- A \(0.55 \mathrm{~K}\)
- B \(0.74 \mathrm{~K}\)
- C \(0.86 \mathrm{~K}\)
- D \(0.96 \mathrm{~K}\)
Answer & Solution
Correct Answer
(B) \(0.74 \mathrm{~K}\)
Step-by-step Solution
Detailed explanation
\(80 \mathrm{~mL} \text { water }=80 \mathrm{~g} \text { water (Density of}\) \(\text{water }= 1 \mathrm{~g} / \mathrm{mL} \text { ) } \)
\( \Delta \mathrm{T}_{\mathrm{f}}=\frac{1000 \mathrm{~K}_{\mathrm{f}} \mathrm{W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \)
\( =\frac{1000 \mathrm{~g} \mathrm{~kg}^{-1} \times 1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 4 \mathrm{~g}}{126 \mathrm{~g} \mathrm{~mol}^{-1} \times 80 \mathrm{~g}} \)
\( =0.74 \mathrm{~K}\)
\( \Delta \mathrm{T}_{\mathrm{f}}=\frac{1000 \mathrm{~K}_{\mathrm{f}} \mathrm{W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \)
\( =\frac{1000 \mathrm{~g} \mathrm{~kg}^{-1} \times 1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 4 \mathrm{~g}}{126 \mathrm{~g} \mathrm{~mol}^{-1} \times 80 \mathrm{~g}} \)
\( =0.74 \mathrm{~K}\)
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