MHT CET · Chemistry · Solutions
If \(K_b\) denote molal elevation constant of water, then boiling point of an aqueous solution containing \(36 \mathrm{~g}\) glucose \((\) molar mass \(=180)\) per \(\mathrm{dm}^3\) is:
- A \(\left(100+\mathrm{K}_{\mathrm{b}}\right)^{\circ} \mathrm{C}\)
- B \(\left(100+2 \mathrm{~K}_{\mathrm{b}}\right)^{\circ} \mathrm{C}\)
- C \(\left(100+\frac{\mathrm{K}_{\mathrm{b}}}{10}\right){ }^{\circ} \mathrm{C}\)
- D \(\left(100+\frac{2 \mathrm{~K}_{\mathrm{b}}}{10}\right){ }^{\circ} \mathrm{C}\)
Answer & Solution
Correct Answer
(D) \(\left(100+\frac{2 \mathrm{~K}_{\mathrm{b}}}{10}\right){ }^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
The aqueous solution contains \(36 \mathrm{~g}\) glucose per \(\mathrm{dm}^3\), so mass of solute \(\mathrm{W}_2\) is \(36 \mathrm{~g}\).
Assuming that the density of solution is \(1 \mathrm{~g} / \mathrm{dm}^3\), the mass of solvent (water) is \(1000 \mathrm{~g}\).
\(\Delta \mathrm{T}_{\mathrm{b}}=\frac{1000 \mathrm{~K}_{\mathrm{b}} \mathrm{W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \)
\( \Delta \mathrm{T}_{\mathrm{b}} =\frac{1000 \mathrm{~g} \mathrm{~kg}^{-1} \times \mathrm{K}_{\mathrm{b}} \times 36 \mathrm{~g}}{180 \mathrm{~g} \times 1000 \mathrm{~g}} \)
\( \Delta \mathrm{T}_{\mathrm{b}} =\frac{2 \mathrm{~K}_{\mathrm{b}}}{10} \)
\( \Delta \mathrm{T}_{\mathrm{b}} =\mathrm{T}_{\mathrm{b}}-\mathrm{T}_{\mathrm{b}}^0 \)
\( \mathrm{~T}_{\mathrm{b}}=\mathrm{T}_{\mathrm{b}}^0+\Delta \mathrm{T}_{\mathrm{b}} \)
\( \therefore \mathrm{T}_{\mathrm{b}}=\left(100+\frac{2 \mathrm{~K}_{\mathrm{b}}}{10}\right)^{\circ} \mathrm{C} \)
Assuming that the density of solution is \(1 \mathrm{~g} / \mathrm{dm}^3\), the mass of solvent (water) is \(1000 \mathrm{~g}\).
\(\Delta \mathrm{T}_{\mathrm{b}}=\frac{1000 \mathrm{~K}_{\mathrm{b}} \mathrm{W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \)
\( \Delta \mathrm{T}_{\mathrm{b}} =\frac{1000 \mathrm{~g} \mathrm{~kg}^{-1} \times \mathrm{K}_{\mathrm{b}} \times 36 \mathrm{~g}}{180 \mathrm{~g} \times 1000 \mathrm{~g}} \)
\( \Delta \mathrm{T}_{\mathrm{b}} =\frac{2 \mathrm{~K}_{\mathrm{b}}}{10} \)
\( \Delta \mathrm{T}_{\mathrm{b}} =\mathrm{T}_{\mathrm{b}}-\mathrm{T}_{\mathrm{b}}^0 \)
\( \mathrm{~T}_{\mathrm{b}}=\mathrm{T}_{\mathrm{b}}^0+\Delta \mathrm{T}_{\mathrm{b}} \)
\( \therefore \mathrm{T}_{\mathrm{b}}=\left(100+\frac{2 \mathrm{~K}_{\mathrm{b}}}{10}\right)^{\circ} \mathrm{C} \)
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