Question

Colligative properties (ΔTf , ΔTb) of sucrose with ethanol as a solvent (20%masse)?

Answer 1

Answer on Question #57652, Chemistry / Other

Colligative properties (ΔTf, ΔTb) of sucrose with ethanol as a solvent (20% masse)?

Answer:

First of all, the cryoscopic and embulioscopic constants for ethanol equal:

$K_{f} = 1.99\ (^{\circ}C\ kg)/mol$ and $K_{b} = 1.19\ (^{\circ}C\ kg)/mol$, respectively.

Then, the molality of solution is found using the following equation:

$M = v(\text{sucrose})/m_s$, where $v(\text{sucrose})$ – the number of moles of sucrose and $m_s$ – the mass of solvent in kg.

If we dissolve sucrose in $1\ \mathrm{kg}$ of ethanol, then the mass of sucrose is determined:

$W\% = m(\text{sucrose})/[m(\text{sucrose}) + 1000)] \times 100\%$

Since $W\% = 20\%$

$0.2 = m(\text{sucrose})/[m(\text{sucrose}) + 1000])$

$0.2\ m(\text{sucrose}) + 200 = m(\text{sucrose})$

$m(\text{sucrose}) = 200/0.8 = 250\ g$

The number of moles of sucrose equals:

$v(\text{sucrose}) = m(\text{sucrose})/M_r(\text{sucrose})$, where $M_r(\text{sucrose})$ – the molecular weight for $C_{12}H_{22}O_{11}$ which is of 342.3 g/mol.

Then, $v(\text{sucrose}) = 250\ g/342.3\ g\ mol^{-1} = 0.73035\ mol$

Finally, the molality of the solution is:

$M = 0.73035\ \mathrm{mol}/1\ \mathrm{kg} = 0.73035\ \mathrm{mol}/\mathrm{kg}$.

The freezing point depression and the boiling point elevation for the solution are determined according to the equations:

$\Delta T_{f} = K_{f} M = 1.99\ (^{\circ}C\ \mathrm{kg})/mol \times 0.73035\ \mathrm{mol}/\mathrm{kg} = 1.453\ ^{\circ}\mathrm{C}$

$\Delta T_{b} = K_{b} M = 1.19\ (^{\circ}C\ \mathrm{kg})/mol \times 0.73035\ \mathrm{mol}/\mathrm{kg} = 0.869\ ^{\circ}\mathrm{C}$

Hence, this solution is solidified at $T = T_f(\text{ethanol}) - 1.453 = -114.6\ ^{\circ}\mathrm{C} - 1.453\ ^{\circ}\mathrm{C} = -116.053\ ^{\circ}\mathrm{C}$

And its boiling point should be found at $T = T_b(\text{ethanol}) + 0.869 = 78.4\ ^{\circ}\mathrm{C} + 0.869\ ^{\circ}\mathrm{C} = 79.269\ ^{\circ}\mathrm{C}$.

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