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7.29 g of naphthalene, [tex]C _{10} H _8[/tex] (molar mass [tex]= 128.16 \, g/mol[/tex]), has been dissolved in 166 g of benzene, [tex]C _6 H _6[/tex] (molar mass [tex]= 78.11 \, g/mol[/tex]). What is the freezing point of this solution? Write your answer to two decimal places.

Some data you may need:
- [tex]K _{ f }[/tex] for [tex]C _6 H _6: 5.07^{\circ} C/m[/tex]
- Freezing point of [tex]C _6 H _6: 5.49^{\circ} C[/tex]



Answer :

GinnyAnswer
To determine the freezing point of the solution, we need to follow these steps:

1. Calculate the moles of naphthalene ([tex]$C_{10}H_8$[/tex]):
The molar mass of naphthalene is given as 128.16 g/mol.

[tex]\[ \text{Moles of naphthalene} = \frac{\text{Mass of naphthalene}}{\text{Molar mass of naphthalene}} = \frac{7.29 \text{ g}}{128.16 \text{ g/mol}} = 0.05688 \text{ moles} \][/tex]

2. Convert the mass of benzene ([tex]$C_6H_6$[/tex]) to kilograms:
The mass of benzene is given as 166 g.

[tex]\[ \text{Mass of benzene in kg} = \frac{166 \text{ g}}{1000} = 0.166 \text{ kg} \][/tex]

3. Calculate the molality of the solution:
Molality is defined as the number of moles of solute per kilogram of solvent.

[tex]\[ \text{Molality} = \frac{\text{Moles of naphthalene}}{\text{Mass of benzene in kg}} = \frac{0.05688 \text{ moles}}{0.166 \text{ kg}} = 0.34266 \text{ mol/kg} \][/tex]

4. Calculate the freezing point depression ([tex]$\Delta T_f$[/tex]):
The freezing point depression ([tex]$\Delta T_f$[/tex]) can be calculated using the formula:

[tex]\[ \Delta T_f = K_f \times \text{molality} \][/tex]

where [tex]\(K_f\)[/tex] for benzene is 5.07 °C/m.

[tex]\[ \Delta T_f = 5.07 \text{ °C/m} \times 0.34266 \text{ mol/kg} = 1.73730 \text{ °C} \][/tex]

5. Calculate the new freezing point of the solution:
The freezing point of pure benzene is given as 5.49 °C.

[tex]\[ \text{Freezing point of the solution} = \text{Freezing point of pure benzene} - \Delta T_f = 5.49 \text{ °C} - 1.73730 \text{ °C} = 3.75 \text{ °C} \][/tex]

Therefore, the freezing point of the solution, rounded to two decimal places, is:

[tex]\[ \boxed{3.75 \text{ °C}} \][/tex]

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