$$C_6H_6$$ freezes at 5.5°C. The temperature at which a solution of 10 g of $$C_4H_{10}$$ in 200 g of $$C_6H_6$$ freeze is ______ °C. (nearest integer value), (The molal freezing point depression constant of $$C_6H_6$$ is 5.12°C/m.)

We use the freezing point depression formula: $$\Delta T_f = K_f \times m$$, where $$m$$ is the molality of the solution.

The molar mass of $$C_4H_{10}$$ (butane) is $$4(12) + 10(1) = 58$$ g/mol.

Moles of $$C_4H_{10} = \frac{10}{58} = 0.1724$$ mol.

Mass of solvent ($$C_6H_6$$) = 200 g = 0.2 kg.

Molality: $$m = \frac{0.1724}{0.2} = 0.862$$ mol/kg.

Freezing point depression: $$\Delta T_f = K_f \times m = 5.12 \times 0.862 = 4.41$$ °C.

The freezing point of the solution = $$5.5 - 4.41 = 1.09$$ °C.

Rounding to the nearest integer, the freezing point is $$\textbf{1}$$ °C.