Answer:
151 g/mol
Explanation:
When a nonvolatile substance is added to a solvent, the freezing point of the solvent is changed, which is called cryoscopy. When temperature change can be calculated by:
ΔT = Kf*W
Where Kf is the molal freezing point constant of the solvent and W is the molality of the solution.
For cyclohexane, Kf = 20.2 °C/molal, and the freezing point is 6.4 °C, so:
6.4 - 1.05 = 20.2 * W
20.2W = 5.35
W = 0.26485 molal
The molality is:
W = m1/m2*M1
Where m1 is the mass of the solute (in g), m2 is the mass of the solvent (in kg), and M1 is the molar mass of the solute. So:
0.26485 = 2.00/0.05M1
0.0132425M1 = 2.00
M1 = 151 g/mol
The molar mass of a substance in a solution of 2.00 g of para-dichlorobenzene in 50.0 g of cyclohexane freezes at 1.05°C is 151g/mol.
The temperature change can be calculated using the following formula:
ΔT = Kf × W
Where;
6.4 - 1.05 = 20.2 × W
20.2W = 5.35
W = 0.26485m
However; W = m1/m2 × M1
Where;
0.26485 = 2.00/0.05M1
0.0132425M1 = 2.00
M1 = 151 g/mol
Therefore, the molar mass of a substance in a solution of 2.00 g of para-dichlorobenzene in 50.0 g of cyclohexane freezes at 1.05°C is 151g/mol.
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