Calculate the Molar Mass of Compound X Dissolved in Cyclohexane

How to calculate the molar mass of compound X dissolved in cyclohexane?

When 718 mg of a certain molecular compound X are dissolved in 45.0 g of cyclohexane C₆H₁₂, the freezing point of the solution is measured to be 6.3 °C. Calculate the molar mass of X. Choose from the following options:

a) 118 g/mol

b) 150 g/mol

c) 200 g/mol

d) 250 g/mol

Answer:

To determine the molar mass, one must calculate the change in the freezing point, then the molality of the solution. With these, the molar mass is found by dividing the mass of the compound by the number of moles. However, the result does not match the given options, indicating potential errors in the provided values or the Kf constant.

Explanation:

To calculate the molar mass of compound X dissolved in cyclohexane, we use the formula for freezing point depression. The formula is ΔTf = Kf * m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent (which for cyclohexane is 20.0 °C/m), and m is the molality of the solution.

First, let's calculate the depression of the freezing point (ΔTf). The freezing point of pure cyclohexane is 6.5 °C, so ΔTf = 6.5 °C - 6.3 °C = 0.2 °C.

Now let's calculate the molality (m) of the solution: m = moles of solute / kg of solvent.

We can rearrange the freezing point depression formula to solve for moles of solute: moles of solute = ΔTf / (Kf * kg of solvent).

Substituting the values in, we get moles of solute = 0.2 °C / (20.0 °C/m * 0.045 kg) = 0.222 moles.

To get the molar mass (M) of compound X, we divide the mass in grams by the moles: M = mass of solute / moles of solute.

So the molar mass of X = 718 mg (or 0.718 g) / 0.222 moles ≈ 3.23 g/mol. Since this result is not an option, there may have been a misunderstanding in the values provided or a typo. Let's check if we have the correct Kf value and recalculate as needed.

None of the given options are correct.