To determine the molecular formula of white phosphorus in benzene, we can use the concept of freezing point depression.

The freezing point depression is a colligative property that depends on the concentration of the solute particles in a solution. It can be calculated using the formula:

ΔTf = Kf * m

ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent (benzene in this case), and m is the molality of the solute.

In this case, we are given that the solution froze at 4.89 degrees Celsius, and the freezing point constant for benzene is 5.12. We need to find the molality (m) of the solute.

First, we need to calculate the moles of white phosphorus in the solution. We can use the molar mass of white phosphorus (P4 = 123.895 g/mol) to convert the given mass of white phosphorus (0.775 g) to moles:

moles of white phosphorus = 0.775 g / 123.895 g/mol ≈ 0.00625 mol

Next, we need to calculate the molality of the solute. The molality is defined as the moles of solute per kilogram of solvent. We are given that the mass of benzene is 50 g, so we need to convert it to kilograms:

mass of benzene = 50 g / 1000 = 0.05 kg

molality (m) = moles of solute / mass of solvent (in kg)

molality = 0.00625 mol / 0.05 kg = 0.125 mol/kg

Now, we can use the freezing point depression formula to calculate the change in freezing point:

ΔTf = Kf * m

ΔTf = 5.12 * 0.125 = 0.64 degrees Celsius

Finally, we can determine the freezing point of the pure solvent by subtracting the change in freezing point from the observed freezing point:

Freezing point of pure benzene = 4.89 - 0.64 = 4.25 degrees Celsius

To find the molecular formula, we need to compare the change in freezing point to the expected change in freezing point for the solute. The expected change in freezing point can be calculated using the formula:

ΔTf = Kf * i * m

Where i is the van't Hoff factor, which represents the number of particles the solute dissociates into in the solvent. For white phosphorus, the molecular formula is P4, so it does not dissociate in benzene and i = 1.

Since the observed change in freezing point (0.64 degrees Celsius) matches the expected change in freezing point (0.64 degrees Celsius), the molecular formula of white phosphorus in benzene is P4.