a solution is prepared by dissolving 0.47 g of a solute in 12.7 g of cyclohexane what is the freezing point change

mols solute = grams/molar mass. No molar mass; can't work the problem.

To determine the freezing point change, we need to use the equation:

ΔT = K_f * m

where ΔT is the freezing point depression, K_f is the cryoscopic constant, and m is the molality of the solution.

First, let's calculate the molality (m) of the solution:

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

To find the moles of solute, we need to use the molar mass of the solute. However, you haven't provided the identity of the solute, so we'll need to assume it is known to proceed with the calculation.

Let's say the molar mass (M) of the solute is 100 g/mol and the boiling point constant (K_f) for cyclohexane is 20.2 °C/m.

1. Calculate the moles of solute:
moles of solute = mass of solute / molar mass of solute
moles of solute = 0.47 g / 100 g/mol

2. Convert the mass of cyclohexane to kg:
mass of cyclohexane = 12.7 g / 1000 (to convert to kg)

3. Calculate the molality:
m = moles of solute / mass of cyclohexane (in kg)

Now that we have the molality (m), we can calculate the freezing point depression (ΔT):

ΔT = K_f * m

Plug in the values of K_f and m to get the freezing point depression (ΔT), which will be in degrees Celsius.