How many moles of antifreeze (a molecular substance) must be added per liter of water to protect the cooling system of a motocar to -30 degrees F.

delta T = Kf*m

Convert -30F to degrees C.
Substitute into the formula and solve for m. Since molality = moles/kg solvent that will be moles/L IF we assume 1 L of water has a mass of 1 kg.

To determine the number of moles of antifreeze needed to protect the cooling system of a motocar to -30 degrees F, we can follow these steps:

Step 1: Determine the freezing point depression constant, Kf.
The freezing point depression constant, also known as the cryoscopic constant, is specific to each solvent. For water, the Kf value is approximately 1.86 °C/m.

Step 2: Calculate the change in temperature required to achieve the desired freezing point.
The freezing point depression can be calculated using the formula:
ΔT = Kf * i * m
where:
ΔT = change in temperature (in degrees Celsius)
Kf = freezing point depression constant of water (1.86 °C/m)
i = van 't Hoff factor (the number of particles the substance dissociates into in water; for antifreeze, typically i = 1)
m = molality of the solution (moles of solute per kg of solvent)

Converting -30 degrees Fahrenheit to Celsius:
-30 °F = -34.44 °C

To calculate ΔT, we use:
ΔT = -34.44 °C - 0 °C

Step 3: Calculate the molality of the antifreeze solution.
The molality (m) is defined as the number of moles of solute (antifreeze) per kilogram of solvent (water).

We have the following formula to calculate the molality:
m = (moles of solute) / (mass of solvent in kg)

To calculate the mass of water in kg, we need to know the density of water, which is approximately 1 g/cm^3 or 1000 kg/m^3.

For simplicity, let's assume we want to protect one liter of water. Therefore, the mass of water in kg is:
mass of water = 1 liter * 1000 g/liter / 1000 kg/g = 1 kg

Step 4: Calculate the moles of antifreeze needed.
Now that we have the values for Kf, ΔT, and m, we can rearrange the formula to solve for moles of solute (antifreeze):
moles of solute = ΔT / (Kf * i * m)

Substituting the values:
moles of solute = (-34.44 °C - 0 °C) / (1.86 °C/m * 1 * 1 kg)

Therefore, the number of moles of antifreeze required to protect the cooling system of a motocar to -30 degrees F would be the value obtained from this calculation.