What mass of glycerin (C3H8O3), a nonelectrolyte, must be dissolved in 216.2 g water to give a solution with a freezing point of -1.62 °C?

delta T = Kf*molality.

Solve for molality.

molality = moles/kg solvent.
Solve for moles.

moles = grams/molar mass.
Solve for grams.

To find the mass of glycerin that must be dissolved in water, we can use the equation for freezing point depression:

ΔT = Kf * molality

where:
ΔT is the change in the freezing point (in Celsius)
Kf is the cryoscopic constant (constant for the solvent)
molality is the concentration of the solute in mol/kg

First, we need to find the molality of the solution. We can use the formula:

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

Let's assume x is the mass of glycerin (C3H8O3) to be dissolved.

To calculate the moles of glycerin, we need to use its molar mass:

Molar mass of glycerin (C3H8O3) = (3 * atomic mass of C) + (8 * atomic mass of H) + (3 * atomic mass of O)

Now, let's calculate:

Molar mass of C = atomic mass of C = 12.01 g/mol
Molar mass of H = atomic mass of H = 1.01 g/mol
Molar mass of O = atomic mass of O = 16.00 g/mol

Molar mass of glycerin = (3 * 12.01) + (8 * 1.01) + (3 * 16.00) g/mol

Next, we can calculate the moles of glycerin:

moles of glycerin = x / molar mass of glycerin

Now, let's calculate the mass of water in kg:

mass of water (in kg) = 216.2 g / 1000 (to convert grams to kilograms)

Next, we can calculate the molality:

molality = moles of glycerin / mass of water (in kg)

Now, we need to find the cryoscopic constant for water (Kf). The cryoscopic constant of water is 1.86 °C/molal.

Finally, we can use the equation for freezing point depression to find ΔT:

ΔT = Kf * molality

Since we know ΔT (-1.62 °C) and Kf (1.86 °C/molal), we can rearrange the equation to solve for molality:

molality = ΔT / Kf

Now we can substitute the known values and solve for x (mass of glycerin):

x = moles of glycerin * molar mass of glycerin

Plug in the values and calculate the mass of glycerin (x) required to give a freezing point of -1.62 °C.

To find the mass of glycerin that must be dissolved in water, we can use the formula:

ΔTf = Kf × m

Where:
- ΔTf is the change in freezing point temperature (in °C)
- Kf is the freezing point depression constant (in °C/m)
- m is the molality of the solution (in mol/kg)

First, we need to calculate m, the molality of the solution.

Molality (m) is defined as the number of moles of solute (glycerin) per kilogram of solvent (water).

The molar mass of glycerin (C3H8O3) can be calculated as follows:

Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol
Molar mass of O = 16.00 g/mol

Molar mass of glycerin (C3H8O3) = (3 × molar mass of C) + (8 × molar mass of H) + (3 × molar mass of O)
= (3 × 12.01 g/mol) + (8 × 1.01 g/mol) + (3 × 16.00 g/mol)
= 92.09 g/mol

Now, we can calculate m (molality) using the following formula:

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

Since we want to calculate the mass of glycerin needed to give a particular freezing point depression, let's assume we have x grams of glycerin.

moles of glycerin = (mass of glycerin) / (molar mass of glycerin) = x / 92.09

mass of water (solvent) = 216.2 g = 0.2162 kg

Using this information, we can calculate m:

m = (x / 92.09) / 0.2162

Next, we need to calculate ΔTf, which is the change in freezing point temperature.

ΔTf = -1.62 °C

Finally, we can rearrange the equation to solve for x, the mass of glycerin:

x = (m × ΔTf × 0.2162 × 92.09) / 1

Substituting the values:

x = ((m × -1.62 × 0.2162 × 92.09) / 1

Note: The freezing point depression constant (Kf) for water is typically provided in the problem, or you can look it up if it's not given.

Plug in the values and calculate x.