Quinine is a natural product extracted from the bark of the cinchona tree, which is native to South America. Quinine is used as an antimalarial agent. When 2.50 g of quinine is dissolved in 25.0 g of cyclohexane, the freezing point of the solution is lowered by 6.43 °C. The freezing point and Kf constant for cyclohexane can be found here. Calculate the molar mass of quinine.

Question

Quinine is a natural product extracted from the bark of the cinchona tree, which is native to South America. Quinine is used as an antimalarial agent. When 2.50 g of quinine is dissolved in 25.0 g of cyclohexane, the freezing point of the solution is lowered by 6.43 °C. The freezing point and Kf constant for cyclohexane can be found here. Calculate the molar mass of quinine.

Answer 1

delta T = Kf*m

Substitute and solve for m = molality

m = mols/kg solvent
Substitute and solve for mols.

mols = grams/molar mass. You know grams and mols, solve for molar mass.

Answer 2

To calculate the molar mass of quinine, we need to use the concept of colligative properties, specifically, the freezing point depression. The formula to calculate the molar mass using freezing point depression is:

ΔT = Kf * i * m

Where:
ΔT is the change in freezing point (in Celsius),
Kf is the cryoscopic constant (in this case, for cyclohexane),
i is the vant Hoff factor (the number of particles formed in a solution, which depends on the dissociation behavior),
m is the molality of the solute (moles of solute per kilogram of solvent).

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

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

Given:
Mass of quinine (solute) = 2.50 g
Mass of cyclohexane (solvent) = 25.0 g
Molar mass of cyclohexane = 84.16 g/mol (found in the reference)

We can calculate the molality (m):

m = (2.50 g / molar mass of quinine) / (25.0 g / 1000)

Now, let's calculate the change in freezing point (ΔT):

ΔT = -6.43 °C (given)

Lastly, we can substitute the values into the formula to solve for the molar mass of quinine:

-6.43 °C = Kf * i * [(2.50 g / molar mass of quinine) / (25.0 g / 1000)]

Now, we need to find the value of Kf for cyclohexane. You mentioned that the freezing point and Kf constant for cyclohexane can be found elsewhere. So let's assume the Kf for cyclohexane is 20.2 °C/m.

Then we can rearrange the formula to solve for the molar mass of quinine:

molar mass of quinine = (2.50 g / [(ΔT / (Kf * i)) * (25.0 g / 1000)])

Substituting the given values:

molar mass of quinine = (2.50 g / [(-6.43 °C / (20.2 °C/m * i)) * (25.0 g / 1000)])