Question

Guinine 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 2.04 g of quinine is dissolved in 25.0 g of cyclohesinc, the freezing point of the solution is lowered by 5.23 ∘ C. Look up the freezing point and K constant for cyclohexane in the oiligative Constants table. Calculate the molar mass of quinine. molar mass:

Answer 1

To calculate the molar mass of quinine, the freezing point depression formula is used with the given data and the cryoscopic constant for cyclohexane. After finding the molality, the moles of quinine are determined, allowing us to solve for its molar mass, which is found to be 312.01 g/mol.

Step-by-step explanation:

To calculate the molar mass of quinine, we use the colligative property of freezing point depression. The formula for freezing point depression is ΔTf = i * Kf * m, where ΔTf is the change in freezing point, Kf is the cryoscopic constant, and m is the molality of the solution. As per colligative properties, i (van't Hoff factor) is assumed to be 1 for non-electrolytes such as quinine.

We are given that 2.04 g of quinine is dissolved in 25.0 g of cyclohexane and the freezing point of the solution is lowered by 5.23°C. Using cyclohexane properties (Kf = 20.0 K kg/mol and freezing point = 6.5°C), the molality (m) of the solution can be calculated.

First, convert the mass of cyclohexane to kilograms: 25.0 g = 0.025 kg.

Then, use the freezing point depression equation: ΔTf = Kf * m
5.23°C = 20.0 K kg/mol * m
m = 5.23 K / 20.0 K kg/mol
m = 0.2615 mol/kg

Next, calculate the moles of quinine: moles = molality * solvent mass in kg
moles = 0.2615 mol/kg * 0.025 kg
moles = 0.0065375 mol

Finally, calculate the molar mass of quinine: molar mass = mass of solute / moles of solute
molar mass = 2.04 g / 0.0065375 mol
molar mass = 312.01 g/mol

Therefore, the molar mass of quinine is 312.01 g/mol.

Answer 2

To calculate the molar mass of quinine, you can use the freezing point depression equation and the freezing point constant for cyclohexane. By plugging in the given values and rearranging the equation, you can solve for the molar mass of quinine.

Step-by-step explanation:

The molar mass of quinine can be calculated by using the freezing point depression equation. The equation is ΔTf = Kf × m, where ΔTf is the freezing point depression, Kf is the freezing point constant for the solvent, and m is the molality of the solution.

In this case, the freezing point depression is 5.23 °C, and the molality can be calculated by dividing the moles of quinine by the mass of the solvent:

molality (m) = (2.04 g quinine / molar mass of quinine) / 0.025 kg cyclohexane

Using the freezing point constant for cyclohexane from the colligative constants table and the known freezing point depression, you can solve for the molality and then rearrange the equation to solve for the molar mass of quinine.