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 3.28 g of quinine is dissolved in 25.0 g of cyclohexane, the freezing point of the solution is lowered by 8.43 °C. The freezing point and Kf constant for cyclohexane can be found here.
Calculate the molar mass of quinine.
delta T = Kf*m
Solve for m.
m = mols quinine/kg solvent
Solve for mol quinine
mol quinine = g quinine/molar mass quinine.
Solve for molar mass.
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To calculate the molar mass of quinine, we can use the freezing point depression equation:
ΔT = Kf * m
where ΔT is the freezing point depression, Kf is the freezing point depression constant, and m is the molality of the solution.
First, we need to calculate the molality (m) of the solution:
m = (moles of solute) / (mass of solvent in kilograms)
Given that 3.28 g of quinine is dissolved in 25.0 g of cyclohexane, we need to convert the grams to kilograms:
mass of quinine = 3.28 g = 0.00328 kg
mass of cyclohexane = 25.0 g = 0.0250 kg
Now we can calculate the molality:
m = (0.00328 mol) / (0.0250 kg)
m = 0.131 mol/kg
Next, we can substitute the values into the freezing point depression equation:
ΔT = Kf * m
Given that the freezing point depression (ΔT) is 8.43 °C, and the freezing point depression constant (Kf) for cyclohexane is 20.0 °C·kg/mol, we can solve for molar mass (M):
8.43 °C = (20.0 °C·kg/mol) * 0.131 mol/kg
Rearranging the equation to solve for M:
M = (8.43 °C) / ((20.0 °C·kg/mol) * 0.131 mol/kg)
M ≈ 20.39 g/mol
Therefore, the molar mass of quinine is approximately 20.39 g/mol.
To calculate the molar mass of quinine, we can use the formula:
ΔTf = Kf * m * i
where:
ΔTf is the change in freezing point (in Celsius),
Kf is the freezing point depression constant (in Celsius per molal),
m is the molality of the solution (in mol solute per kg solvent), and
i is the van't Hoff factor (the number of particles formed per formula unit).
First, we need to calculate the molality (m) of the solution using the given mass of quinine (3.28 g) and the mass of cyclohexane (25.0 g). The molality can be calculated using the formula:
m = (moles of solute) / (mass of solvent in kg)
To find the moles of quinine, we can use the formula:
moles = mass / molar mass
Now, we can substitute the values into the equation:
ΔTf = Kf * m * i
Rearrange the equation to solve for molar mass:
molar mass = mass / moles
Substitute the known values:
molar mass = mass / (m * i)
Given:
Mass of quinine = 3.28 g
Mass of cyclohexane = 25.0 g
Freezing point depression (ΔTf) = 8.43 °C
Freezing point depression constant (Kf) for cyclohexane = -20.0 °C/m
Now we can calculate the molality:
moles of quinine = 3.28 g / molar mass of quinine
molality (m) = (moles of quinine) / (mass of cyclohexane in kg)
= (3.28 g / molar mass of quinine) / (25.0 g / 1000)
Now we can substitute the given values into the equation:
8.43 °C = -20.0 °C/m * ((3.28 g / molar mass of quinine) / (25.0 g / 1000)) * i
Simplify the equation by rearranging:
molar mass of quinine = (3.28 g / (8.43 °C / (-20.0 °C/m) * (25.0 g / 1000))) / i
Substitute the values and calculate the molar mass of quinine.