isha took two aqueous solutions — one containing 7·5 g of urea (Molar mass = 60 g/mol)and the other containing 42·75 g of substance Z in 100 g of water, respectively. It wasobserved that both the solutions froze at the same temperature. Calculate the molar mass of Z
Question
isha took two aqueous solutions — one containing 7·5 g of urea (Molar mass = 60 g/mol)and the other containing 42·75 g of substance Z in 100 g of water, respectively. It wasobserved that both the solutions froze at the same temperature. Calculate the molar mass of Z
Solution
The freezing point of a solution is a colligative property and depends on the number of solute particles. Since both solutions freeze at the same temperature, they have the same molality.
First, calculate the molality of the urea solution.
Molality (m) = moles of solute / mass of solvent in kg
The moles of urea can be calculated by dividing the mass of the urea by its molar mass.
Moles of urea = 7.5 g / 60 g/mol = 0.125 mol
The mass of the solvent (water) is 100 g, or 0.1 kg.
So, the molality of the urea solution is:
m = 0.125 mol / 0.1 kg = 1.25 mol/kg
Since the solutions have the same molality, the molality of the solution of substance Z is also 1.25 mol/kg.
We can use this to find the molar mass of Z.
First, calculate the moles of Z in the solution:
Moles of Z = molality * mass of solvent in kg = 1.25 mol/kg * 0.1 kg = 0.125 mol
Then, calculate the molar mass of Z:
Molar mass of Z = mass of Z / moles of Z = 42.75 g / 0.125 mol = 342 g/mol
So, the molar mass of substance Z is 342 g/mol.
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