Question

A student determines the molar mass of a compound by the method used in this experiment. She found the temperature of the ice water to be 1.0°C. When she added 11.1g of her unknown solute to the mixture, the temperature fell to -3.0°C. The mass of the solution was 90.4g. Calculate mass of solute in solution 1kg of water

Answer 1

Answer:

139.94 grams of solute is present in  kilograms of water

Explanation:

Temperature of the ice water = T = 1.0°C

Temperature of the mixture = $T_f$ =-3.0°C

Depression in freezing point $\Delta T_f=T-T_f$

$\Delta T_f$ =1.0°C-( -3.0°C)=4°C

$\Delta T_f=k_f\times m=k_f\times \frac{\text{Moles of solute}}{\text{mass of solvent (kg)}}$

m = molality of the solution

$k_f$ = Molal depression constant

$4^oC=1.86^oC kg/mol\times \frac{\text{Moles of solute}}{0.0793 kg}$

Mole of solute = 0.1705 moles

Mass of solute = 11.1 g

Moles of solute = $0.1705 mol=\frac{11.1 g}{M}$

Molar mass of the solute= M

M = 65.088 g/mol

Molality of the solution = m = $\frac{0.1705 mol}{0.0793 kg}$

$m\times M=\frac{0.1705 mol}{0.0793 kg}\times 65.088 g/mol=139.94$g of solute /kg of water

139.94 grams of solute is present in  kilograms of water