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

139.94 grams of solute is present in kilograms of water

Step-by-step 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* m=k_f* \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* \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=(11.1 g)/(M)`

Molar mass of the solute= M

M = 65.088 g/mol

Molality of the solution = m =
`(0.1705 mol)/(0.0793 kg)`

`m* M=(0.1705 mol)/(0.0793 kg)* 65.088 g/mol=139.94`g of solute /kg of water

139.94 grams of solute is present in kilograms of water