Question

How many grams of NaCl should be added to 500 g of water to produce a solution which freezes at –5.00 C? (The K f for water is 1.86°C/m.) Please provide step by step.

Answer 1

39.31 grams of NaCl

Step-by-step explanation:

Let x be the mass of NaCl added.

Decrease in freezing point = ΔTf = 5°C

Kf for water = 1.86 °C/m

Molality of the solution = m =
`(Number\ of\ moles\ of\ solute)/(Mass\ of\ solvent\ in\ kg)`

i = Vant hoff factor =
`(Observed\ number\ of\ particles)/(Theoretical\ number\ of\ particles)`

Formula for depression in freezing point:

ΔTf = i×Kf×m

i for NaCl = 2 (As NaCl dissociates into Na+ and Cl- ions in solution)

molar mass of NaCl = 58.5 g/mol

`5=2*1.86*(x*1000)/(58.5*500)`

`x=39.31\ grams`