Question

An urban legend suggests that some people add salt to water used for boiling potatoes or noodles in order to raise the temperature and help them cook faster. One tablespoon of salt is about 20 g (or one-third of a mole). Assume that the cooking pot contains 1000 g (or 1 liter) of water. What would be the new boiling point of the salted water in degrees Celsius?

Answer 1

Given,

Mass of salt(NaCl) = 20 g

Mass of water(Solvent) = 1000 g x ( 1Kg /1000 g) = 1 kg

We know, the formula for elevation in boiling point,

T_b = i x K_b x m

Here, m = molality of the solution

i = Van't Hoff factor [ For NaCl, i = 2]

K_b for water = 0.512 ^oC/m

Also we know,

T_b = T_b(solution) - T_b(Solvent)

Now, Firstly calculating the number of moles for salt(NaCl),

= 20 g NaCl x ( 1 mol / 58.44 g)

= 0.3422 mol of NaCl

Now, Molality(m) = Number of moles of solute/ kg of solvent

Molality(m) = 0.3422 mol/ 1 kg

Molality(m) = 0.3422 m

Now,

T_b = 2 x 0.512 ^oC/m x 0.3422 m

T_b = 0.35 ^oC

Now,

T_b = T_b(solution) - T_b(Solvent)

0.35 ^oC =  T_b(solution) - 100 ^oC

T_b(solution) = 100.35 ^oC