You like boiled eggs for breakfast, but they take too long to cook, and you are always late to your early morning class. Lucky you! You have learned that adding table salt, NaCl (58.4 g/mol, 2.16 g/cm³), to water (K_b = 0.52 $\circ$ C/m) increases the temperature at which it boils. You figure that you can cook eggs faster at a higher temperature in boiling salty water! What increase in the boiling point do you expect if you add 1 tablespoon (1 tbsp = 14.8 cm³) of salt to one 8-oz cup of water (237 mL)? A)1.0 $\circ$ C B)2.4 $\circ$ C C)28 $\circ$ C D)1.5 $\circ$ C E)3.7 $\circ$ C

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the equation: ΔTb = Kb * m * i
ΔTb = increase in boiling point
Kb = boiling point elevation constant for water (0.52°C/m)
m = molality of salt solution (moles of solute per kilogram of solvent)
i = van't Hoff factor, which is the number of particles into which one molecule of the solute dissociates in solution (NaCl dissociates into two ions, so i = 2)

First, we need to calculate the molality of the salt solution. We know that 1 tablespoon of salt is equivalent to 14.8 cm3 = 0.0148 L. The density of water is 1 g/mL or 1000 g/L, so the mass of water in 237 mL (8-oz cup) is 237 g or 0.237 kg. Assuming that all of the salt dissolves in the water, we can use the following equation to calculate the molality:

molality = moles of salt / mass of solvent in kg

moles of salt = mass of salt / molar mass
mass of salt = 1 tbsp = 14.8 g
molar mass of NaCl = 58.4 g/mol

moles of salt = 14.8 g / 58.4 g/mol = 0.253 mol

molality = 0.253 mol / 0.237 kg = 1.07 mol/kg

Now we can use the equation for ΔTb:

ΔTb = Kb * m * i
ΔTb = 0.52°C/m * 1.07 mol/kg * 2

ΔTb = 1.12°C

Therefore, the boiling point of the saltwater will increase by 1.12°C. The closest answer choice is B) 2.4°C, which is the correct choice.

You Like Boiled Eggs for Breakfast, but They Take Too ∘\circ∘

You Like Boiled Eggs for Breakfast, but They Take Too $\circ$