General chemistry

Question

Determine the freezing point depression of a solution that contains 50.7 g glycerin (C3H8O3, molar mass = 92.09 g/mol) in 376 mL of water. Some possibly useful constants for water are 

Kf = 1.86°C/m and Kb = 0.512°C/m.

determine the boiling point elevation for the same solution

Answer 1

Freezing point depression

The formula we will use for freezing point depression is

T_f^o - T_f = K_fmi

Where T_f^o is the standard freezing point of the liquid, T_f is the new freezing point, K_f is the freezing point constant, m is the molality of the solution, and i is a constant that describes dissociation (called the Vant Hoff factor)

First, the T_f^o of water is 0 ^oC. Then, we know that the given K_f is 1.86. Finally, as the solute (the molecule being dissolved) is a non-electrolyte, we can assume that i=1.

Now, all we need to do to solve this problem is find the molality (m) as we have all of the other variables. Molality is a ratio of moles of solute divided by kilograms of solvent.

First, we have to find how many moles of solute we have

50.7g solute 1 mol solute = 0.551 mol solute

92.09g solute

Next, we need to find how much our solvent weighs, in kilograms (the density of water is 1 gram per 1 mL)

376mL water 1g 1kg = 0.376 kg of solvent

1ml 1000g

Now molality

0.551 mol solute / 0.376 kg solvent = 1.47 molal

We now have all the variables needed to solve. So, plugging in the numbers

0 - T_f = (1.86)*(1.57)*(1)

-T_f = 2.92

T_f = -2.92 ^oC is the new freezing point

Boiling point elevation

The boiling point elevation equation is

T_b - T_b^o = K_bmi

The variables here are similar to the freezing point equation, where T_b is the new boiling point, T_b^o is the standard boiling point, K_b is the boiling point constant, m is molality, and i is the Vant hoff factor.

We know that T_b^o = 100 ^oC, K_b = 0.512, m = 1.47 (from the previous calculation), and that i = 1

So, plugging in the values

T_b - 100 = (0.512)*(1.47)*(1)

T_b = 100 + 0.753

T_b = 100.753 ⁰C is the new boiling point