# Question #a0ccf

##### 2 Answers

The student had to use 3.2 L of methanol.

#### Explanation:

**Step 1. Calculate the molality of the solution.**

The formula for calculating freezing point depression is

#color(blue)(bar(ul(|color(white)(a/a)ΔT_"f" = K_fmcolor(white)(a/a)|)))" "#

where

We can rearrange the above formula to get

#m = (ΔT_"f")/ K_"f"#

In this problem,

∴

**Step 2. Calculate the mass of the solution.**

When we mix two liquids, we cannot assume that their volumes are additive,

For example, 1 L of methanol + 2 L of water gives 3.1 L of solution.

This complicates the calculation.

**(a)** Calculate the percent composition of the solution.

**(b)** Look up the density of the solution.

The density of 34.0 % aqueous MeOH is 0.945 g/mL.

**(c)** Calculate the mass of the solution.

**Step 3. Calculate the mass of methanol**

**Step 4. Calculate the volume of methanol**

The student had to use 3.2 L of methanol.

#### Explanation:

This question appears to assume (incorrectly) that the volumes on mixing of liquids are additive.

We can use only two significant figures, so we might get away with it.

**Step 1. Calculate the molality of the solution.**

#color(blue)(bar(ul(|color(white)(a/a)ΔT_"f" = K_fmcolor(white)(a/a)|)))" "#

**Step 2. Calculate the volumes of methanol and water in the above solution.**

**Step 3. Calculate the volume of methanol in 8.0 L of solution**

It worked! We get the correct answer with much less work.