A solution of methanol in water is 20% by volume. If the solution and pure methanol have densities of 0.964 kg and 0.793 kg `L^(-1)` respectively, find the per cent of methanol by weight?

Options

A. 15.8
B. 16.45
C. 17.6
D. 14.8

Explanation

To find the percentage of methanol by weight in a solution that is 20% methanol by volume, we can follow these steps:

### Step 1: Understand the Given Information
- The solution is 20% methanol by volume.
- The density of the solution is 0.964 kg/L.
- The density of pure methanol is 0.793 kg/L.

### Step 2: Define Volumes
Assume we have 100 L of the solution. This means:
- Volume of methanol = 20% of 100 L = 20 L
- Volume of water = 100 L - 20 L = 80 L

### Step 3: Calculate the Mass of Methanol
Using the density of methanol:
\[ \text{Mass of methanol} = \text{Density} \times \text{Volume} = 0.793 \, \text{kg/L} \times 20 \, \text{L} = 15.86 \, \text{kg} \]

### Step 4: Calculate the Mass of the Solution
Using the density of the solution:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} = 0.964 \, \text{kg/L} \times 100 \, \text{L} = 96.4 \, \text{kg} \]

### Step 5: Calculate the Percentage of Methanol by Weight
The percentage by weight of methanol in the solution can be calculated using the formula:
\[ \text{Percentage by weight} = \left( \frac{\text{Mass of methanol}}{\text{Mass of solution}} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage by weight} = \left( \frac{15.86 \, \text{kg}}{96.4 \, \text{kg}} \right) \times 100 \approx 16.45\% \]

### Final Answer
The percentage of methanol by weight in the solution is approximately **16.45%**.

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