When `10 mL` of ehtyl alcohol (density `= 0.7893 g mL^(-1))` is mixed with `20 mL` of water (density `0.9971 g mL^(-1))` at `25^(@)C`, the final solution has a density of `0.9571 g mL^(-1)`. The percentage change in total volume on mixing is

Options

A. `3.1%`
B. `2.4%`
C. `1%`
D. None of these

Explanation

To solve the problem of percentage change in total volume when mixing ethyl alcohol and water, we will follow these steps:

### Step 1: Calculate the mass of ethyl alcohol
Given:
- Volume of ethyl alcohol (V_ethanol) = 10 mL
- Density of ethyl alcohol (D_ethanol) = 0.7893 g/mL

Using the formula:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
\[ \text{Mass of ethyl alcohol} = 0.7893 \, \text{g/mL} \times 10 \, \text{mL} = 7.893 \, \text{g} \]

### Step 2: Calculate the mass of water
Given:
- Volume of water (V_water) = 20 mL
- Density of water (D_water) = 0.9971 g/mL

Using the same formula:
\[ \text{Mass of water} = 0.9971 \, \text{g/mL} \times 20 \, \text{mL} = 19.942 \, \text{g} \]

### Step 3: Calculate the total mass of the solution
Now, we add the masses of ethyl alcohol and water:
\[ \text{Total mass of solution} = \text{Mass of ethyl alcohol} + \text{Mass of water} \]
\[ \text{Total mass} = 7.893 \, \text{g} + 19.942 \, \text{g} = 27.835 \, \text{g} \]

### Step 4: Calculate the volume of the final solution
Given:
- Density of the final solution (D_solution) = 0.9571 g/mL

Using the formula for volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
\[ \text{Volume of final solution} = \frac{27.835 \, \text{g}}{0.9571 \, \text{g/mL}} \approx 29.083 \, \text{mL} \]

### Step 5: Calculate the initial total volume before mixing
The initial total volume before mixing is simply the sum of the volumes of ethyl alcohol and water:
\[ \text{Initial total volume} = V_{\text{ethanol}} + V_{\text{water}} = 10 \, \text{mL} + 20 \, \text{mL} = 30 \, \text{mL} \]

### Step 6: Calculate the percentage change in total volume
Now we can calculate the percentage change in volume using the formula:
\[ \text{Percentage change} = \frac{\text{Initial volume} - \text{Final volume}}{\text{Initial volume}} \times 100 \]
\[ \text{Percentage change} = \frac{30 \, \text{mL} - 29.083 \, \text{mL}}{30 \, \text{mL}} \times 100 \]
\[ \text{Percentage change} \approx \frac{0.917 \, \text{mL}}{30 \, \text{mL}} \times 100 \approx 3.06\% \]

### Final Answer
The percentage change in total volume on mixing is approximately **3.1%**.

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