A 0.016 M of an acid solution in benzene is dropped on a water surface, the benzene evaporates and the acid forms a monomolecular film of solid type. What volume of the above solution would be required to cover a 500 surface area of water with monomolecular layer of acid? Area covered by single acid molecule is `0.2 xx 10^(-17) cm^(2)`

Options

A. `24.94xx10^(-3)ml`
B. `25.94xx10^(-3)ml`
C. `3.67xx10^(-3)ml`
D. `20.78xx10^(6)ml`

Answer

To solve the problem, we need to determine the volume of a 0.016 M acid solution required to cover a 500 cm² area of water with a monomolecular layer of acid. The area covered by a single acid molecule is given as \(0.2 \times 10^{-17} \, \text{cm}^2\).

### Step-by-Step Solution:

1. **Calculate the total number of molecules needed to cover the area:**
\[ \text{Total area to cover} = 500 \, \text{cm}^2 \]
\[ \text{Area covered by one molecule} = 0.2 \times 10^{-17} \, \text{cm}^2 \]
\[ \text{Total number of molecules} = \frac{\text{Total area}}{\text{Area per molecule}} = \frac{500 \, \text{cm}^2}{0.2 \times 10^{-17} \, \text{cm}^2} \]
\[ = \frac{500}{0.2 \times 10^{-17}} = 2.5 \times 10^{19} \, \text{molecules} \]

2. **Calculate the number of moles of acid needed:**
Using Avogadro's number (\(6.022 \times 10^{23} \, \text{molecules/mol}\)):
\[ \text{Number of moles} = \frac{\text{Total number of molecules}}{N_A} = \frac{2.5 \times 10^{19}}{6.022 \times 10^{23}} \approx 4.15 \times 10^{-5} \, \text{moles} \]

3. **Calculate the volume of the acid solution required:**
Given the concentration of the acid solution is \(0.016 \, \text{mol/L}\):
\[ \text{Volume} = \frac{\text{Number of moles}}{\text{Concentration}} = \frac{4.15 \times 10^{-5} \, \text{moles}}{0.016 \, \text{mol/L}} \]
\[ = 2.59 \times 10^{-3} \, \text{L} = 2.59 \, \text{mL} \]

### Final Answer:
The volume of the acid solution required to cover a 500 cm² surface area of water with a monomolecular layer of acid is approximately **2.59 mL**.