To find the molecular size of oleic acid, we will follow these steps:
### Step 1: Calculate the volume of one drop of oleic acid.
Given the radius of each drop \( r = 1.4 \, \text{mm} = 0.14 \, \text{cm} \).
The volume \( V \) of a spherical drop is given by the formula:
\[
V = \frac{4}{3} \pi r^3
\]
Substituting the radius into the formula:
\[
V = \frac{4}{3} \pi (0.14)^3
\]
Calculating \( (0.14)^3 \):
\[
(0.14)^3 = 0.002744
\]
Now substituting this value back:
\[
V = \frac{4}{3} \pi (0.002744) \approx 0.01149 \, \text{cm}^3
\]
### Step 2: Calculate the total volume of 10 drops.
Since there are 10 drops, the total volume \( V_{total} \) of the drops is:
\[
V_{total} = 10 \times V = 10 \times 0.01149 \approx 0.1149 \, \text{cm}^3
\]
### Step 3: Determine the concentration of oleic acid in the solution.
The concentration of oleic acid is given as \( \frac{1}{400} \, \text{cm}^3/\text{cm}^3 \) of alcohol. This means that in \( 1 \, \text{cm}^3 \) of solution, there is \( \frac{1}{400} \, \text{cm}^3 \) of oleic acid.
### Step 4: Calculate the volume of oleic acid in the total solution.
The volume of oleic acid in the total solution can be calculated as:
\[
V_{oleic} = V_{total} \times \text{Concentration} = 0.1149 \times \frac{1}{400} \approx 0.00028725 \, \text{cm}^3
\]
### Step 5: Calculate the area of the circular film produced.
The radius of the circular film is given as \( R = 10 \, \text{cm} \).
The area \( A \) of the film is:
\[
A = \pi R^2 = \pi (10)^2 = 100\pi \approx 314.16 \, \text{cm}^2
\]
### Step 6: Relate the volume of oleic acid to the area and thickness of the film.
The volume of the film can also be expressed as:
\[
V_{oleic} = A \times t
\]
where \( t \) is the thickness of the film.
Rearranging for thickness \( t \):
\[
t = \frac{V_{oleic}}{A} = \frac{0.00028725}{314.16} \approx 9.15 \times 10^{-6} \, \text{cm}
\]
### Step 7: Calculate the molecular size of oleic acid.
The molecular size can be approximated using the thickness of the film. Assuming that the thickness of the film corresponds to the molecular size of oleic acid, we have:
\[
\text{Molecular size} \approx t \approx 9.15 \times 10^{-6} \, \text{cm} = 9.15 \times 10^{-4} \, \text{mm}
\]
### Final Result
The molecular size of oleic acid is approximately \( 9.15 \times 10^{-6} \, \text{cm} \) or \( 9.15 \times 10^{-4} \, \text{mm} \).
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