As part of studying the effect of oil on surface waves in open waters, Ben Franklin poured a small amount of oil on the surface of a lake. He discovered that 2 mL of oil gave a circle of radius 30 m. Estimate the volumetric size of an oil molecule in angstroms, give one significant digit. Do not write down units in your answer. The answer to the preceding question and your knowledge of a typical atomic size suggests that the oil molecules could contain alkane chains that are

To estimate the volumetric size of an oil molecule, we can assume that the oil spreads out to form a monolayer, or a single layer of molecules, on the surface of the water. The volume of oil poured is given, and the area of the circle it forms is also known. 

### Step-by-Step Solution:

1. **Volume of Oil:**
   The volume of oil poured by Ben Franklin is 2 mL. This is equivalent to \(2 \times 10^{-3}\) liters or \(2 \times 10^{-6}\) cubic meters (since \(1 \, \text{mL} = 10^{-6} \, \text{m}^3\)).

2. **Area Covered by the Oil:**
   The oil spreads to cover a circle of radius 30 meters. The area \(A\) of this circle is:

   \[
   A = \pi r^2 = \pi \times (30)^2 = 900\pi \, \text{m}^2
   \]

3. **Thickness of the Oil Layer:**
   Assuming the oil forms a monolayer of molecules, the thickness \(d\) of this layer can be estimated using the volume \(V\) of the oil:

   \[
   V = A \times d
   \]

   Solving for \(d\):

   \[
   d = \frac{V}{A} = \frac{2 \times 10^{-6}}{900\pi}
   \]

   Let's calculate the value of \(d\).

   \[
   d \approx \frac{2 \times 10^{-6}}{2827} \approx 7.1 \times 10^{-10} \, \text{m}
   \]

4. **Converting Thickness to Angstroms:**
   \(1 \, \text{m} = 10^{10} \, \text{angstroms}\), so:

   \[
   d \approx 7.1 \times 10^{-10} \, \text{m} = 7.1 \, \text{angstroms}
   \]

   This thickness represents the approximate size of one molecule of oil. 

### Conclusion:

The volumetric size of an oil molecule is approximately **7 angstroms** (to one significant digit).

### Suggestion Based on the Result:

Given this size, which is on the order of a typical atomic diameter, it suggests that the oil molecules could contain alkane chains. Alkanes are long, hydrocarbon chains that are typically 1-2 angstroms thick but can extend several angstroms in length, aligning with the estimated size.

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Would you like more details or have any questions about this? Here are 5 related questions you might find interesting:

1. How does the molecular size relate to the properties of different types of oils?
2. What are alkane chains, and why are they common in oils?
3. How would the thickness of the oil layer change if a different substance were used?
4. What are other real-world applications of studying molecular monolayers on surfaces?
5. How can this type of experiment be used to estimate molecular sizes of other substances?

**Tip:** Remember, when converting units, always check for unit consistency to avoid calculation errors!

Learn how to estimate the volumetric size of an oil molecule in angstroms based on a given volume of oil spread on water. Detailed step-by-step solution using geometric and volume calculation concepts. Suitable for advanced high school students.

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