In water conservation, chemists spread a thin film of certain inert material over the surface of water to cut down the rate of evaporation of water in reservoirs. Franklin found that 0.10 mL of oil could spread over the surface of water of about 49 m squared in area.

Assuming that the oil forms a monolayer (one molecule thick) estimate the length of each oil molecule in nanometers.
(1nm= 1 x 10^-9 m)

I tried solving this but I'm stuck.
This is what I did 0.10/40 than /1x 10^-9 = 2.5 x10^6 as my answer

but the real answer is 2.5 nm

Could someone please write the steps to getting 2.5 nm.

assume the oil molecule has an area of PI(D/2)^2 where D is the length of each molecule. THen the volume of each oil molecule is area*D=PI*D^3 / 4

Total volume=49*D m^3
That is equal to the total volume of oil, .10ml=.1*e-6 m^3

so the volumes are equal
49D=.1E-6
D=.1/49 E-6=2.0E-9

I am not certain if you mean 49 0r 40m^2

Ignore my first paragraph. You can use that to get the number of molecules in .1ml.

Sorry i meant 40 m squared

To estimate the length of each oil molecule in nanometers, you need to calculate the length of the oil film by using the given information.

Let's break down the problem step by step:

1. Determine the area of the oil film: The given information states that 0.10 mL of oil spreads over an area of 49 m². To convert 0.10 mL to m², you need to multiply it by the conversion factor of 1 x 10^-6 (since 1 mL = 1 x 10^-6 m³).
Area = 0.10 mL * (1 x 10^-6 m³ / 1 mL) = 0.10 x 10^-6 m² = 1 x 10^-7 m².

2. Find the length of the oil film: Since the oil is spread as a monolayer, with a thickness of one molecule, the length will be equal to the area. Therefore, the length of the oil film is also 1 x 10^-7 m.

3. Convert the length to nanometers: To convert meters to nanometers, you need to multiply the length by the conversion factor 1 x 10^9 (since 1 nm = 1 x 10^-9 m).
Length in nanometers = 1 x 10^-7 m * (1 x 10^9 nm / 1 m) = 1 x 10^2 nm = 100 nm.

Therefore, the correct answer is 100 nm, not 2.5 nm as mentioned.