Question

A drop of oil (volume 0.05cm3) is released from a medicine dropper on to the calm surface of a pond where it spreads out to cover an area of 40cm2. Assume that the oil film has a uniform thickness equal to the diameter of a oil molecule.

Calculate the diameter of an oil molecule and express in Scientifc notation to an appropriate number of sig figs.



The appropriate number of significant figures is just one, since there is just one significant figure in the volume. Personally, I prefer to use one extra significant figure, especially when the first significant figure is 1, as will be the case here. Otherwise some accuracy is lost. I don't know what your school's policy is on this.

Are you sure the problem did not say the oil film area was 40 m^2 instead of 40 cm^2? Forty square meters is closer to what you would get in this kind of an experiment.

40 m^2 = 4.0*10^5 cm^2

To get the molecular diameter D, set these to volumes equal to each other:
D*area = drop volume = 5*10^-3 cm^3

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