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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To calculate the diameter of an oil molecule, we need to use the equation D * area = drop volume, where D is the diameter of the oil molecule, area is the area of the oil film, and drop volume is the volume of the oil drop.

In this case, the area of the oil film is given as 40 cm^2 and the drop volume is 0.05 cm^3. Substituting these values into the equation, we have:

D * 40 cm^2 = 0.05 cm^3

To solve for D, we divide both sides of the equation by 40 cm^2:

D = 0.05 cm^3 / 40 cm^2

Simplifying the expression, we have:

D = 0.00125 cm

Now, we need to express the diameter of the oil molecule in scientific notation with the appropriate number of significant figures.

The given drop volume has only one significant figure, so it is appropriate to use only one significant figure in the answer.

The diameter of the oil molecule in scientific notation with one significant figure is:

D = 1.3 x 10^-3 cm

Therefore, the diameter of the oil molecule is approximately 1.3 x 10^-3 cm.