Question

in an experimen to estimate the size of a molecule of olive oil, a drop of volume 0.12cm3 was placed on a clean water surface. the oil spread on a patch of diameter 6.0 multiplied by 10^6 mm

Answer 1

To estimate the size of a molecule of olive oil using the given information, we can assume that the drop of olive oil spreads out in a thin layer on the water surface, with a uniform thickness.

First, we convert the volume of the drop from cm^3 to mm^3:

0.12 cm^3 = 0.12 x (10 mm)^3 = 120,000 mm^3

Next, we can calculate the area covered by the olive oil patch on the water surface using the diameter given:

radius = 6.0 x 10^6 mm / 2 = 3.0 x 10^6 mm

area = πr^2 = π(3.0 x 10^6 mm)^2 = 2.83 x 10^13 mm^2

Now, we can estimate the thickness of the olive oil layer by dividing the volume by the area:

thickness = 120,000 mm^3 / 2.83 x 10^13 mm^2 ≈ 4.23 x 10^-9 mm

This thickness represents the average distance between olive oil molecules in the layer.

To estimate the size of a molecule of olive oil, we can use the fact that the molecules are roughly spherical and calculate their volume using the formula for the volume of a sphere:

V = (4/3)πr^3

where r is the radius of the molecule. Rearranging this formula to solve for r, we get:

r = (3V/4π)^(1/3)

Assuming a typical molecular weight for olive oil of around 900 g/mol, we can calculate the volume of one molecule using Avogadro's number:

V = (1/mol) x (1 g/cm^3) = 1.1 x 10^-22 cm^3

Converting this to mm^3 and plugging it into the formula for r, we get:

r = (3 x 1.1 x 10^-22 mm^3 / 4π)^(1/3) ≈ 0.48 nm

This means that the radius of a molecule of olive oil is approximately 0.48 nm. However, it's important to note that this estimate is based on several assumptions and simplifications, and the actual size and shape of olive oil molecules can vary.

Answer 2

wrong right from the start!
0.12 cm^3 = 0.12 x (10 mm)^3 = 120 mm^3

Answer 3

I apologize for the mistake. Indeed, the correct conversion of 0.12 cm^3 to mm^3 is:

0.12 cm^3 = 0.12 x (10 mm)^3 = 120 mm^3.