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
volume of drop = pi*r^2*thickness
You know volume, (pi*r^2=area =40 cm^2). Solve for thickness.
I don't know if im being really silly but i still do not understand fully
To find the diameter of an oil molecule, we need to calculate the thickness of the oil film. Let's start with the formula you provided:
volume of drop = π * r^2 * thickness
We are given the volume of the drop (0.05 cm^3) and the area it covers (40 cm^2). The area can be expressed as:
40 cm^2 = π * r^2
Let's rearrange this equation to solve for r:
r^2 = (40 cm^2) / π
r^2 = 12.73 cm^2
Taking the square root of both sides:
r = √(12.73 cm^2)
r ≈ 3.57 cm
Now we have the radius of the spread-out oil film. Since the thickness of the oil film is assumed to be equal to the diameter of an oil molecule, we can say:
thickness = 2 * r
thickness ≈ 2 * 3.57 cm
thickness ≈ 7.14 cm
Therefore, the thickness of the oil film is approximately 7.14 cm.
To express the diameter of an oil molecule in scientific notation with an appropriate number of significant figures, we need to convert the thickness from centimeters to meters, and then divide it by Avogadro's number (6.022 x 10^23 molecules per mole) to find the size of an individual molecule.
7.14 cm = 0.0714 meters
Now, we can calculate the diameter of an oil molecule:
diameter = thickness / Avogadro's number
diameter = 0.0714 meters / (6.022 x 10^23 molecules per mole)
Calculating this value, we get:
diameter ≈ 1.187 x 10^-25 meters
So, the diameter of an oil molecule, expressed in scientific notation to an appropriate number of significant figures, is approximately 1.187 x 10^-25 meters.