The actual diameter of an atom is about a tenth of a nanometer (10 -10 m). In or

Question

The actual diameter of an atom is about a tenth of a nanometer (10-10 m). In order to develop some intuition for the molecular scale of a gas, assume that you are considering a liter of air (mostly N2 and O2) at room temperature and a pressure of one atmosphere -- 105 Pa. Put all your answers in the answer box, labeling each one by its letter and putting a blank line between each answer.

A. Calculate the number of molecules in the sample of gas.
B. Estimate the average spacing between the molecules.
C. Estimate the average speed of a molecule using the relation between the KE of a molecule and the temperature.
D. Suppose that the gas were rescaled upwards so that each atom was the size of a tennis ball. What would be the average spacing between molecules?

Explanation / Answer

A. Number of molecules = n * Na(avagadro number) , n- number of moles.

B.Average spacing = diameter of the sphere = 10^-10

C. K.E = 3/2 * k * T , k- boltzman contanst, T - temperature

K.E = 3/2 * 1.38 * 10^-23 * 301 = 6.23 * 10^-21 J

K.E = 1/2 M * V^2 , M- mass of air (nitrogen)

V = (2K.e/M)^1/2 = 518m/s

D.Average spacing will be the diameter of the ball sized atom ( 6.5cm)

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