Average Spacing of Gas Molecules Consider an ideal gas at 27.0 degrees Celsius a

Question

Average Spacing of Gas Molecules

Consider an ideal gas at 27.0 degrees Celsius and 1.00 atmosphere pressure. Imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube.

Part A

What is the length L of an edge of each small cube if adjacent cubes touch but don't overlap?

Express your answer numerically in meters.

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Average Spacing of Gas Molecules

Consider an ideal gas at 27.0 degrees Celsius and 1.00 atmosphere pressure. Imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube.

Part A

What is the length L of an edge of each small cube if adjacent cubes touch but don't overlap?

Express your answer numerically in meters.

SubmitHintsMy AnswersGive UpReview Part

Explanation / Answer

By PV=nRTo find volume of one mole of gas.

v = (0.0821)(27+273) = 24.6 m^3

1L = 1m3

24.6m3 = 0.0246 L

2) Now I'll find the volume surrounding one molecule using Avagadro's number.

(0.0246) / (6.02 x 1023) = 4.09 x 10-26
The volume V of a cube is related to its edge length l by V=l^3. Therefore, the length of one side L equals the cube root of V.

Since V = 4.09 x 10-26
L= (4.09 x 10^-26)^(1/3) = 3.45 x 10-9 m.

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