Consider 1 mol an ideal gas at 28 C and 1.06 atm pressure. To get some idea how

Question

Consider 1 mol an ideal gas at 28 C and 1.06 atm pressure. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube.

A) What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

B) How does this distance compare with the diameter of a typical molecule? The diameter of a typical molecule is about 10-10 m. (in l/dmolecule)

C) How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart? (in l/lsolid)

Explanation / Answer

Using the ideal gas law,
PV = nRT
V = nRT/P
n = 1, R = 8.314 JK-1mol-1, T = 301 K, P = 1.07 x 105 Pa.
Substituting,
V = 2338.8 x 10-5 m3.
One mol contains 6.02214179 × 1023 number of atoms.
One atom requires a space of 2338.8 x 10-5 m3 / 6.02214179 × 1023
= 388.5 x 10-28 m3.

Assuming this space is a cube of edge a,
a3 = 38.85 x 10-27 m3.
a = 3.37 x 10-9 m.

B)

Compared with the diameter,
a / D = 3.39 x 10-9 m / 10-10 m = 33.9

C)

Compared with the spacing of atoms,
a/S = 3.39 x 10-9 m / 0.3 x 10-9 m = 11.3.

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