How close together are gas molecules? Consider 1 mol an ideal gas at 25 degrees

Question

How close together are gas molecules?

Consider 1 mol an ideal gas at 25 degrees C and 1.05 atm. 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 10^-10.

C. How does their separation compare with the spacing of atoms in solids, which typically are about .3 nm apart?

Explanation / Answer

1. Avogadro's hypothesis states that 1 mole of gas occupies 22.4 L at STP. Hence, volume occupied by 1 mole of gas at 1.05 atm pressure and temperature of 25'C (= 298 K), by the ideal gas equation, is (1x 22.4/273) x (298/1.05) L = 23.86 L = 0.02386 m^3

Since 1 mole of gas contains 6.02 x 10^23 molecules, hence volume occupied by a molecule = 0.02386/6.02x10^23 m^3 = 3.96 x 10^-26 m^3
Length of an edge of the cube = cube-root[3.96x10^-26] m = 3.40 x 10^-9 m

2. The distance ia bout 3.40x10^-9/10^-10 = 34 times the diameter of a molecule.

3 The separation is about 3.40x10^-9/0.3x10^-9 = 11.33 times the atomic spacing in solids.

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