Exercise 18.26 Part A Consider 1 mol an ideal gas at 28 C and 1.04 atm pressure.

Question

Exercise 18.26 Part A Consider 1 mol an ideal gas at 28 C and 1.04 atm pressure. To get some idea how dose these molecules are to each other, on the average, imagine them to be uniformly spaced, with each What is the lenglh of an edge of each cube if adjacent cubes touch but do not ovelap? My Andwers Give Up Part B ow does this distance compare with the diameter of a typical molecule? The diamer of a typical molecule is aboul 10- Express your answer using one significant igure My Answers give Up Part c How does their separation compare with the spacing of atoms in solids, which typically are about 0 3 nm apert? Express your answer using one significant figure

Explanation / Answer

Using the ideal gas law,
PV = nRT
V = nRT/P
n = 1, R = 8.314 JK-1mol-1, T = 301 K, P = 1.05 x 105 Pa.
Substituting,
V = 2383.3 x 10-5 m3.
One mol contains 6.02214179 × 1023 number of atoms.
One atom requires a space of 2383.3 x 10-5 m3 / 6.02214179 × 1023
= 395 .76x 10-28 m3.

Assuming this space is a cube of edge a,
a3 = 39.576 x 10-27 m3.
a = 3.4 x 10-9 m.

B)

Compared with the diameter,
a / D = 3.4 x 10-9 m / 10-10 m = 34

C)

Compared with the spacing of atoms,
a/S = 3.4x 10-9 m / 0.3 x 10-9 m = 11.33

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