Consider 1 mol an ideal gas at 25 degree C and 1.06 atm pressure. To get some id

Question

Consider 1 mol an ideal gas at 25 degree 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. What is the length of an edge of each cube if adjacent cubes touch but do not overlap? How does this distance compare with the diameter of a typical molecule? The diameter of a typical molecule is about 10^-10 m. Express your answer using one significant figure. How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart? Express your answer using one significant figure.

Explanation / Answer

a]

Use the ideal gas equation

PV = nRT

=> L = [V]1/3 = [nRT/P]1/3 = [1(8.31)(273+25)/(107404.5)]1/3 = 0.285 m

b] L/dmolecule = 0.285/10-10 = 0.285 x 1010 = 3 x 109 [1 significant figure]

c] L/Lsolid = 0.285/0.3 x 10-9 = 9 x 108 [1 significant figure].

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