Consider an ideal gas at 29 C and 1.03 atmpressure. To get some idea how close t
ID: 1469109 • Letter: C
Question
Consider an ideal gas at 29 C and 1.03 atmpressure. 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 10^10m. (Hint: L/dmolecule. Express answer using one significant figure).
c)How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart? (Hint: L/Lsolid. Express answer using one significan figure).
I also do not understand what dmolecule and Lsolid are refering to?
Explanation / Answer
T = temperature = 29 C = 29 + 273 = 302 K
P = pressure = 1.03 atm = 1.03 x 1.01 x 105 Pa
N = number of molecules = 1
Using the formula
PV = NkT
(1.03 x 1.01 x 105 ) V = 1 (1.38 x 10-23) (302)
V = 4.01 x 10-26 m3
let the length of edge of cube = L
V = L3
4.01 x 10-26 = L3
L = 3.42 x 10-9 m
b)
L /dmolecule = (3.42 x 10-9 ) / (10-10) = 34.2
c)
L/Lsolid = (3.42 x 10-9 ) / (0.3 x 10-9) = 11.4