Question

Consider an ideal gas at 27.0 degrees Celsius and 1.00 atmosphere pressure. Imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube. Part A What is the length L of an edge of each small cube if adjacent cubes touch but don't overlap

Answer 1

To solve the exercise it is necessary to keep in mind the concepts about the ideal gas equation and the volume in the cube.

However, for this case the Boyle equation will not be used, but the one that corresponds to the Boltzmann equation for ideal gas, in this way it is understood that

$PV =NkT$

Where,

N = Number of molecules

k = Boltzmann constant

V = Volume

T = Temperature

P = Pressure

Our values are given as,

$N = 1$

$k = 1.38*10^{-23}J/K$

$T = 27\°C = 27\°C + 273 = 300K$

$P = 1atm = 101325Pa$

Rearrange the equation to find V we have,

$V = \frac{NkT}{P}$

$V = \frac{1(1.38*10^{-23})(300K)}{101325Pa}$

$V = 4.0858*10^{-26}m^3$

We know that length of a cube is given by

$V = L^3$

Therefore the Length would be given as,

$L = V^{1/3}$

$L = (4.0858*10^{-26})^{1/3}$

$L = 3.445*10^{-9}m$

Therefore each length of the cube is 3.44nm