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. What is the length of an edge of each small cube if adjacent cubes touch but don't overlap?

Answer 1

Answer:

The length of an edge of each small cube  is 3.43 nm.

Explanation:

Given that,

Temperature of ideal gas =27.0°C

Pressure = 1.00 atm

We need to calculate the length of an edge of each small cube

Using gas equation

$PV=nRT$

$PV=NkT$

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

For, N = 1

Where,

N = number of molecule

k = Boltzmann constant

T = temperature

P= pressure

Put the value into the formula

$V=\dfrac{1\times1.38\times10^{-23}\times(27+273)}{1.03\times10^{5}}$

$V=4.019\times10^{-26}\ m^3$

Now, for the cube

$V=L^3$

$L=V^{\frac{1}{3}}$

$L=(4.019\times10^{-26})^{\frac{1}{3}}$

$L=3.43\times10^{-9}\ m$

$L=3.43 nm$

Hence, The length of an edge of each small cube  is 3.43 nm.