# Size of a cube for a molecule of ideal gas

## Homework Statement

The temperature of an ideal gas is 00C and the pressure is 1[atm]. imagine every molecule is enclosed in a cube, what's it's side length?

## Homework Equations

PV=nRT
Avogadro's number: 6.023E23

## The Attempt at a Solution

I assume volume of i liter:
$$1[atm]\cdot 1[liter]=n\cdot 0.08208\cdot 273\rightarrow n=0.0446[mole]$$
Molecules per 1 liter:
$$0.0446\cdot 6.023\cdot 10^{23}=2.687\cdot 10^{22}$$
How many molecules are on one side?
$$\sqrt{2.687\cdot 10^{22}}=29951774$$
The length of a side:
$$\frac{10[cm]}{2995177}=3.34\cdot 10^{-7}[cm]$$
The answer in the book: 3E-7[cm]

## Answers and Replies

Related Introductory Physics Homework Help News on Phys.org
Bystander
Science Advisor
Homework Helper
Gold Member
No specification of significant figures anywhere in the problem statement? Haven't checked your arithmetic in detail, but the set-up and execution looks great.

Thanks, that's what i asked

Quantum Defect
Homework Helper
Gold Member
I always like to draw a picture of what the molecule in the box looks like when I teach this, to give students a sense of scale.

The box is about 30 Angstrom on a side. How big is a typical molecule? How big is the typical box for a liquid?

A bi atomic molecule is about 1[A] am i right? then the side is bigger 30 times more, but in the book it's written that's it's only 10 times larger.
The volume of one mole of water is 18[cm3]. Molecular weight 18:
$$\sqrt{6.023\times 10^{23}}=84450901,\ \sqrt{18}=2.62[cm]$$
$$\frac{2.62}{84450901}=31\times10^{-9}[cm]=31\times 10^{-11}[m]=3.1\times 10^{-10}[m]=3.1[Angstram]$$
Water molecule's size is about 1.5[A]

BvU
Science Advisor
Homework Helper
Water molecule is a bit bigger (diameter 2.75 A here); O-H centers are .94 Angstrom apart.

And here are a few other molecules. 3 to 4 A appears to be a good estimate

Last edited:
Thanks