# Homework Help: Calibrated 2% Hydrogen sample gas accuracy

1. Oct 1, 2011

### onereddog

hi all,
Real life industry question...
An accurately calibrated cylinder of compressed gas sample of Hydrogen (certified 2% H2 and air 98%) is used to calibrate a hydrogen sensor by turning on its top regulator sample tap. It can be used for numerous calibration runs until it is empty. As H2 does not mix with air and is very much lighter/less dense wouldn't the H2 rise to the top of the cylinder and come out of the sample tap first, thereby making the "calibrated" sample remaining even more air; i.e. uncalibrated? How does cylinder remain a perfect mix ratio of 2% H2 if the Hydrogen can escape first? There is no indication or advisory on the cylinder that its accuracy will deteriorate.

2. Oct 2, 2011

### Spinnor

You wrote,

" As H2 does not mix with air ..."

Why do you think that is true?

Calculate the potential energy difference for any of the gas molecules to be at the top of the container verses the bottom and compare that with a typical kinetic energy of the molecules. Compare mV^2/2 with mgh , compare V^2/2 with gh

Using 500 m/s for V (see http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html ) and 1m for h

I don't think gravity comes into play.

From page 83, Modern Physics, Paul Tipler

Equilibrium height distribution of particles in a gravitational field,

n(h) = n_o*exp(-mgh/kT)

3. Oct 2, 2011

### onereddog

" As H2 does not mix with air ..."

Why do you think that is true?

Aha! Thanks Spinnor,

I’m sure this has the makings of a good exam question!

What I meant to say was when H2 is mixed with air, it quickly separates and rises up; hence the absence of H2 in earth’s atmosphere. I assumed the same would occur in the cylinder.

The math is a bit beyond me but I guess the key factor here is the Kinetic energy of the gas molecules (Brownian motion?) override the effect of gravity & keep the “mix“ in the cylinder even.

Hypothetically, if the cylinder was large enough, would there be a point where gravity would have an effect and the gases would separate?

Regards..

4. Oct 3, 2011

### Staff: Mentor

For the separation process to be effective you need very high columns and very low temperatures, this is called cryogenic distillation then and has its commercial uses. But it almost doesn't work in normal circumstances.

Hydrogen doesn't have to quickly separate and rise up - from what I remember it runs into space from the upper parts of the atmosphere, that means mixing is enough to remove it completely, especially taking account scarcity of elemental hydrogen sources.