Solve Katharometer Question: Limit Errors to +0.1% Oxygen

[cjm181]

Homework Statement

It is proposed to use a katharometer to measure the amount (about 5%) of oxygen in nitrogen, in the presence of a small amount (0.5%) hydrogen. How constant would the proportion of hydrogen have to be in order to limit errors in measurement of % oxygen to + 0.1%?The thermal conductivities are:

nitrogen 0.993

oxygen 1.052

hydrogen 6.993

Homework Equations

The Attempt at a Solution

So I understand from the notes that the thermal conductivity is proportional to the composition. So, the thermal conductivity of nitrogen (99.995%) and hydrogen (0.005%) would be:

6.993 - 0.993 =6
6 * 0.005 = 0.03

0.993 + 0.03 = 1.023

So nitrogen (99.995%) mixed with hydrogen (0.005%) would have a k value of 1.023

So, to find the K value of the nitrogen / hydrogen mix with oxygen (5%):

1.052 - 1.023 = 0.029
0.029 & 0.05 = 0.00145

0.00145 + 1.023 = 1.02445

So the value of nitrogen / hydrogen (95%) and oxygen (5%) is 1.02445

So, to find the percentage of hydrogen change that would give a 0.1% change in oxygen? that's where I am stuck!

 

[cjm181]

If the oxygen content changed by 0.1%, then the k value would be:

To find the K value of the nitrogen / hydrogen mix with oxygen (5.1%):

1.052 - 1.023 = 0.029
0.029 & 0.051 = 0.001479

0.001479 + 1.023 = 1.024479

So I need to find the percentage change of hydrogen that would give a total k value of 1.024479?