# Units Conversion

1. Oct 12, 2013

### foxtrotalpha

Hey guys I am having a big problem with this question

1. The problem statement, all variables and given/known data

The adsorbtion isotherm for the removal of a contaminant from waste water is givern by the langmuir equation: q=(bkC)/(1+bC) where q is the loading of contaminant of the adsorbent and C is the concentration of the contaminant in solution. Literature data gives values for the constants b and k of 1.16 and 130 respectively for the case where q is grains per lb and C is grains per gal . Determine the values for b' and k' for the Langmuir equation between loading q' in mg per g and C' in mg per dm^3 .

Data : 1 lb=7000 gr(grains)

2. Relevant equations

3. The attempt at a solution
I am sort of stuck as the 2 variables will have changes in their unis simultaneously, all I have done is to convert 1mg=0.01544 gr and 1 dm^3=0.220 gal .

2. Oct 12, 2013

### Simon Bridge

Dimensional analysis will probably work here:
With equation: $$q=\frac{bkC}{1+bC}$$ ... are k and b dimensionless?
Did the values you looked up have units at all? There's a clue right there.

What are the units of b and k in terms of the units of q and C?

You can work it out - either by reading the tables or dimensional analysis:
i.e. notice that, in the denominator "1+bC" has to make sense in terms of units?
so (square brackets reads "units of"): [1+bC]=[1]+[bC] means that must have some relation to [C].

Note: 1 cubic decimeter = 1 liter.

3. Oct 13, 2013

### foxtrotalpha

THANKS !! , you made me realised that b and k are not dimensionless at all ,before this I had always assumed them to be dimensionless.

4. Oct 13, 2013

### Simon Bridge

Well done.

Checking the dimensions is very powerful.