Convert Units: q,C from gr/lb, gr/gal to mg/g, mg/dm^3

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The discussion revolves around converting the Langmuir equation parameters from grains per pound and grains per gallon to milligrams per gram and milligrams per cubic decimeter. Participants emphasize the importance of dimensional analysis to determine the units of the constants b and k, clarifying that they are not dimensionless as previously assumed. The conversion factors provided include 1 lb = 7000 gr and 1 dm^3 = 1 liter. The analysis highlights that the denominator of the equation must maintain consistent units, leading to insights about the relationships between the variables. Ultimately, the discussion underscores the significance of understanding unit conversions in solving adsorption isotherm problems.
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Hey guys I am having a big problem with this question :frown:

Homework Statement



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)

Homework Equations





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 .
 
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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.
 
Simon Bridge said:
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.


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

Checking the dimensions is very powerful.
 

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