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

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Discussion Overview

The discussion revolves around converting units for the Langmuir equation used in adsorption isotherms, specifically transitioning from grains per pound and grains per gallon to milligrams per gram and milligrams per cubic decimeter. Participants explore the implications of these unit changes on the constants involved in the equation.

Discussion Character

  • Homework-related
  • Dimensional analysis

Main Points Raised

  • One participant presents a homework problem involving the Langmuir equation and seeks help with unit conversion for the constants b and k.
  • Another participant suggests using dimensional analysis to determine the units of the constants b and k, questioning whether they are dimensionless.
  • There is a focus on ensuring that the units in the equation are consistent, particularly in the term "1+bC".
  • A later reply acknowledges the realization that b and k are not dimensionless, which was previously assumed.

Areas of Agreement / Disagreement

Participants generally agree on the importance of dimensional analysis in understanding the units of the constants, but there is no consensus on the specific values or relationships of b and k in the new units.

Contextual Notes

The discussion highlights the need for clarity regarding the units of the constants b and k, but does not resolve the specific conversions or calculations needed to derive their values in the new units.

foxtrotalpha
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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.