Deriving Equation x1m=(x1CMC2)/(x1CMC2+x2CMC1) | Tinkering with Equations

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Discussion Overview

The discussion revolves around deriving the equation x1m=(x1CMC2)/(x1CMC2+x2CMC1) from a set of related equations. Participants are exploring the mathematical relationships between variables in the context of a homework problem involving concentration and mass balance equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents an initial attempt at deriving the equation, outlining steps involving inverting Eq 2 and eliminating x2m using the relationship x2m=(1-x1m).
  • Another participant requests more detailed work to understand where the first participant might have gone astray, emphasizing the need for clarity in the derivation process.
  • A third participant suggests that x1 and x2 can be solved directly from equations 1 and 3, indicating that these equations are linear.
  • A later reply questions the basis for the assumption that x2m = (1 - x1m) and seeks clarification on whether the request is for deriving or solving the equations.

Areas of Agreement / Disagreement

There is no consensus on the approach to take for deriving the equation, as participants express different perspectives on whether the focus should be on deriving or solving the equations. Multiple viewpoints on the steps involved remain present.

Contextual Notes

Participants have not fully resolved the assumptions underlying the relationships between the variables, particularly regarding the derivation of x2m and its relationship to x1m. The discussion reflects uncertainty about the correct approach to take in the derivation process.

jajajujujojo
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1. Please could you give me a hand with deriving the following equation:

x1m=(x1CMC2)/(x1CMC2+x2CMC1)

Homework Equations



Eq 1: 1/CMC=x1/CMC1+x2/CMC2
Eq 2: CMC=x1mCMC1+x2mCMC2
Eq 3: x1+x2=1

The Attempt at a Solution


[/B]
1. invert Eq 2 and equate with Eq 1.
2. eliminate x2m using the fact that x2m=(1-x1m)
3. Rearrange..

I get to the following and don't know how to get closer to the solution. I've got a feeling I'm missing something obvious.

x1m=[(CMC1/x1)+(CMC2/x2)-CMC2)]/(CMC1-CMC2)

Please help!

Thank you in advance.
 
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jajajujujojo said:
1. Please could you give me a hand with deriving the following equation:

x1m=(x1CMC2)/(x1CMC2+x2CMC1)

Homework Equations



Eq 1: 1/CMC=x1/CMC1+x2/CMC2
Eq 2: CMC=x1mCMC1+x2mCMC2
Eq 3: x1+x2=1

The Attempt at a Solution


[/B]
1. invert Eq 2 and equate with Eq 1.
2. eliminate x2m using the fact that x2m=(1-x1m)
3. Rearrange..
Please show the work that you have done. Telling us a result you have gotten to does not help us understand where you might have gone astray.
jajajujujojo said:
I get to the following and don't know how to get closer to the solution. I've got a feeling I'm missing something obvious.

x1m=[(CMC1/x1)+(CMC2/x2)-CMC2)]/(CMC1-CMC2)

Please help!

Thank you in advance.
 
What are you ultimately trying to solve for?

You can solve for x1 and x2 immediately by working exclusively with eqns. 1 and 3. The equations are linear.

Chet
 
the fact that x2m = ( 1 - x1m )
Is based on what, exactly ?

And: you say you want help in deriving these equations. You mean solving ?
 

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