Why Multiply the Rate Equation by the Coefficient?

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Discussion Overview

The discussion revolves around the application of stoichiometric coefficients in rate equations for chemical reactions. Participants explore the reasoning behind multiplying the rate of a reactant or product by its coefficient and the implications of this practice on the consistency of reaction rates observed for different substances involved in a reaction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about why the rate equation is multiplied by the stoichiometric coefficient and questions if this is merely for convenience.
  • Another participant requests an example to clarify the context of this practice.
  • A participant provides a link to a general definition, highlighting the multiplication of rates by reciprocal coefficients.
  • It is suggested that this method allows for consistent observation of reaction rates across different reactants and products.
  • One participant proposes that the adjustment is indeed for convenience, aiming for a one-to-one rate representation.
  • A specific reaction example is discussed, where the decomposition of AB to form A2 and B2 is analyzed, illustrating how the rates of consumption and production differ based on stoichiometry.
  • Questions arise regarding the consistency of rates when considering the moles of products formed relative to reactants consumed.
  • Clarification is sought on the relationship between the rate of consumption of AB and the rate of production of A2, leading to a discussion about the calculation of these rates using stoichiometric coefficients.

Areas of Agreement / Disagreement

Participants appear to agree on the concept that stoichiometric coefficients are used to maintain consistency in the rates of different substances in a reaction. However, there is ongoing uncertainty and debate regarding the implications of this practice and the calculations involved.

Contextual Notes

Some participants express difficulty in calculating rates based on the definitions provided, indicating potential limitations in their understanding of the relationship between concentration changes and time in the context of stoichiometric coefficients.

Bashyboy
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Hi,

I am reading about rates of reactions, and I am confused about why we multiply the rate equation of a particular product or reactant by its respective coefficient, only taking the reciprocal of it. Could someone explain to me why this is done? Is it done merely out of convenience?
 
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Please show an example. In what context was it done?
 
The general definition is in the given link: http://s906.photobucket.com/albums/ac261/Bashyboy/?action=view&current=2012-01-19_16-12-18_579.jpg

You should see in the highlighted region that the multiply each rate of each reactant/product by its respective reciprocal coefficient.
 
This way it doesn't matter which substance you observe - for a given reaction reaction rate is identical for every reactant and product.
 
So then it is done out of convenience? We divide it by its stoichiometric coefficient so that we have a one-to-one rate?
 
Like Borek said, it's done so you can look at the rate of consumption or production of any particular component and the answer will remain the same.

If AB decomposes to form A2 and B2, you have the following reaction:

2AB → A2 + B2

The rate at which AB decomposes will be twice as fast as the formation of the products. If you just looked at the raw rate of decomposition of AB or of production of either product, it would be inconsistent.
 
I'm sorry, could you possibly explain why it would be inconsistent?
 
How many moles of A2 will appear while 1 mole of AB is consumed? It happens in the same time - is the ratio of number of moles to time constant?
 
Oh, one mole of A2 will appear.
 
  • #10
Borek said:
How many moles of A2 will appear while 1 mole of AB is consumed?

Bashyboy said:
Oh, one mole of A2 will appear.

No, not 1 mole.
 
  • #11
Is it 1/2? And is that where the inconsistency is?
 
  • #12
Yes, 1/2 mole of A2.

Now, let's assume it happened in - say - 1 minute. Rate of the AB consumption was 1 mole per minute, and rate of A2 production was 1/2 mole per minute. Same reaction - and potentially two different rates. Can you calculate both rates using the definition with stoichiometric coefficients?
 
  • #13
Well, Borek, I just attempted to calculate what you told me to do, and, unfortunately, I could not. To calculate it I need a change in concentration over a change in time, correct; so would that change in time 0 min - 1 min?
 

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