Why Multiply the Rate Equation by the Coefficient?

Click For Summary
SUMMARY

The discussion centers on the necessity of multiplying the rate equation of a chemical reaction by the stoichiometric coefficients of reactants and products. This method ensures that the reaction rates are consistent across different substances involved in the reaction. For example, in the reaction 2AB → A2 + B2, the rate of AB decomposition is twice that of A2 formation, highlighting the importance of using coefficients to maintain a one-to-one rate comparison. This approach is not merely for convenience; it provides a clear framework for understanding the relationship between reactants and products in terms of their rates of consumption and production.

PREREQUISITES
  • Understanding of chemical reaction rates
  • Familiarity with stoichiometry
  • Basic knowledge of molarity and concentration changes
  • Ability to interpret rate equations
NEXT STEPS
  • Study the concept of stoichiometric coefficients in chemical kinetics
  • Learn how to derive rate laws from balanced chemical equations
  • Explore the relationship between concentration changes and reaction rates
  • Investigate the use of the rate equation in different types of chemical reactions
USEFUL FOR

Chemistry students, educators, and professionals involved in chemical engineering or reaction kinetics who seek to deepen their understanding of reaction rates and stoichiometric relationships.

Bashyboy
Messages
1,419
Reaction score
5
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?
 
Chemistry news on Phys.org
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?
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
4K
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
Replies
7
Views
3K
  • · Replies 9 ·
Replies
9
Views
6K
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 8 ·
Replies
8
Views
5K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K