Why Multiply the Rate Equation by the Coefficient?

In summary, the rate equation of a particular product or reactant is multiplied by its respective reciprocal coefficient in order to have a consistent rate of consumption or production for all reactants and products in a given reaction. This is done out of convenience and allows for the calculation of the rate using stoichiometric coefficients. This can be seen in an example where the decomposition of AB to form A2 and B2 has a rate that is twice as fast as the formation of the products. Without taking into account the stoichiometric coefficients, there would be inconsistencies in the rates of consumption or production.
  • #1
Bashyboy
1,421
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?
 
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  • #2
Please show an example. In what context was it done?
 
  • #3
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.
 
  • #4
This way it doesn't matter which substance you observe - for a given reaction reaction rate is identical for every reactant and product.
 
  • #5
So then it is done out of convenience? We divide it by its stoichiometric coefficient so that we have a one-to-one rate?
 
  • #6
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.
 
  • #7
I'm sorry, could you possibly explain why it would be inconsistent?
 
  • #8
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?
 
  • #9
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?
 

Related to Why Multiply the Rate Equation by the Coefficient?

1. What is the rate of a chemical reaction?

The rate of a chemical reaction is the speed at which the reactants are converted into products. It is typically measured in terms of the change in concentration of a reactant or product per unit time.

2. How is the rate of a chemical reaction determined?

The rate of a chemical reaction can be determined by measuring the concentration of a reactant or product at different points in time and calculating the change in concentration over a specific time interval. This can be done experimentally or mathematically using the rate law equation.

3. What factors affect the rate of a chemical reaction?

The rate of a chemical reaction can be affected by several factors, including temperature, concentration of reactants, surface area, presence of a catalyst, and the nature of the reactants and products. These factors can either increase or decrease the rate of a reaction.

4. How does temperature affect the rate of a chemical reaction?

Increasing the temperature generally increases the rate of a chemical reaction. This is because higher temperatures provide more energy for molecules to collide and react, leading to a faster rate of reaction. However, extreme temperatures can also denature enzymes and slow down reactions.

5. What is a catalyst and how does it affect the rate of a chemical reaction?

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. It works by lowering the activation energy required for the reaction to occur, making it easier for reactant molecules to collide and react. This results in a faster rate of reaction. Catalysts can also be reused, making them more efficient and cost-effective in industrial processes.

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