Why can the rate of one reactant reveal the whole reaction rate?

[Chemer]

Hi,
Can anyone explain me that in chemical kinetics, the rate of reaction can be determined by just determining the rate of any reactant of product involved in the reaction, but how? How the rate of change of concentration of just one specie can tell you about the whole reaction?
I found the example of fermentation of sucrose at a site and I couldn't understand this point:
" The coefficients show us that the reaction produces four molecules of ethanol and four molecules of carbon dioxide for every one molecule of sucrose consumed. As before, we can find the reaction rate by looking at the change in the concentration of any reactant or product. In this particular case, however, a chemist would probably use the concentration of either sucrose or ethanol because gases are usually measured as volumes and, the volume of CO2gas formed will depend on the total volume of the solution being studied and the solubility of the gas in the solution, not just the concentration of sucrose."
I can't understand the CO2 point, how Co2 volume depends on volume of solution and why ignoring it wouldn't affect the rate determination?

 

[Borek]

How the rate of change of concentration of just one specie can tell you about the whole reaction?

Reaction follows stoichiometry, so if you know change in the amount of any reagent, you can easily calculate how much of every other reagent involved was produced/consumed.

how Co2 volume depends on volume of solution

Again, stoichiometry. The more the solution, the more gas is produced.

 

[Chemer]

Can you give me an example? How just one reactant concentration change is enough to calculate reaction rate? If you have two reactants forming two or more products?

 

[Borek]

A + 2B -> 3C + 4D

Let's say, 1 second passed, and the amount of A consumed was 1 mole.

Apparently, reaction rate for A is 1 mole per second.

How many moles of B were consumed?

What is the reaction rate for B?

How many moles of C were produced?

What is the reaction rate for C?

 

[Chemer]

Is it based on:
Rate of consumption of A = Rate of consumption of B and are equal to rate of production of C= rate of production of D?
Then the reaction rate of B will also be 1mol/sec? Confused!

 

[Quantum Defect]

Is it based on:
Rate of consumption of A = Rate of consumption of B and are equal to rate of production of C= rate of production of D?
Then the reaction rate of B will also be 1mol/sec? Confused!

The stoichiometry of the reaction tells you how many moles of B get chewed up per mole of A. If one molecule of A reacts, two molecules of B must have also reacted, no? If the rate of consumption of A is 1 mole per second, how many moles of B are consumed in one second?

 

[Chemer]

But how this explain that the reaction rate can be found by just looking at the rate of any specie involved in the reaction?
And if just one reactant is enough to determine the rate of the reaction, then why we use the product of concentration of reactants in rate equation?

 

[Quantum Defect]

But how this explain that the reaction rate can be found by just looking at the rate of any specie involved in the reaction?
And if just one reactant is enough to determine the rate of the reaction, then why we use the product of concentration of reactants in rate equation?

You are confusing two things, which are often confused by people. The rate versus the rate law.

Rate = How fast reactants (or products) are disappearing (or appearing). Rate law = expression that relates the rate to concentrations.

Once you know how fast one reactant is disappearing (the rate), you can use the stoichiometry to calculate how fast other reactants are disappearing, as well as how fast products are forming.

Determining a rate law is much more difficult.