## unique rate

$aR \to bP, Rate = -\frac{1}{a} \frac{d[R]}{dt} = \frac{1}{b}\frac{d[P]}{dt}$

josmit_1D
Posts: 107
Joined: Fri Aug 09, 2019 12:17 am

### unique rate

why do we use fractions instead of whole number coefficients in the unique rate?

Sydney Myers 4I
Posts: 100
Joined: Fri Aug 09, 2019 12:17 am

### Re: unique rate

We use the coefficients to make fractions because the relationship is inverse. That's why we need the fraction.

Ashley Wang 4G
Posts: 103
Joined: Wed Sep 11, 2019 12:16 am

### Re: unique rate

Hi!

I'm not sure what you mean... If you're referring to why we would write the unique rate for 2NO2 --> 2NO + O2 as

-(1/2) d[NO2]/dt = (1/2) d[NO]/dt = d[O2]/dt instead of - d[NO2]/dt = d[NO]/dt = 2 d[O2]/dt

It's just a convention because it allows you to easily determine the unique rate just from the balance equation, by relating the coefficient in the rate law as 1 over the stoichiometric coefficient. In this case, if you were given 2NO2 --> 2NO + O2 you can then easily write the rate law without having to think about how the rate at which [NO2] decreases is related to the rates at which [NO] and [O2] increase

I hope this helps!

Frank He 4G
Posts: 50
Joined: Tue Nov 12, 2019 12:19 am

### Re: unique rate

A form of the equation with whole numbers exists as well, but we usually have the form with fractions since it neatly matches up with the stoichiometry of the balanced reaction. That is, if we have a reaction where we know the amount of species X changes at 1/2 the speed of another species Y, or (1/1)d[X]/dt = (1/2)d[Y]/dt, then we know that in the balanced reaction, there is a 2 in front of Y and nothing (since it's just 1) in front of X. The stoichiometry are just the denominators of the fractions.

If we used whole numbers instead, the equation would be 2d[X]/dt = 1d[Y]/dt, which is a little bit more confusing in terms of how you'd write the balanced equation, especially if you have more than 2 species involved.