## General Rate Law

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

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Daniel Yu 1E
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Joined: Sat Aug 24, 2019 12:15 am

### General Rate Law

What is a general rate law? What is the equation for a general rate law? Is it k[a]^m*[b]^n...? How do you interpret this?

Ryan Yee 1J
Posts: 101
Joined: Sat Aug 17, 2019 12:16 am

### Re: General Rate Law

The general rate law is the equation that you have listed, derived from rate=(-1/a)(d[A]/dt)=(1/b)(d[B]/dt) where a and b are stoichiometric coefficients for reactant A and product B. In the equation you mentioned, k is the rate constant, which is determined experimentally, and the concentrations [A] and [B] are raised to powers m and n which, when added up, form the order of the reaction. m and n are determined by changing the concentration of the reactant. If changing the reactant concentration affects rate linearly, then the exponent is 1. If changing the reactant concentration affects rate quadratically, then the exponent is 2. If changing the reactant concentration doesn't affect rate, then the exponent is 0

Chris Tai 1B
Posts: 102
Joined: Sat Aug 24, 2019 12:16 am

### Re: General Rate Law

We can use the general rate law to determine several different items of general importance.
The first of these includes a quite fantastical situation in which we are called to determine the order of such a reaction, in which we can simply take the however-many exponents and add up their given values, for instance adding up a+b+c if the rate late is given to be something such as rate law = k[A]^a[B]^b[C]^c, or perhaps even add up the values of a+b when the rate law = k[A]^a[B]^b, or perhaps even just keep it at a if the rate law = k[A]^a. Once we have a value derived from our additions of such derivative values, we can then determine the order of the reaction; if the result of our additions is one, then this is a first order reaction; if it is two, this a second order reaction; if it is three, this is a third order reaction; if it is four, this is a fourth order reaction; if it is five, this is a fifth order reaction, if it is six, this is a sixth order reaction, and so on and so forth.
The second of these amazing insights that we can glean from the existence of such a beautiful rate law is that of the rate constant, which is a value that is constant at a given temperature that will, unless under heavy duress or extenuating circumstances, be provided to you on any respectable exam. This rate constant, denoted by the singular letter k as in kangaroo, will help us to determine the rate at which some given reaction is occuring at any moment in which we are provided with three givens of the concentrations of the items that are present in the rate law.
Hope this was helpful!

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