## Differential vs Integrated

$\frac{d[R]}{dt}=-k[R]^{2}; \frac{1}{[R]}=kt + \frac{1}{[R]_{0}}; t_{\frac{1}{2}}=\frac{1}{k[R]_{0}}$

Michelle Steinberg2J
Posts: 73
Joined: Fri Sep 29, 2017 7:04 am

### Differential vs Integrated

I have a general question as to when to know to use the differential or integrated equations for first, second, or zero order.

Thanks.

Luke Bricca 1H
Posts: 30
Joined: Fri Sep 29, 2017 7:06 am

### Re: Differential vs Integrated

Usually the question tells you if a reaction is first, second, or zero order, but if you need to calculate it you can by comparing the rates of separate equations and how reactant concentrations change with them.

You use the differential rate law when determining a rate of an equation (either a general rate or a rate at a specific time (t)) and the integrated rate law for finding a specific concentration and deriving the half-life formula.

ZoeHahn1J
Posts: 63
Joined: Sat Jul 22, 2017 3:01 am
Been upvoted: 1 time

### Re: Differential vs Integrated

Since differential would be something like rate=k[A]^x[B]^y[C]^z, we can use it to:
calculate the rate given k, concentration of reactants, and order of reactants
calculate the rate constant k given rate, concentration of reactants, order of reactants
etc.
We cannot use it to calculate a new rate given an initial rate, or to calculate the time taken to get from x amount of reactant to y amount of reactant; we must use the integrated rate laws for this. Also, use integrated rate laws to find k given t, [A], and [A] initial.

Veronica Rasmusen 2B
Posts: 49
Joined: Sat Jul 22, 2017 3:01 am

### Re: Differential vs Integrated

You would use differential rate law if you need to find the rate given certain concentrations.
Integrated rate law is used for finding concentrations given a certain time, or finding a final concentration from an initial concentration.

Shreya Ramineni 2L
Posts: 50
Joined: Fri Sep 29, 2017 7:07 am

### Re: Differential vs Integrated

If you are given the concentration and time, use integrated rate law.