## Differential v Integrated rate law

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

McKenna_4A
Posts: 115
Joined: Sat Aug 24, 2019 12:18 am

### Differential v Integrated rate law

What is implied when we say that an integrated rate law depends on time? Could the differential not be written as a function of time?

Sally Qiu 2E
Posts: 105
Joined: Fri Aug 30, 2019 12:18 am

### Re: Differential v Integrated rate law

i believe if you tried to write the differential rate law as a function of time, you would have to manipulate it into the integrated rate law. the differential rate law equation as is relates rate to concentration

Diana Chavez-Carrillo 2L
Posts: 122
Joined: Fri Sep 28, 2018 12:18 am

### Re: Differential v Integrated rate law

The integrated rate law tells us how much reactant concentration changes over time. The differential rate law tells us the rate as a function of concentration. In other words, it is the overall reaction as a function of reactant concentration. The differential rate law can help us figure out the integrated rate law.

Matt F
Posts: 100
Joined: Sat Aug 17, 2019 12:17 am

### Re: Differential v Integrated rate law

The integrated rate law is the differential rate law written as a function of time. In other words, rather than rate being a function of concentration, rate is a function of time. This can be seen with the graphs of zero order, first order, and second order reactions, in which [A], ln[A], and 1/[A] are plotted against time, giving linear slopes (values for k)