## Rate constant and half life

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Amy Lefley 1J
Posts: 60
Joined: Fri Sep 28, 2018 12:15 am

### Rate constant and half life

Why does a higher rate constant mean a shorter half life?

Gillian Murphy 2C
Posts: 30
Joined: Fri Sep 28, 2018 12:22 am

### Re: Rate constant and half life

It goes through the reaction faster, so it will go down to half it's original concentration at a faster speed, making it take a shorter amount of time to do so

josie 1C
Posts: 18
Joined: Fri Sep 28, 2018 12:19 am

### Re: Rate constant and half life

the half life is the time it take for a reactant to lessen its concentration by 1/2. the faster (or higher) the rate of reaction, the less time it will take for the reactants to reach 1/2 of their original concentration.

Ray Guo 4C
Posts: 90
Joined: Fri Sep 28, 2018 12:15 am

### Re: Rate constant and half life

Because $t_{1/2}=(ln2)/k$ for first-order reactions.