## Half Life

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

Lisa Tang 1C
Posts: 62
Joined: Fri Sep 29, 2017 7:05 am
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### Half Life

I have a general question about the half life of reactions. Why does the half life of a zero order and second order reaction depend on the initial concentration of the reactant, but the concentration of a first order reaction does not? Can someone explain this conceptually?

Curtis Tam 1J
Posts: 105
Joined: Thu Jul 13, 2017 3:00 am

### Re: Half Life

Conceptually I am not totally sure but mathematically, the half life of first order reactions only include the term k, which is the reaction constant. I think if you look at how they plot different concentrations of the reactant versus their respective initial reaction rates, you'll notice that they form a straight line. So at no matter what initial concentration you start at, the graph will always take on the same form y=kx or y=kx+c. For zero and second order reactions, you'll notice the graphs take on different shapes based on the initial condition, so ultimately the half life does depend on the initial condition.

Kaileigh Yang 2I
Posts: 49
Joined: Sat Jul 22, 2017 3:00 am

### Re: Half Life

Also, if you simply plot the half life reactions for all three types of reactions you can see that in the zero order reaction and the second order reaction, the slope changes as the concentration changes, whereas in the first order reaction graph, the length of the half-life remains at a constant, independent of the concentration.