## second order half life calculation

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

505166714
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### second order half life calculation

For exercise 15.35 on the 6th edition book, can I use the half-life and multiply by 4 to find the time for the reactant to become 1/16 of the original amount in a second-order reaction?
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LilyL1C
Posts: 24
Joined: Fri Sep 28, 2018 12:20 am

### Re: second order half life calculation

No you cannot. If you do one half life, you'll end up with half of the initial concentration. If you take another half life, you get 1/4 of the initial concentration. Another half life, and it's 1/8. One more half life, and you finally get 1/16. So it was 4 half lives, which is (1/2)^4 = 1/16. You need to take the half life to the 4th power, not multiply by 4.

For part b, you need to square the half life because (1/2)^2 = 1/4.

And for part c, 1/5 is not a multiple of 1/2, so you need to go back to the original 1/[A] = kt + 1/[A(initial)] and plug in [A]=1/5[A(initial)], and solve for an equation.