## 15.35

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

Sabah Islam 1G
Posts: 50
Joined: Sat Jul 22, 2017 3:01 am

### 15.35

The solutions manual states that the equation for the half-life of a 2nd order reaction must be obtained, being [A]t=[A]0/1+[A]0*kt. How was this equation obtained/derived?

Vasiliki G Dis1C
Posts: 53
Joined: Fri Sep 29, 2017 7:04 am

### Re: 15.35

The equation for the half-life of a second order reaction is t1/2=1/k[A]o. This is derived from the integrated rate law for a second order reaction. The equation is 1/[A]=kt+1/[A]o, and we know that at t=t1/2 [A]=1/2[A]o. Therefore, 1/[A]=2/[A]o. When you plug this into the equation, you get 2/[A]o=kt1/2 + 1/[A]o. You move the 1/[A]o to the other side and get kt1/2=1/[A]o, or t1/2=1/k[A]o. Hope this helps!