## 7B.13

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

Ellis Song 4I
Posts: 102
Joined: Thu Jul 11, 2019 12:17 am

### 7B.13

The half-life of A in a second-order reaction is 50.5 s when [A]0 = 0.84 mol/L. Calculate the time needed for the concentration of A to decrease to (a) one-sixteenth (b) one-fourth; (c) one-fifth of its original value.

Can someone please explain this problem

Brooke Yasuda 2J
Posts: 102
Joined: Sat Jul 20, 2019 12:17 am

### Re: 7B.13

One way you could do this problem is by using the equation for a second order half life reaction and calculating the K value. With this you can then use the integrated rate law for a second order reaction to find the time needed to reach the concentration that is being asked.

Long Luong 2H
Posts: 51
Joined: Thu Sep 19, 2019 12:16 am

### Re: 7B.13

What I did was find k using the second order half-life equation. Following that, I divided the original original concentration by 16, 4, and 5 for a), b), and c). With both initial and final concentrations and k, I plugged those values into the second order integrated rate law equation to find t.