## 15.35

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

ClaireHW
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Joined: Fri Sep 29, 2017 7:07 am
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### 15.35

How does one go about setting up the equations used for this question step by step?

Thanks!

(Claire Woolson Dis 1K)

Cali Rauk1D
Posts: 51
Joined: Fri Sep 29, 2017 7:03 am

### Re: 15.35

use the half life equations

Nicole 1F
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Joined: Fri Sep 29, 2017 7:05 am

### Re: 15.35

You would use the second order half life equation, which is t1/2= 1/k[A]initial to solve for k. Then plug your values into 1/[A] = kt + 1/[A]initial to find the time.

Xin He 2L
Posts: 38
Joined: Fri Sep 29, 2017 7:05 am

### Re: 15.35

You use the half-life equation for second order reactions. You then just plug the values into the equation 1/A=kt+1/A0, which can be rearranged into (1/A+1/A0)/k=t to find out the time needed.

Brandon Fujii 1K
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### Re: 15.35

We cannot simply multiply the half life by a factor of 4 because the half life of a second order reaction is reliant on the initial concentration of the reactant (while the first order half life reaction only relies on the equilibrium constant.)

Second order half life equation: 1/k[A]o
First order half life equation: ln2/k

Gurkriti Ahluwalia 1K
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### Re: 15.35

why is the fraction subtracted from 1 when we asking for the time for the concentration to reach that value of the initial? subtracting implies that it is the remainder after the said fraction gets used up in the reaction.

Timothy Kim 1B
Posts: 62
Joined: Fri Sep 29, 2017 7:04 am

### Re: 15.35

Use the half-life equation for the second-order reaction. then substitute A for the fraction of A naught.