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- Jun 13th 2011, 02:41 PM #1
## NO2 decomposes into NO and O2.

**1.****At high temperatures, nitrogen dioxide,***NO*2, decomposes into*NO*and*O*2. If*y*(*t*) is the concentration of*NO*2 (in moles per liter), then at 600º*K*,*y*(*t*) changes according to the reaction law*dy*/*dt*= −.05*y*2 for time*t*in seconds.

**A.****Express***y*in terms of*t*and the initial concentration*y*o.

**Equation of y in terms of t and initial concentration y****o**

*Solve for constant of integration.*

Solve for differential equation.

Hello, I can't seem to find the proper method to set up this problem. The chem. stuff is slightly misleading and I can't seem to come up with anything satisfying.**Any help on setting this up would be appreciated!**

The one below is merely an extension of the aforementioned question, when I figure out the one above it shouldn't be too difficult.

**B.****Assuming that the concentration of***NO*2 is twice as high at*t*= 20 seconds as it is at 100 seconds, find the exact initial concentration of the*NO*2. Reminder: “Exact” means no calculator numbers.

**Exact initial concentration y****o**

- Jun 13th 2011, 04:11 PM #2

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- Jun 13th 2011, 05:06 PM #3
## Re: NO2 decomposes into NO and O2.

Thanks!

I had a similar setup but I made some err on the orientation. Moreover I was wondering as to how this equation can be set up to include Y sub-zero(the initial concentration) and again how to utilize the temperature so nicely conceded in the problem. I'm having issue's weaving all this together .

- Jun 13th 2011, 05:16 PM #4

- Jun 13th 2011, 05:43 PM #5
## Re: NO2 decomposes into NO and O2.

When I try solving for dy/dt=-.05y^2 I yield 20/Y=t. And isolating for Y I get Y(x)=20/t + the constant. However in this situation I can't plug in t=0 as it would be undefined. I'm probably messing up somewhere, thanks for your guys patience!

- Jun 13th 2011, 06:56 PM #6

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- Jun 13th 2011, 07:29 PM #7

- May 1st 2012, 07:33 PM #8

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## Re: Need help on setting up differential equation.

I'm sorry for necroing an old thread but I am currently working on the same problem and was also thrown off by the chemistry presented in the problem and I was able to follow but do they want the y

_{0}to come from y(0) = 1/(.05t + C) and solve for C yielding C = 1/y_{0}so you would end up with y(t) = 1/(.05t + 1/y_{0})