What Temperature Makes the Reaction Rate Constant One Thousand Times Smaller?

[fileen]

Homework Statement

The activation energy for the reaction
N2O(g) --> N2(g) + O(g)
is 250 kJ/mol. If the rate constant is 3.4 s–1 at 1050 K, at what temperature will the rate constant be one thousand times smaller?

The correct answer is : 846 K

Homework Equations

Arrhenius equation:
ln{k2/k1} = Ea/R {(1/T1) - (1/T2)}

The Attempt at a Solution

Ok, I can use this equation to find other variables, and I know that I am making some sort of calculator error or something, and I know its probably the stupidest of mistakes. I am trying to study for an exam, and I am aware that this probably won't even show up, but its driving me crazy that I continually get the wrong answer, and I am off by soooo much.it looks simple, plug in the numbers and out pops an answer but I just can't get it.

T1 =1050K
K1 = 3.14/s
Ea = 250KJ
K2 = 3.14E3

I have tried this a number of ways and its only confused me more. Do I change KJ to J? I know Temp. should be in Kelvin, what about R, could I be using the wrong one? I can't look at this question any longer, any help would be much appreciated.
(when I emailed my T.A. he emailed me back to inform me that I won't fail the exam just because I don't know how to do this question... that's real helpful!)
Thank you,
M

 

[Barfolumu]

Which version of the gas constant are you using, and what are the units on it? You could be using the wrong one, but I don't know which one you're using.

Also, you're looking for temperature, yes? So what units should the gas constant possesses so that you find temperature?

Admittedly, temperature in the Arrhenius equation is the hardest to dig out algebraically. It may help if you first find what T2 is equal to, then use your calculator with the numbers given. I prefer to work with variables.

 

[fileen]

Ive tried with 8.3145J/(K*mol) with no luck. Its a good idea to work backwards, I think Ill try it. A friend suggested a different version of the equation : K = A exp (- Ea/RT) she said to solve for A with K1 and T1, and then using that A solve for T2 with K2. I am not sure if this is a good equation though, can I use this equation and depend on it to get the right answers every time. Also, what is A?

 

[Barfolumu]

Just as a general rule, I wouldn't suggest using an equation that you don't understand.

The equation you posted is the Arrhenius equation. The one you posted in your first post is just it, after some mathematical manipulation. "A" refers to the collision frequency. The method you posted may work, may not, because A is temperature dependent, but it can be treated as a constant over a fairly large temperature range.

A modification to the Arrhenius equation that may be easier for you, if you don't like manipulating the other one: ln k1/k2 = Ea/R(T1-T2/T1*T2).

And you're using the correct gas constant. but remember that your units need to cancel to equal T.EDIT: I just noticed something with the equation you posted: it should read k =Ae^(-Ea/RT)
Just wanted to make sure that you weren't raising A to the power of (-Ea/RT).

 

[fileen]

Thank you for all your help, analyzing the units was a big help. I do all the time when I'm working through physics problems, but I always forget I can do that with chemistry. Your equation was very helpful also. My trouble was with mathematical manipulations more than anything.