Solving Equilibrium Reactions with a Given KC and Initial Concentrations

[Lancelot59]

Homework Statement

1. A flask initially contains only NOBr gas. Once heated to a temperature T, 34.0 % of the original gas decomposes via the following equation to give a total pressure of 0.25 atm at equilibrium:

2NOBr_(g) $$\Leftrightarrow$$ 2NO_(g) + Br2_(g)

Given a K_C of 3.94 x 10-4 I need to find the temperature. I've already gotten the K_P and initial concentration as being 9.66x10^-6 and 0.213675 atm respectively. I didn't see any equations for this in my notes...so how can one go about this business?

 

[Borek]

You have to calculate number of moles of all gases present. Seems to me like 34% and Kp should be enough for that, just remember that pressure is directly proportional to n.

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methods

 

[Lancelot59]

Well I can assume that it's a total of 1L for volume. I do have the partial pressures for all three gasses, so I can probably just work from those. I'll post again once I try this out.

 

[Lancelot59]

Ok, I got nowhere.

I used PV/RT = n to try and get the mols, which failed for obvious reasons.

So I tried to use the K_c to solve for it:

3.94X10^-4 = [Br2][NO]² / [NOBr]²

Can I just throw X in for each of the concentrations and solve? If so then x is equal to the K_c...that seems wrong.

 

[Borek]

If there were initially n moles of NOBr, how many moles will be present after 34% reacted? How many moles of both products? Can you build Kp from these values?

Hm, now I started to wonder if you have enough information for that approach, but it is 2 am here and my thinking is a little bit blurred. CU tomorrow.

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[Lancelot59]

From other parts of the question, I calculated the initial pressure of NOBr, as well as the final equlibrium pressures of all the gasses, as well as the Kp.

 

[Borek]

What 'other parts'?

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[Lancelot59]

Oh, there was an A and B part to that question. This final one I'm stuck on is Part C

 

[Lancelot59]

The initial pressure of NOBr was .214 atm, the K_p I found was 9.66x10^-6.

 

[Borek]

Was there any other data given in these 'other' parts?

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[Lancelot59]

1. A flask initially contains only NOBr gas. Once heated to a temperature T, 34.0 % of the original gas decomposes via the following equation to give a total pressure of 0.25 atm at equilibrium:

2NOBr(g) $$\leftrightarrow$$ 2NO(g) + Br2(g)

a) Determine the original pressure of NOBr in the flask.
b) What is the value of Kp at this temperature T?
c) If the value of Kc at this temperature T is 3.94 x 10-4, determine the temperature T.

That is the whole question.

 

[Borek]

http://oxygen.chem.uidaho.edu/ifcchem1123/relating_kc_and_kp.htm

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[Lancelot59]

That formula is on my formula sheet...ah well. So if $$\Delta$$n is 1 then the answer is a decimal...

9.66x10^-6 = 3.94x10^-4(0.08206 T)¹

T=.298778534 ^oK

Is that right?

 

[Borek]

Can't be - 0.3K is so close to absolute zero you can be sure all substances will be liquid, not gaseous. Even helium.

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[Lancelot59]

So what went wrong? I see nothing else that failed. My calculations for the K_p and initial pressure look right.

Can you check my answers please?

 

[Borek]

Pressure looks OK, but Kp seems way too small to me.

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methods

 

[Lancelot59]

Ugh...lemme re-run it.

I ended up with 9.65x10^-6 again...

 

[Borek]

Show.

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[Lancelot59]

K_p = [Br₂][NO]² / [NOBr]²

K_p = (0.003638)(0.007275)² / (0.14124)²

K_p = 9.66 x10^-6

 

[Borek]

No, where did you get these values from.

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methods

 

[Lancelot59]

The preceding part using an ICE table and some math.

Hopefully this attachment can get approved soon...

It's part 1a.

 

[Borek]

Unfortunately it is 1 am here and tomorrow is Monday, so I have to go to sleep.

ICE table sounds OK, but values are wrong. From the data given in question [NO]/[NOBr] = 0.34/(1-0.34) - they should be comparable when it comes to value, you have them differ almost 100 times.

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[Lancelot59]

I don't get it...

 

[Borek]

Show your ICE table and how you calculated - for example - 0.007275.

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[Lancelot59]

I re-did it this morning with some hints from my Prof:

2NOBr $$\leftrightarrow$$ 2NO + Br₂

I 2x / 0 / 0
C -2x(.34) / +2x(.34) / +.34x
E 2x(.66)/ +2x(.34) / .34x

The total pressure was .25 atm, so:

0.25 = P_NOBr + P_NO + P_Br

0.25 = 2x(.66) + 2x(.34) + .34x

X = .02136752137

Then I just plugged it into the expression for each gasses concentration, and shoved those values into the K_p equation to get .1926125012.

That I plugged into K_p=K_c(RT)^$$\Delta$$n to get a temperature of 5957.399661^oK... Is something wrong here?