Equilibrium concentrations?

Question

Carbonyl bromide, COBr2, decomposes to CO and Br2 by the following simple, gas-phase, reaction:

COBr2(g) ↔ Br2(g) + CO(g)

If a 2.5 liter flask is found to contain 0.063 mol of COBr2 at equilibrium, what will be the equilibrium concentrations of CO and Br2 in the same flask? The equilibrium constant for this reaction is Kc = 0.190. Enter your answer in scientific notation.

Please help, if possible could you show me the steps on how to do this.

Thanks

Answer 1

well hmm..

I think CO and Br2 will have the same concentrations since they have the same coefficient (1)

ok so we have .190=Kc=[Br2][CO]/[COBr2] as our expression.

ok, we said that [Br2]=[CO] so let's call that concentration X, so then you'd have

(X)(X)/[COBr2] or just X^2 / [COBr2]

you know your Kc and your [COBr2] (don't forget that it's concentration and you'll need to do moles over liters for the molarity)

so use algebra to solve for X^2 and then square root that for X , and    X=[CO]=[Br2].  I also got .069 or whatever it was.

______

it's hard to use an ICE chart here because we don't know the intial concentration.  BUT they will all probably be +X and -X

i'm not exactly sure.  is this a book problem?  because the book might have answers for odd# problems in the back.

oh wait hold on hold on hold on

if it were

COBr2:  i=1, C= -X and E=1-X=.063/2.5

Br2 AND CO are i=0, C=+X and E=X

i mean, just saying if 1 was the intial, well, it doesn't even matter since we know what 1-X = .063/2.5 we don't need it to solve for X

oh god i'm so confused.

Answer 2

COBr2(g) ↔ Br2(g) + CO(g)

Kc = [Br2] [CO] / [COBr2]

Initially, there is only COBr2 with a concentration of 0.0252M.

At equilibrium the concentrations of the products are each x and the concentration of COBr2 is 0.0252 - x.

Kc = x^2 / (0.0252-x) = 0.190

Since Kc is relatively large, we can't make the assumption that 0.0252 - x = 0.0252, and so we will use a bit more algebra.  Did you hear that???  Making the "assumption" violates the 5% rule.  You can't make the assumption that x is small compared to 0.0252, because it's not.

x = 0.0225

[Br2] = [CO] = 0.0225M

[COBr2] = 0.0027 M

Note:  Ok, Ok. If  you must know, I used the "solver" function on my TI-86, but we could have used some algebra.  Preferably, you should rearrange it into a quadratic.  You will get two roots, but only one of them "will make any sense", since in this case the other root is negative.

======= Follow up =======

If you do make the assumption that x is small compared to 0.0252, then you will get an answer that may satisfy the math, but it won't make any sense from a chemistry standpoint.  Always look at your answer and ask, "Is this reasonable?"

COBr2(g) ↔ Br2(g) + CO(g)

Is it reasonable to start with 0.0252 mole per liter of COBr2 and end up with 0.069 moles per liter of Br2?  How could you get more moles of Br2 than you had of COBr, particularly since they are in a 1 to 1 ratio?  You see, 0.069 is not a reasonable result.

Answer 3

Kc= [Br2] [CO] "over" [COBr2]

(Br2) [CO2]= [COBr2] x Kc

X^2= .063mol X / 2.5 L  "multiplied by" 190