If someone could check my work on this, I'd appreciate it:
Number fits the data given, but is an insult to the logic - 8000M concentration doesn't make sense.
That's what made me question the answer myself. 8000 mol/L sounds ridiculous.
I quadruple checked the work though, and put the 8.8x10^3 value back into the original equilibrium expression, and it does come out to 1.60773043 × 10^(-2) (2 s.f. in that, as well), so I guess that it's correct. *shrug*
Well at least congratulations on realizing the answer was ridiculous, a criterion and useful habit not every student realizes and puts to use.
The reciprocal of 8,000 is, I don't know if right, but not so ridiculous.
The other thing that you needed to recognize was that you have quoted (or misquoted) an equilibrium constant without any units. But an equilibrium constant for that reaction should have units like M2 or M-2 and if you are given that - I very much doubt you weren't - it is informative about which way up you should be writing your equation. ;)
@epenguin, it's an equilibrium constant (K), not a rate constant (k).
One thing about this reaction that someone at school mentioned was that in real life it takes place in a pressurized system, so 8000 Molarity CO isn't that ridiculous if we're talking about a system at 100 atmospheres. Supposedly they use catalysts as well (which, I know, shouldn't actually affect concentrations, but I bring it up just to drive home the point that this problem isn't providing all of the information about the reaction process).
Check what would be the density of 8000 M CO. Compare that to the density of osmium.
Think again about that though. If I had thought it was a rate constant I would have been looking for time as well as possibly molarity in the dimensions, e.g sec-1 or M-1sec-1 etc.
Only if you have the same number of molecules on both sides of the reaction as in A ⇔ B,
or A + B ⇔ C + D , which is common but not your case, is the molar dimension of an equilibrium constant zero, you could call it dimensionless.
So that constant should not have been given you without dimensions. Can you trace to where you got it from? If not does the constant upside-down give results that are reasonable by any way you can check?
Gen chem, so all equilibrium constants are dimensionless. Period.
You're talking about stuff in physical chem. I have enough on my plate without adding unnecessary complexity, thanks.
Here's a more complete explanation, though:
Besides, this problem was about finding the concentration of one of the reactants. The units work out to Molarity^1, which makes perfect sense, so... what's the problem?
To Borek: ok, fine. This is an actual reaction that is used in industry every day, so how about you tell us all what the "real" concentration is supposed to be?
I could not come back earlier, for one thing I could not see your inserts on my device.
Maybe I am out of date then but I remember we always used physical units for equilibrium constants in biochemistry and biophysics as far as I remember. We seem to be finding that a disadvantage of the convention you quote is that we cannot do or check the calculation so I wouldn't agree it has simplified life. Unfortunately I could not find this equilibrium constant in a Wiki search.
You are following the implicit convention of your quoted text K = (product of concs. on right)/(product concs. on left) , then I get the same as your calculation
[CO] = 141.54/K which gives result agreeing with your absurd one.
I wondered if the convention were otherwise and K = 1/1.6*10-2. Then I get a more reasonable sounding 2.26M for the CO.
But still that is about 50 atm. In a flask?. The other concentrations are small fractions of atmospheric. Quite far from a reasonable concentration for an industrial operation and even a laboratory experiment.
All the numbers sound rather screwy, I wonder if anything has been mistranscribed at any stage. Unless your papers are marked by computers you get credit for showing you know when an answer is somehow wrong. I hope you will come back and tell us more if this is class work that is marked or discussed.
Edit: corrected a key typo
Separate names with a comma.