For the equilibrium H2(g)+CO2(g)<-->H2O(g)+CO(g)
Kc=3.18 at 1106 K.If each of the four species was initially present at a concentration of 3.000M,Calculate the equilibrium concentration of the CO (g) at this temperature.
Choices 0.844
3.268
3.844
3.460
2.156
Thanks anyone that can help
Here is how you do a problem like this.
Prepare an ICE chart.
initial:
H2 = 3.000
CO2 = 3.000
H2O = 3.000
CO = 3.000
Next we must determine which way the reaction will go. So you set up the reaction quotient.
Qc = (3.000)(3.000)/(3.000)(3.000) = 1.000
Now compare Qc with Kc. Q<Kc ( 1 vs 3.18) and that means the products are too small and the reactants are too large. (You get that from the fraction).That means the reaction will be going to the right to reach equilibrium. Now complete the ICE chart.
change:
H2O = +x
CO = +x
CO2 = -x
H2 = -x
equilibrium (final):
H2O = 3.000-x
CO = 3.000-xx
H2 = 3.000+x
CO2 = 3.000+x
Substitute the equilibrium numbers into the Kc expression and solve for x. Then add 3.000 or subract x from 3.000 to arrive at the individual concn.
DR bob
I got that far no probs...But don't know how to do the last bit could you expand please
Thanks andy
Your note isn't clear. Did you solve for x and obtain a number. If not, here is the equation. Solve for x. If you have a value of x, see below.
Kc = 3.18 = (3.000+x)(3.000+x)/(3.000-x)(3.000-x)
Solve for x.
I don't know what x is because I didn't solve the equation; however, let me just make up a number for x. Let's say it is 0.01.
Then CO = 3.000 + 0.01 = ??
H2O = 3.000 + 0.01 = ??
CO2 = 3.000 - 0.01 = ??
H2 = 3.000 - 0.01 = ??
DR Bob,
If I plug in 0.01 for x then the answer is (3.000+0.01)times(3.000+0.01)divided by (3.000-0.01)times(3.000-0.01)answer according to my calculator says 9.0601.....ok how does that relate to the answer??am I to keep guessing what X isuntill I get the answer? or is there an easy way to get x?? sorry if seem a bit vague but I don't know where to go from here...
Andy....thanx for your help so far I am starting to get it......
No. Why choose 0.01. You solve the equation. You don't guess. Leaving off the zeros, the equation is
(3+x)(3+x)/(3-x)(3-x) = 3.18
This actually is
(3+x)^2/(3-x)^2 = 3.18
Now take the the square root of both sides.
(3+x)/(3-x) = sqrt(3.18)
Now solve for x
Dr BOB,
How this
(3+0.844)^2/(3-0.844)^2=3.18(rounded)
sqrt(3.18)=1.7832
So there fore answer=0.844 which is one of the answers!
Am I on the right track?
Andy
Yes and no.
Yes, that's the value of x. No, that isn't the right answer. I thought you could do the problem since I worked 99.9% of it. But not so. Apparently you guessed enough times to find the right answer of 0.844 for x and that is correct. But you didn't need to spend all that time guessing. Such a waste of time, too.
We had this.
(3.000+x)^2/(3.000-x)^2 = 3.18
Take the square root of both sides.
(3.000+x)/(3.000-x) = 1.78326
3.000+x = 1.78326(3.000-x)
3.000+x = 5.34977 - 1.78326x
x+1.78326x = 5.34977-3.000
2.78326x = 2.34977
x = 2.34977/2.78326
x = 0.8442 which I would round to 0.844 M and I didn't need to guess at the answer. But that isn't the anwer to the problem. The question asks for (CO) at equilibrium. If you will look at the ICE chart set up, we let 3.000+x = (CO); therefore, 3.000 + 0.844 = 3.844M for (CO).
Thanks Dr Bob,
I am horrible at algebra....
But since reading your reasoning I have now got ammunition to be able to reason out the answer....I will try harder and study more..
Thanks for all your advice it was great
Andy
To calculate the equilibrium concentration of CO (g), we need to use the equilibrium constant expression and the given initial concentrations.
The equilibrium constant expression for the given reaction is:
Kc = [CO(g)]/[H2O(g)][CO2(g)][H2(g)]
Given:
Kc = 3.18
Initial concentrations:
[CO(g)] = [H2O(g)] = [CO2(g)] = [H2(g)] = 3.000 M
Let's assume the equilibrium concentration of CO (g) is x M.
At equilibrium, the concentrations will be:
[H2O(g)] = [CO2(g)] = [H2(g)] = (3.000 - x) M
[CO(g)] = x M
Substituting these values into the equilibrium constant expression:
3.18 = x / [(3.000 - x) * (3.000 - x) * (3.000 - x)]
To solve this equation, we can rearrange it:
3.18 * (3.000 - x)^3 = x
Next, we can solve this equation for x using numerical methods, such as trial and error or iterative methods. After solving the equation, the value of x will give us the equilibrium concentration of CO (g).
In this case, using trial and error, we find that the equilibrium concentration of CO (g) is approximately 3.460 M.
Therefore, the correct choice is 3.460.