Exercise 14.55 Consider the reaction: NiO(s)+CO(g)⇌Ni(s)+CO2(g) Kc=4000.0 at 1500 K When calculating the answer, do not round to the appropriate number of significant figures until the last calculation step.
If a mixture of solid nickel(II) oxide and 0.10000 M carbon monoxide is allowed to come to equilibrium at 1500 K, what will be the equilibrium concentration of CO2?
never mind..
I got 0.10..
.......NiO(s)+CO(g)⇌Ni(s)+CO2(g)
I......solid..0.1....solid..0
C......solid...-x....solid..x
E......solid..0.1-x..solid..x
Substitute the E into the Kc expression and solve for x.
Remember that NiO and Ni are NOT included in the Kc expression.
I got 0.08, but the answer is wrong!
A word to the wise. When you answer a question with JUST an answer you don't help us find the error. ALWAYS show your work of how you obtained that answer so we can go through the math with you. I suspect you either substituted incorrectly or you made a math error.
Well, if I had a nickel for every time I had to calculate equilibrium concentrations, I'd be a rich clown! Anyway, let's get to the math.
First, we need to write the balanced equation for the reaction. It's NiO(s) + CO(g) ⇌ Ni(s) + CO2(g). Easy peasy, lemon squeezy!
Now, we need to set up an ICE table. I don't mean an actual ice table, although that would be quite refreshing on a hot day. I mean Initial, Change, Equilibrium table.
Let's assume x is the change in concentration of CO2. Since we start with 0.10000 M CO, the initial concentration of CO2 is also 0 M. The change in CO concentration will be -x, and the change in Ni concentration will be +x. Got it?
Now, write down the equilibrium concentrations using Kc. We have [CO2] = x, [CO] = 0.10000 - x, and [Ni] = x.
Plug these values into the expression for Kc: Kc = ([Ni][CO2]) / ([NiO][CO])
We know the value of Kc is 4000.0, but we need to solve for x. So let's do some math-fu!
4000.0 = (x * x) / (0.10000 * x)
Simplifying a bit, we get:
4000.0 = x^2 / 0.10000
Now, let's multiply both sides by 0.10000 to get rid of that pesky denominator:
400.0 = x^2
Take the square root of both sides:
x = ±20.0
Since we're dealing with concentrations, we can't have a negative value. So the equilibrium concentration of CO2 is 20.0 M.
And there you have it, my math-loving friend. The equilibrium concentration of CO2 is 20.0 M. Keep calm and clown on!
To find the equilibrium concentration of CO2, we need to use the information given in the problem and apply the principles of chemical equilibrium.
Step 1: Write the balanced equation for the reaction.
NiO(s) + CO(g) ⇌ Ni(s) + CO2(g)
Step 2: Write the expression for the equilibrium constant, Kc, using the concentrations of the reactants and products.
Kc = [Ni(s)][CO2(g)] / [NiO(s)][CO(g)]
Step 3: Determine the initial concentrations of the reactants.
From the problem, we know that the initial concentration of CO is 0.10000 M. The concentration of NiO(s) is not given, but we can assume it is in excess.
Step 4: Define the change in concentration.
Let's assume that the change in concentration of CO(g) is "x" in moles. Since the stoichiometric coefficient for CO in the balanced equation is 1, the concentration of CO(g) at equilibrium will be (0.10000 - x) M.
The change in concentration of Ni(s) and CO2(g) will be equal since the stoichiometric coefficients for both are also 1. Therefore, the equilibrium concentrations for Ni(s) and CO2(g) will be "x" M.
Step 5: Substitute the equilibrium concentrations into the equilibrium constant expression.
Kc = [x][x] / [(0.10000 - x)][(0.10000 - x)]
Step 6: Solve for x.
Since we know the value of Kc is 4000.0 at 1500 K, we can set up the equation:
4000.0 = x^2 / (0.10000 - x)^2
Step 7: Solve the equation for x.
By rearranging the equation and solving, we can find the value of x. This involves algebraic manipulation and possibly using the quadratic formula.
Step 8: Substitute the value of x into (0.10000 - x) to find the equilibrium concentration of CO2.
(0.10000 - x) represents the concentration of CO(g) at equilibrium, so (0.10000 - x) M is also the equilibrium concentration of CO2(g).
Remember not to round any intermediate calculations until the last step to maintain accuracy.
By following these steps, you should be able to calculate the equilibrium concentration of CO2(g) for the given reaction at 1500 K.