for the equilibrium H2+CO2<-->H2O+CO
Kc=3.18 at 1106K. if each of the four species was initially present at 3.000M calculate the equilibrium concentration of the CO at this temperature.....
OK I can get as far as equilibrium (final)
H2O=3.000-x
CO=3.000-xx
H2=3.000+x
CO2=3.000+x
substitute the equil.numbers into the KC expression and solve for x.Then add 3.000 or subtract x from 3.000 to arrive at individual concentration...
This is the bit I don't know how to do Could some one please go through it step by step please and show me how to get final answer...
Choices
0.844
3.268
3.844
3.460
2.156
Thanks Andy
see below at original post. I have two scenarios there
1. if you did not solve the equation.
2. if you did solve and obtained a value for x.
Dr bob,
can you check out my theory on previous post....thanx Andy
To find the equilibrium concentration of CO, we need to substitute the equilibrium concentrations of H2, CO2, H2O, and CO into the equilibrium expression for Kc and solve for x.
Given the initial concentrations:
[H2] = 3.000 M
[CO2] = 3.000 M
[H2O] = 3.000 M
[CO] = 3.000 M
Substituting these into the Kc expression, we get:
Kc = [H2O][CO] / [H2][CO2]
Let's substitute the equilibrium concentrations:
Kc = (3.000 - x)(3.000 + x) / (3.000 + x)(3.000 - x)
Now, we can solve for x by setting up an equation and solving it:
Kc = (3.000 - x)(3.000 + x) / (3.000 + x)(3.000 - x) = 3.18
Cross multiplying the equation gives us:
(3.000 - x)(3.000 + x) = 3.18(3.000 + x)(3.000 - x)
Expanding the equation:
9.000 - x^2 = 9.540 (3.000^2 - x^2)
Simplifying:
9.000 - x^2 = 9.540 (9 - x^2)
Collecting like terms:
9.000 - x^2 = 9.540 - 9x^2
Moving all terms to one side of the equation:
8x^2 - x^2 = 9.540 - 9.000
Simplifying:
8x^2 - x^2 = 0.540
Combining like terms:
7x^2 = 0.540
Dividing both sides by 7:
x^2 = 0.077
Taking the square root of both sides:
x = ±√0.077
The equilibrium concentration of CO can be obtained by substituting the value of x into [CO] = 3.000 - x.
Using the positive square root:
[CO] = 3.000 - √0.077
Calculating this, we get:
[CO] ≈ 2.156 M
Therefore, the correct answer is 2.156.
To solve this problem, you need to set up and solve an equation using the given equilibrium constant expression.
Here's what you need to do step by step:
1. Write down the balanced chemical equation for the reaction:
H2 + CO2 ⇌ H2O + CO
2. Set up an expression for the equilibrium constant (Kc):
Kc = [H2O][CO] / [H2][CO2]
3. Substitute the initial concentrations into the equilibrium constant expression as follows:
Kc = ([H2O]eq [CO]eq) / ([H2]eq [CO2]eq)
Since the initial concentration for each species is 3.000 M, you can substitute these values into the equation:
Kc = ([3.000 - x][3.000 - x]) / ([3.000 + x][3.000 + x])
4. Simplify the equation by multiplying out the terms:
Kc = (9.000 - 6.000x + x^2) / (9.000 + 6.000x + x^2)
5. Set up and solve the quadratic equation to find the value of x:
Kc = (9.000 - 6.000x + x^2) / (9.000 + 6.000x + x^2)
Multiply both sides of the equation by (9.000 + 6.000x + x^2) to eliminate the denominator:
Kc * (9.000 + 6.000x + x^2) = (9.000 - 6.000x + x^2)
Expand the equation and move all terms to one side to form a quadratic equation:
Kc * 9.000 + Kc * 6.000x + Kc * x^2 = 9.000 - 6.000x + x^2
Combine like terms:
Kc x^2 + (6.000Kc + 6.000)x + (9.000Kc - 9.000) = 0
6. Solve the quadratic equation using any suitable method, such as factoring, completing the square, or using the quadratic formula.
The quadratic equation obtained:
Kc x^2 + (6.000Kc + 6.000)x + (9.000Kc - 9.000) = 0
To find the value of x, you can use the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / (2a)
The coefficients for the quadratic equation are:
a = Kc
b = (6.000Kc + 6.000)
c = (9.000Kc - 9.000)
Substitute the values of a, b, and c into the quadratic formula and solve for x.
7. Once you find the value of x, substitute it back into the expressions for [CO]eq = 3.000 - x to calculate the equilibrium concentration of CO.
Evaluate each of the choices given using the equilibrium expression [CO]eq = 3.000 - x, and choose the option that matches your computed value of [CO]eq.
Hope this helps!