The equilibrium constant for thermal dissociation of F2
F2(g)<->2F(g)
is 0.300. If initially 1.00 mol F2 is placed in a 1.00 L container, which of the following is the correct number of moles of F2 that have dissociated at equilibrium?
1. 0.130 mol
2. 0.418 mol
3. 0.548 mol
4. 0.474 mol
5. 0.239 mol
6. 0.176 mol
7. 0.956 mol
8. 0.213 mol
I would like to know if this is Kc or Kp. I will assume Kc and you want to know the x of 1-x although that's a funny way of asking. Perhaps I've misinterpreted the question.
........F2 ==> 2F
I......1.00.....0
C......-x.......2x
E.....1-x......2x
To determine the number of moles of F2 that have dissociated at equilibrium, we need to use the equilibrium constant expression and the given information.
The equilibrium constant, K, is defined as the ratio of the concentration of the products to the concentration of the reactants, each raised to the power of their respective stoichiometric coefficients. In this case, the equilibrium constant expression can be written as:
K = [F]^2 /[F2]
where [F] represents the concentration of F atoms at equilibrium and [F2] represents the concentration of F2 at equilibrium.
Given that the equilibrium constant (K) is 0.300, and the initial concentration of F2 is 1.00 mol in a 1.00 L container, let's denote the number of moles of F2 that have dissociated at equilibrium as x.
Since F2 dissociates to form 2 moles of F, the concentration of F at equilibrium will be 2x, and the concentration of F2 at equilibrium will be 1.00 - x.
Now we can substitute these values into the equilibrium constant expression:
K = (2x)^2 / (1.00 - x)
0.300 = 4x^2 / (1.00 - x)
Cross-multiply:
0.300(1.00 - x) = 4x^2
0.300 - 0.300x = 4x^2
Rearrange the equation:
4x^2 + 0.300x - 0.300 = 0
Solve the quadratic equation for x:
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
a = 4, b = -0.300, c = -0.300
x = (-(-0.300) ± √((-0.300)^2 - 4(4)(-0.300)))/(2(4))
x = (0.300 ± √(0.090 - (-4.800)))/8
x = (0.300 ± √(0.090 + 4.800))/8
x = (0.300 ± √4.890)/8
Since the value of x cannot be negative (since it represents a number of moles), we take the positive root:
x = (0.300 + √4.890)/8
x ≈ 0.1746
Therefore, the correct number of moles of F2 that have dissociated at equilibrium is approximately 0.1746 mol.
Among the given options, the closest value to 0.1746 mol is 0.176 mol (option 6).