The following system is at equilibrium,at 699K in a 5L container.
H2(g)+I2(g)--->2HI(g) Kc = 54.9
Initially,the system had 2.50 moles of HI.What is the moles of H2 at equilibrium?
Can Dr.Bob check if my steps are correct?
My solution:
Initially,the concentrations of H2 & I2 are 0,whereas concentration of H1 is 2.50mol/5L = 0.50 mol/L .At equilibrium,the concentrations of H2 & I2 are assumed to be x,whereas concentration of HI is 0.50-2x
Using equlibrium constant equation with respect to concentration,
Kc = [HI]^2/[H2][I2]
54.9 = (0.50-2x)^2/x.x
Since 2x is assumed to be negligible,therefore the equation above further simplified to :
54.9 = (0.50)^2/x.x
x^2 = (0.50)^2/54.9
x = 0.06748 mol/L = [H2] = [12]
Therefore moles of H2 at equilibrium is
0.06748 mol/L X 5L = 0.337 mol
Is my steps and answer correct? Thank you in advance
The set up looks good but you can't neglect the 2x. I ran through it quickly and obtained 0.266 for mols H2 by solving the quadratic.
But why I can't ignore the 2x? Could Dr.Bob please explain?
Your steps and answer are almost correct, but there is a slight error in your calculations. Let's go through the solution step by step to identify the mistake:
1. At the start of the reaction, the concentrations of H₂ and I₂ are both 0, while the concentration of HI is 2.50 mol / 5 L = 0.50 mol/L. This part is correct.
2. At equilibrium, let's assume the concentrations of H₂ and I₂ to be x, while the concentration of HI is 0.50 - 2x (as you correctly mentioned). This part is also correct.
3. Using the equilibrium constant expression, Kc = [HI]² / ([H₂] * [I₂]), you correctly wrote the equation as 54.9 = (0.50 - 2x)² / (x * x).
4. Here is where the error occurs. When you simplified the equation, you wrote:
54.9 = (0.50)² / (x * x)
However, it should be:
54.9 = (0.50 - 2x)² / (x * x)
This is because you need to substitute the expression for the concentration of HI at equilibrium, which is (0.50 - 2x).
5. Now, let's correct the calculation. Starting from:
54.9 = (0.50 - 2x)² / (x * x)
Expand the square on the left side:
54.9 = (0.50)² - 4 * 0.50 * 2x + (2x)² / (x * x)
54.9 = 0.25 - 4x + 4x² / (x * x)
Simplify:
54.9 = 0.25 - 4x + 4x² / x²
Rearrange the equation:
4x² - 4x + (54.9 - 0.25) = 0
4x² - 4x + 54.65 = 0
6. Now you can solve this quadratic equation to find the value of x, which represents the concentration of H₂ at equilibrium. Based on the nature of the root, it seems that factoring or using the quadratic formula would be involved.
Once you find the value of x, you can calculate the moles of H₂ at equilibrium as [H₂] = x * 5 L = moles of H₂.
Overall, your steps are correct, but there was a mistake in simplifying the equation. Correcting that mistake and proceeding with the proper equation will give you the accurate answer.