For the system, H2(g) + X2(g) <--> 2HX(g), Kc = 24.4 at 300 K. A system was charged with 2.00 moles of HX in a 3.00 liter container. The catalyst was introduced using a remote unit, and the system was allowed to come to equilibrium. How many moles of H2(g) will be present when the system reaches equilibrium?
I'm actually completely stumped on this one. I know you have to do 2 moles of HX and divide by 3 Liters and you get .67 moles/liter. But they don't give you the other two so what do you have to do? The answer is .288, but I've no idea how to get that. Anyone got an idea??
Right, since Kc is given to 3 places, I would calculate M to 3 places; i.e., 2 mols/3 L = 0.667.
.......H2 + X2 ==> 2HX
I......0....0.......0.667
C.....+x...+x........-2x
E......x....x.......0.667-2x
Substitute the E line into the Kc expression and solve for x, then convert from M to mols. 0.288 is the correct answer for mols. x is 0.09 approx.
To solve this problem, we can use the information given, along with the principles of equilibrium and the equation for the reaction.
Given:
- The balanced equation: H2(g) + X2(g) ⇌ 2HX(g)
- The equilibrium constant: Kc = 24.4
- Initial moles of HX: 2.00 moles
- Volume of the container: 3.00 liters
To find the number of moles of H2(g) at equilibrium, we need to set up an expression for the equilibrium concentration of H2. Here's how to proceed:
1. Start by writing down the balanced equation for the reaction: H2(g) + X2(g) ⇌ 2HX(g)
2. Let x represent the number of moles of H2 that reacts or forms at equilibrium.
3. Use the stoichiometry of the reaction to determine the equilibrium concentration of H2 in terms of x. Since 1 mole of H2 reacts to form 2 moles of HX, the change in concentration of H2 is -2x (negative because it is being consumed, and the coefficient of H2 is 1).
4. Write the equilibrium concentration expression for H2 in terms of x:
[H2] = (initial moles of H2 - 2x) / volume of the container
5. Plug in the given values:
[H2] = (2.00 moles - 2x) / 3.00 liters
6. Use the equilibrium constant expression:
Kc = [HX]^2 / ([H2] * [X2])
7. Substitute the equilibrium concentrations and constants into the expression:
24.4 = ([2x]^2) / ((2.00 - 2x) / 3.00 * [X2])
8. Rearrange the equation to solve for x:
24.4 * (2.00 - 2x) / 3.00 * [X2] = [2x]^2
9. Simplify and solve the quadratic equation to find the value of x. This can be done by substituting [X2] = 1 and solving for x:
24.4 * (2.00 - 2x) / 3.00 * 1 = [2x]^2
10. After solving the quadratic equation, you should obtain two values for x. One value will be positive and the other negative. Since we're dealing with moles, the negative value doesn't make physical sense. Therefore, we discard the negative solution.
11. The positive solution represents the moles of H2 formed at equilibrium.
The answer, as you mentioned, is 0.288 moles of H2.
I hope this explanation helps you understand how to solve this kind of equilibrium problem. Let me know if you have any further questions!