For the system, H2(g)+X2(g) <-> 2HX(g) Kc=24.4 at 300K. A system was charged with 1 mole of H2 and 1 mole of I2 in a 3 liter container. The catalyst was introduced using a remote unit, and the system was allowed to come to equilibrium. How many moles of H2 will be present when the system reaches equilibrium?
You have the equation.
Convert 1 mol to molarity. 1 mole/3 liters.
Set up an ICE chart, plug in the numbers and solve for the unknown. Subtract from 1/3 to find how much H2 remains after equilibrium is established, then multiply by 3 L to find moles H2.
To determine the number of moles of H2 present at equilibrium, we need to use the given equilibrium constant (Kc) and the initial concentrations of the reactants.
Let's break down the given information:
Equilibrium equation: H2(g) + X2(g) ⇌ 2HX(g)
Equilibrium constant: Kc = 24.4
Initial concentrations: [H2]₀ = 1 mole, [X2]₀ = 1 mole, and [HX]₀ = 0 mole
Volume of the container: V = 3 liters
Since the given reaction involves gases, we can use the ideal gas law to calculate the concentrations of the reactants based on their initial moles and the volume of the container.
First, let's calculate the initial concentration of H2 ([H2]₀):
[H2]₀ = (moles of H2) / (volume of container)
[H2]₀ = 1 mole / 3 liters
[H2]₀ = 0.33 M
Similarly, the initial concentration of X2 ([X2]₀) would also be 0.33 M.
Now, we can set up the equilibrium expression for this reaction:
Kc = ([HX]eq²) / ([H2]eq × [X2]eq)
Since the reaction has not yet come to equilibrium and we do not know the equilibrium concentrations, we can represent them as [HX]eq, [H2]eq, and [X2]eq.
Let's assume that at equilibrium, x moles of H2 will be consumed, and 2x moles of HX will be formed. Therefore, the equilibrium concentrations will be:
[H2]eq = [H2]₀ - x
[X2]eq = [X2]₀ - x
[HX]eq = 2x
Substitute these values into the equilibrium expression:
Kc = ([HX]eq²) / ([H2]eq × [X2]eq)
24.4 = (2x)² / ((0.33 - x) × (0.33 - x))
24.4 = 4x² / (0.1089 - 0.66x + x²)
Now, we can solve the quadratic equation to find the value of x, which represents the moles of H2 consumed:
4x² = 24.4(0.1089 - 0.66x + x²)
4x² = 2.66196 - 16.0744x + 24.4x²
Combine like terms:
20.4x² + 16.0744x - 2.66196 = 0
Use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / (2a)
Where a = 20.4, b = 16.0744, and c = -2.66196.
After solving this quadratic equation, you will get two values for x. However, we only take the positive value because we are looking for the number of moles consumed. Let's assume that x = x₁ is the positive value.
Finally, we can calculate the moles of H2 present at equilibrium:
[H2]eq = [H2]₀ - x₁
[H2]eq = 0.33 - x₁
Therefore, the number of moles of H2 present when the system reaches equilibrium is 0.33 - x₁.