A study of the system, H2(g) + I2(g) == 2 HI(g), was carried
out. Kc = 54.9 at 699.0 K (Kelvin) for this reaction. A system was charged with 2.50 moles of HI in a 5.00 liter vessel as the only component initially. The system was brought up to 699.0 K and allowed to reach equilibrium. How many moles of H2 should there be in the container at that time?
2.50mols/5.00L = 0.500 M
............H2 + I2 ==> 2HI
initial.....0.....0.....0.500
change......x.....x......-2x
equil........x.....x.....0.500-2x
Kc = (HI)^2/(H2)(I2)
Substitute into the Kc expression and solve for x.
To find the number of moles of H2 present at equilibrium, we need to use the stoichiometry of the reaction and the given equilibrium constant (Kc) value.
The balanced equation for the reaction is:
H2(g) + I2(g) ⇌ 2 HI(g)
The equilibrium constant expression for this reaction is:
Kc = [HI]^2 / [H2][I2]
Given:
Initial moles of HI = 2.50 moles
Volume of the vessel = 5.00 liters
Temperature = 699.0 K
Kc = 54.9
Since there are no initial moles of H2 or I2, we can assume that the concentrations of both H2 and I2 are zero at the start. Therefore, [H2] = [I2] = 0.
Using the equilibrium constant expression, we can rearrange it to solve for [HI]:
Kc = [HI]^2 / ([H2][I2])
54.9 = [HI]^2 / (0 * 0)
Since [H2] and [I2] are both zero, the denominator is zero.
Since the denominator is zero, this means that the reaction did not occur to produce any HI. Therefore, at equilibrium, the moles of H2 present in the container would still be zero.
In conclusion, there would be no moles of H2 present in the container at equilibrium.
To determine the number of moles of H2 at equilibrium, we can use the equilibrium constant (Kc) and the given initial conditions.
First, let's set up the equilibrium expression for the chemical equation:
Kc = [HI]^2 / ([H2] * [I2])
Since the initial concentration of HI is given as 2.50 moles in a 5.00 liter vessel, we can calculate its initial concentration:
[HI]initial = 2.50 moles / 5.00 liters = 0.50 M (molarity)
Next, we assume that the initial concentrations of H2 and I2 are both zero (because they weren't initially present in the system). Therefore, we can substitute these values into the equilibrium expression to calculate the moles of H2 at equilibrium:
Kc = (0.50 M)^2 / (0 moles * 0 moles)
Kc = 0.50 M^2 / 0
Since we cannot divide by zero, this equation implies that the concentration of H2 at equilibrium is zero. Therefore, there are no moles of H2 in the container at that time.