At a very high temperature, Kc=65.0 for the following reaction.
2HI H2+I2
The following concentrations were detected in a mixture. Is the system at equilibrium? If not, in which direction must the reaction proceed for equilibrium to be established?
(HI) =0.500M, (H2) =2.80M, and (I2)=3.40M
To determine if the system is at equilibrium, we can calculate Qc, the reaction quotient, using the given concentrations:
Qc = [H2][I2]/[HI]^2
Plugging in the given values, we get:
Qc = (2.80)(3.40)/(0.500)^2 = 38.08
Since Kc = 65.0 and Qc = 38.08, the system is not at equilibrium.
To establish equilibrium, the reaction must proceed in the direction that will increase the value of Qc. Since Qc is smaller than Kc, it means that the concentrations of H2 and I2 are too low and the concentration of HI is too high compared to the equilibrium conditions. Therefore, the reaction must proceed in the forward direction to increase the concentrations of H2 and I2 and decrease the concentration of HI until Qc reaches the value of Kc.
To determine if the system is at equilibrium, we can use the expression for the equilibrium constant, Kc, and compare it to the concentrations given.
The equilibrium constant expression for the given reaction, 2HI ⇌ H2 + I2, is:
Kc = ([H2][I2]) / [HI]^2
Given:
[HI] = 0.500 M
[H2] = 2.80 M
[I2] = 3.40 M
Kc = 65.0
Let's substitute these values into the equilibrium constant expression:
Kc = ([2.80][3.40]) / (0.500)^2
Kc = (9.52) / (0.25)
Kc = 38.08
Since Kc (38.08) is not equal to the given equilibrium constant (65.0), the system is not at equilibrium.
To determine which direction the reaction must proceed for equilibrium to be established, we compare the calculated value of Kc (38.08) with the given value of Kc (65.0).
A higher calculated value of Kc (38.08) indicates that the concentrations of the products ([H2][I2]) are relatively lower compared to the concentration of the reactant ([HI]).
Hence, for equilibrium to be established, the reaction must proceed in the forward direction (from left to right), meaning more H2 and I2 should be formed, and HI should be consumed until the concentrations reach a ratio that satisfies the equilibrium constant expression.