For the following equilibrium process:
CO2 + H2 = CO + H2O
The equilibrium concentrations of reacting species are: [CO]= .050 M; [H2]= .045 M; [CO2]= .086 M; [H2O]= .040 M.
(a) Calculate Kc for the reaction
(b) If we add CO2 to increase its concentration to 0.50 mol/L, what will the concentrations of all gases be when equilibrium is reestablished?
To calculate Kc for the reaction CO2 + H2 = CO + H2O, you will need to use the equilibrium concentrations given in the question:
[CO] = 0.050 M
[H2] = 0.045 M
[CO2] = 0.086 M
[H2O] = 0.040 M
(a) To calculate Kc, you will need to write the balanced chemical equation and determine the stoichiometry. The stoichiometry can be determined by the coefficients in the balanced equation, which is:
CO2 + H2 -> CO + H2O
The stoichiometry shows that for every 1 mole of CO2 and 1 mole of H2, 1 mole of CO and 1 mole of H2O are produced. Therefore, the stoichiometric ratio for this reaction is 1:1:1:1.
Kc is the equilibrium constant expressed in terms of concentrations. First, calculate the reactant quotient (Qc) using the given concentrations:
Qc = [CO][H2] / [CO2][H2O]
Substituting the given concentrations:
Qc = (0.050)(0.045) / (0.086)(0.040)
Next, calculate Kc using the equation:
Kc = Qc
Substituting the calculated value of Qc into the equation:
Kc = (0.050)(0.045) / (0.086)(0.040)
At this point, you can calculate the numerical value of Kc, which will provide the equilibrium constant for the reaction.
(b) If you add CO2 to increase its concentration to 0.50 mol/L and allow the system to reach equilibrium, you can use the same approach described above to calculate the concentrations of all gases when equilibrium is reestablished. However, you will need to account for the change in the initial concentration of CO2.
The change in CO2 concentration is (0.500 - 0.086) M = 0.414 M. This will result in a decrease in the concentrations of CO, H2, and H2O at equilibrium, while the concentration of CO2 will increase and reach 0.50 mol/L.
Considering the stoichiometry, if the concentration of CO2 decreases by 0.414 M, then the concentrations of CO, H2, and H2O will each decrease by 0.414 M at equilibrium.
Therefore, after the addition of CO2, the concentrations at equilibrium will be:
[CO] = 0.050 - 0.414 = -0.364 M (negative value indicates that this species is not present at equilibrium)
[H2] = 0.045 - 0.414 = -0.369 M (negative value indicates that this species is not present at equilibrium)
[CO2] = 0.500 M
[H2O] = 0.040 - 0.414 = -0.374 M (negative value indicates that this species is not present at equilibrium)
Note: Concentrations cannot be negative, so negative values indicate that the species is not present at equilibrium.
To calculate Kc for the given equilibrium reaction, we need to use the equilibrium concentrations of the reacting species. The equilibrium constant expression for this reaction is:
Kc = ([CO] * [H2O]) / ([CO2] * [H2])
Let's substitute the given equilibrium concentrations into this expression:
Kc = (0.050 * 0.040) / (0.086 * 0.045)
Kc ≈ 0.117
So, the value of Kc for this reaction is approximately 0.117.
Now, let's move to part (b) of the question. If we add CO2 to increase its concentration to 0.50 mol/L, we need to consider the effect of this change on the equilibrium system. According to Le Chatelier's principle, when the concentration of one component of a system is increased, the system will shift in the direction that reduces the concentration of that component.
In this case, adding more CO2 will drive the equilibrium to produce more products (CO and H2O) and consume more reactants (CO2 and H2). As a result, the concentrations of CO and H2O will increase, while the concentrations of CO2 and H2 will decrease.
However, to determine the exact new concentrations of all gases when equilibrium is reestablished, we need to know the new value of Kc after adding CO2. Without this information, we cannot calculate the new concentrations accurately.