When H2(g) is mixed with CO2(g) at 2,000 K, equilibrium is achieved according to the following equation
CO2(g) + H2(g) « H2O(g) + CO(g)
In one experiment, the following equilibrium concentrations were measured.
[H2] = 0.20 mol/L
[CO2] = 0.30 mol/L
[H2O] = [CO] = 0.55 mol/L
The given equilibrium reaction is
The equilibrium concentrations at 2000 K are
Hence, the mole fraction of CO in the equilibrium mixture can be calculated as
Hence, the mole fraction of CO in the equilibrium mixture is about 0.34.
For a generic reaction , the equilibrium constant Kc is given as
Where the concentrations are the equilibrium values.
Hence, for our reaction, the equilibrium constant can be calculated as
Hence, the equilibrium constant Kc of the reaction is 5.04 approximately.
The equilibrium constant Kp (in terms of partial pressure) is related to Kc as follows:
Where
is the difference in number of gaseous product and number of moles of gaseous reactants in the balanced reaction.
In our reaction 2 moles of gas are reacting to give two moles of other gases.
Hence,
Hence,
Hence, Kp and Kc are equal for our reaction.
When the system is cooled, 30.0% of the CO is converted back to CO2. Hence, we can create the following ICE table to find the Kc at the lower temperature
Initial, ,mol/L | 0.30 | 0.20 | 0.55 | 0.55 |
Change, mol/L | +x | +x | -x | -x |
Equilibrium, mol/L | 0.30+x | 0.20+x | 0.55-x | 0.55-x |
Note that since 30.0 % of CO is being converted, the same number of moles of CO must react with equal number of moles of H2O to from same number of moles of CO2 and H2.
Initial concentration of CO = 0.55 mol/L.
Hence, concentration change for CO after 30.0% is converted is
Hence, 0.165 mol/L of CO and H2O will combine to form 0.165 mol/L of H2 and CO2.
Hence, the equilibrium concentrations at the lower temperature will be
Hence, the new equilibrium constant can be calculated as
Hence, the equilibrium constant Kc at the lower temperature is 0.873 approximately.
When H2(g) is mixed with CO2(g) at 2,000 K, equilibrium is achieved according to the following...
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