When CO2(g) (0.118 mol/L) and H2(g) (3.90 mol) in a 33.0 L reaction vessel at 980K are allowed to come to equilibrium the mixture contains 0.0853 mol/L of H20(g). What concentration (mol/L) of CO2(g) reacted?
CO2(g) + H2(g) <--> CO(g) + H2O(g)
If you will do the ICE chart I think you can see the answer.
CO2 + H2 <==> H2O + CO
I= initial concn:
(CO2)=0.118 M
(H2) = 3.90 M if the problem means mols/L or 3.90/33 = 0.118 M if it means mols in 33.0 L.
(H2O) = 0
(CO) = 0
C = change in concn:
(H2O) = +x
(CO) = +x
(CO2) = - x
(H2) = -x
E = equilibrium concn:
(H2O) = 0.0853 from the problem.
(CO) we know from the equation that this is also 0.0853.
(CO2) = 0.118 - x but you know what x is. It is 0.0853.
Check my work. Check my thinking.
To find the concentration of CO2(g) that reacted, we need to use the concept of the equilibrium constant (K) and the stoichiometry of the reaction. Here's how you can approach this problem:
1. Write the balanced chemical equation:
CO2(g) + H2(g) ⇌ CO(g) + H2O(g)
2. Define the initial concentrations of the reactants and products given in the problem:
[CO2]initial = 0.118 mol/L
[H2]initial = 3.90 mol/L
[H2O]equilibrium = 0.0853 mol/L
3. Use the stoichiometry of the reaction to determine the change in concentration of CO2:
Since the reaction coefficient of CO2 is 1 in the balanced chemical equation, the change in concentration of CO2 is also equal to -1 × [CO2]reacted.
4. Define the equilibrium concentrations:
Let [CO2]reacted be the concentration of CO2(g) that reacted at equilibrium.
5. Determine the equilibrium concentrations of the reactants and products:
[CO2]equilibrium = [CO2]initial - [CO2]reacted
[H2]equilibrium = [H2]initial - [CO2]reacted
[H2O]equilibrium = [H2O]initial + [CO2]reacted
6. Plug in the given values and the calculated equilibrium concentrations into the equation for the equilibrium constant (K):
K = ([CO(g)]equilibrium × [H2O(g)]equilibrium) / ([CO2(g)]equilibrium × [H2(g)]equilibrium)
7. Calculate the value of K using the given equilibrium concentrations and the given temperature of 980K.
8. Using the equilibrium constant expression, solve for [CO2]reacted.
Remember that the equilibrium constant expression is specific to the balanced chemical equation. In this case, both reaction sides have a coefficient of 1, so the expression is simplified.
Once you have the value of [CO2]reacted, you can calculate its concentration by dividing the moles of CO2 reacted by the volume of the reaction vessel (33.0 L in this case).
By following these steps, you should be able to find the concentration (mol/L) of CO2(g) that reacted in the given reaction.