The system
CO2(g) + H2(g) *) H2O(g) + CO(g)
is at equilibrium at some temperature. At
equilibrium a 4.00 L vessel contains 1.00 mole
CO2, 1.00 mole H2, 2.40 moles H2O, and 2.40
moles CO. How many moles of CO2 must be
added to the system to bring the equilibrium
CO concentration to 0.731 mol/L?
Answer in units of moles
..........CO2 + H2 ==> H2O + CO
.........0.25.0.25...0.60...0.60
Kc = (H2O)(CO)/((CO2)(H2)
Substitute and solve for Kc.
For the second part, if the final concn for CO = 0.731, it follows final concn H2O must be 0.731; therefore, you must have added 0.731-0.600 = 0.131 for both H2O and CO. That means H2 must have contributed the 0.131 so H2 at equilibrium will be 0.25-0.131 = 0.119
Substitute those values into Kc expression and solve for (CO2). Then you know CO2 initially was 0.25 and final concn is the new calculated value. Find the difference to know how much must be added. That will be in M, convert to mols in 4L. Post your work if you get stuck.
3.1 moles
To solve this problem, we can use the stoichiometry of the reaction and the given equilibrium concentrations to determine the number of moles of CO2 that must be added.
First, let's write the balanced equation for the reaction:
CO2(g) + H2(g) → H2O(g) + CO(g)
Based on the equation, we can see that 1 mole of CO2 reacts to produce 1 mole of CO. Therefore, to calculate the number of moles of CO2 needed to produce a certain concentration of CO, we need to use the stoichiometric ratio.
Given:
Initial moles of CO2 = 1.00 mole
Initial moles of CO = 2.40 moles
Target concentration of CO = 0.731 mol/L
Using the equation,
moles CO2 = moles CO x (moles CO2 / moles CO) = 2.40 moles x (1 mole CO2 / 1 mole CO)
Substituting the given values:
moles CO2 = 2.40 moles x (1 mole CO2 / 1 mole CO) = 2.40 moles x (1 mol CO2 / 1 mol CO) = 2.40 moles CO2
So, 2.40 moles of CO2 must be added to the system to bring the equilibrium CO concentration to 0.731 mol/L.
To solve this problem, we need to use the stoichiometry of the chemical equation and the given information to find the number of moles of CO2 that need to be added to the system.
First, let's write the balanced chemical equation for the reaction:
CO2(g) + H2(g) -> H2O(g) + CO(g)
The coefficients in the balanced equation represent the molar ratios of the reactants and products. According to the equation, one mole of CO2 reacts to form one mole of CO. Therefore, the molar ratio of CO2 to CO is 1:1.
Given that the equilibrium CO concentration is 0.731 mol/L, we can use this information to find the total volume of the system. Since the volume is not given directly, we'll use the fact that the number of moles in a given volume is equal to the concentration multiplied by the volume. Therefore,
CO concentration = number of moles of CO / total volume
0.731 mol/L = 2.40 moles CO / total volume
Rearranging the equation, we can solve for the total volume:
total volume = 2.40 moles CO / 0.731 mol/L
total volume ≈ 3.285 L
Now, we know that the initial volume of the system is 4.00 L. Since we are adding CO2 to the system, the final volume will be the sum of the initial volume and the volume of CO2 added.
final volume = initial volume + volume of CO2 added
final volume = 4.00 L + volume of CO2 added
We want to find the number of moles of CO2 needed to bring the CO concentration to 0.731 mol/L. This means we need to determine the change in moles of CO2 required. We can do this by using the volume calculation:
total volume = 3.285 L = 4.00 L + volume of CO2 added
Solving for the volume of CO2 added:
volume of CO2 added = total volume - initial volume
volume of CO2 added = 3.285 L - 4.00 L
volume of CO2 added ≈ -0.715 L
Since we cannot have a negative volume, this means that we don't need to add any CO2 to the system. The equilibrium CO concentration is already at 0.731 mol/L, so no additional CO2 is required.
Therefore, the answer is 0 moles of CO2.