CO(g) + H2O(g)-->CO2 + H2 (g) reaction occurs in a 2.0 Ll reactor at 800 degrees celsius. The reaction conditions are such that a complete conversion of reactants into products results. The reactor is charged initially with 5.0 atm of CO and 8.0 atm of water vapor. Calculate the final pressure of hydrogen in the reactor.
(The reaction is balanced already and I know that final pressure can be found by Pf = (initial pressure)(initial volume)/final volume but this has already be hinted at being a limited reactant question of which I'm awful at. So I would assume that I would need to find the mass of H2 (water vapor) and CO but not sure about the mass used in this question in order to divide it by molar mass. Any suggestions or tips?)
Since these are 1:1:1:1 you can take a short cut and see that CO is the limiting reagent. So 5 atm CO reacts with 5 atm H2O to form 5 atm CO2 and 5 atm H2 with 3 atm H2O left over. The final P is 16 atm. Your prof may not like this so you can do it conventionally this way.
Calculate mols CO and mols H2O using PV = nRT. All of the information is there to do so. I obtained about 0.11 mols CO and about 0.18 mols H2O but these are estimates and you need to do them more accurately. That will produce about 0.11 mols CO2 and 0.11 mols H2 leaving zero mols CO and about 0.05 mols H2O. Finally, convert mols to pressure and add the total pressure and you will get 16 atm.
To determine the final pressure of hydrogen (H2) in the reactor, we need to consider the concept of limiting reactants.
In this particular reaction, we have CO (carbon monoxide) and H2O (water vapor) as reactants, which will produce CO2 (carbon dioxide) and H2 (hydrogen gas) as products. The balanced equation suggests that one mole of CO reacts with one mole of H2O, resulting in one mole of CO2 and one mole of H2.
To identify the limiting reactant, let's compare the moles of CO and H2O present initially and determine which one will be fully consumed.
To calculate the moles of each reactant, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
For CO:
n(CO) = (P(CO) * V) / (R * T)
= (5.0 atm * 2.0 L) / (0.0821 L.atm/mol.K * (800 + 273) K)
≈ 0.4835 mol
For H2O:
n(H2O) = (P(H2O) * V) / (R * T)
= (8.0 atm * 2.0 L) / (0.0821 L.atm/mol.K * (800 + 273) K)
≈ 0.774 mol
According to the balanced equation, the stoichiometric ratio between CO and H2O is 1:1. This means that the reactant with fewer moles will be fully consumed, limiting the production of products.
Since CO has fewer moles (0.4835 mol) compared to H2O (0.774 mol), CO is the limiting reactant. This means that the reaction will cease once all the CO is consumed.
Now, we need to calculate the moles of H2 formed using the moles of limiting reactant (CO):
From the balanced equation: 1 mole of CO reacts to form 1 mole of H2
Therefore, moles of H2 = moles of CO = 0.4835 mol
Finally, using the ideal gas law again, we can determine the final pressure of H2:
P(H2) = (n(H2) * R * T) / V
= (0.4835 mol * 0.0821 L.atm/mol.K * (800 + 273) K) / 2.0 L
≈ 17.19 atm
Thus, the final pressure of hydrogen (H2) in the reactor is approximately 17.19 atm.