2C3H6(g) + 2NH3(g) + 3O2(g) -> 2C3H3N(g) + 6H2O(g)
A 150.0 liter steel reactor at 25 ºC is filled with the following partial pressures of reactants: 0.500 MPa C3H6, 0.800 MPa ammonia, and 1.500 MPa oxygen gas.
If the reaction proceeds to 90% yield, and no side reactions take place, what is the final total pressure in the reaction vessel at 400 ºC?
This is a bear of a problem but I will get you started.First you must determine the limiting reagent(LR). Start by using PV = nRT and calculating mols of each material. Find the LR from that and determine how much of each product is formed. Then multiply by 0.9 to correct for the 90% yield. Determine how much of the non-limiting reagents remain and add all of the mols together, then convert using PV = nRT to total pressure.
To find the final total pressure in the reaction vessel at 400 ºC, we need to consider the stoichiometry of the reaction, the partial pressures of the reactants, and the reaction conditions.
The balanced chemical equation for the reaction is:
2C3H6(g) + 2NH3(g) + 3O2(g) -> 2C3H3N(g) + 6H2O(g)
From the equation, we can see that the stoichiometric ratio between C3H6:NH3:O2:C3H3N is 2:2:3:2. This means that for every 2 moles of C3H6, we need 2 moles of NH3 and 3 moles of O2 to produce 2 moles of C3H3N.
Given the partial pressures of the reactants in the steel reactor:
Partial pressure of C3H6 = 0.500 MPa
Partial pressure of NH3 = 0.800 MPa
Partial pressure of O2 = 1.500 MPa
To determine the final total pressure at 400 ºC, we need to calculate the moles of each reactant present in the reactor and then determine the moles of the limiting reactant.
Step 1: Calculate the moles of each reactant:
Moles of C3H6 = (Partial pressure of C3H6 * Volume of reactor) / (Ideal gas constant * Temperature)
Moles of NH3 = (Partial pressure of NH3 * Volume of reactor) / (Ideal gas constant * Temperature)
Moles of O2 = (Partial pressure of O2 * Volume of reactor) / (Ideal gas constant * Temperature)
Step 2: Determine the moles of the limiting reactant:
Moles of limiting reactant = min(Moles of C3H6 / 2, Moles of NH3 / 2, Moles of O2 / 3)
Step 3: Calculate the moles of the products formed:
Moles of C3H3N = (Moles of limiting reactant) x (Yield % / 100)
Step 4: Calculate the volume of the reactor at 400 ºC:
Volume of reactor at 400 ºC = (Moles of products x Ideal gas constant x Temperature) / (Total pressure)
Finally, to find the final total pressure at 400 ºC, we need to divide the initial total moles by the calculated volume at 400 ºC:
Final total pressure = (Initial total moles) / (Volume of reactor at 400 ºC)
Remember to convert temperatures to Kelvin by adding 273.15, and the ideal gas constant (R) is 0.0821 L⋅atm/(mol⋅K).
Plug in the given values and carry out the calculations to find the final total pressure in the reaction vessel at 400 ºC.