FeS2 (s) + O2(g) -----> SO2(g) +Fe203(s) (unbalanced)

a production error leads to the sulfide being placed in a 950-L vessel with insufficient oxygen. Initially, the partial pressure of O2 is 0.64 atm, and the total pressure is 1.05 atm, with the balance due to N2. The reaction is run until 85% of the O2 is consumed, and the vessle is then cooled to its initial temperature. What is the total pressure and the partial pressure of each gas in the vessel?

To solve this problem, we need to follow a systematic approach and perform calculations using the given information. Here's how we can go about it:

Step 1: Write the balanced chemical equation for the reaction:
FeS2 (s) + O2(g) ---> SO2(g) + Fe2O3(s)

Step 2: Determine the stoichiometry of the reaction.
According to the balanced equation, for every 1 mole of FeS2, 3 moles of O2 are required to react. Therefore, the amount of O2 consumed can be calculated as follows:
Moles of O2 consumed = (85/100) * Moles of O2 initially present

Step 3: Calculate the moles of O2 remaining and the moles of SO2 produced.
Moles of O2 remaining = Moles of O2 initially present - Moles of O2 consumed
Moles of SO2 produced = Moles of O2 consumed (since the stoichiometric ratio is 1:1)

Step 4: Convert moles of O2 remaining and SO2 produced to partial pressures using the ideal gas law.
Partial Pressure = (Moles of gas * Universal Gas Constant * Temperature) / Volume

Step 5: Calculate the partial pressure of N2 remaining.
Partial Pressure of N2 = Total Pressure - Partial Pressure of O2 remaining - Partial Pressure of SO2 produced

Now, let's calculate the values step by step:

Step 1: Balanced chemical equation:
FeS2 (s) + O2(g) ---> SO2(g) + Fe2O3(s)

Step 2: Moles of O2 consumed:
Moles of O2 consumed = (85/100) * (0.64 atm / 1.00 atm) * 950 L = 514.88 L

Step 3: Moles of O2 remaining and SO2 produced:
Moles of O2 remaining = 950 L - 514.88 L = 435.12 L
Moles of SO2 produced = Moles of O2 consumed = 514.88 L

Step 4: Partial pressures of O2 remaining and SO2 produced:
Convert moles of O2 remaining to partial pressure:
Partial Pressure of O2 remaining = (435.12 L * 0.64 atm) / 950 L = 0.2930 atm

Convert moles of SO2 produced to partial pressure (assuming the temperature remains constant):
Partial Pressure of SO2 produced = (514.88 L * 0.64 atm) / 950 L = 0.3478 atm

Step 5: Partial pressure of N2:
Partial Pressure of N2 = 1.05 atm - 0.2930 atm - 0.3478 atm = 0.4092 atm

Therefore, the total pressure and partial pressures of each gas in the vessel are as follows:
Total Pressure: 1.05 atm
Partial Pressure of O2: 0.2930 atm
Partial Pressure of SO2: 0.3478 atm
Partial Pressure of N2: 0.4092 atm