Final answer:
By subtracting the known partial pressures of oxygen and carbon dioxide from the total pressure in the vessel, we find that the partial pressure of nitrogen is 35 atm.
Step-by-step explanation:
To determine the partial pressure of nitrogen in a closed vessel where the total pressure is 65 atm, and we know the partial pressures of oxygen and carbon dioxide, we apply Dalton's Law of Partial Pressures. This law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each component in the gas mixture.
The partial pressure of oxygen (O2) is given as 12 atm, and the partial pressure of carbon dioxide (CO2) is given as 18 atm. To find the partial pressure of nitrogen (N2), we subtract the known partial pressures from the total pressure:
Ptotal = PN2 + PO2 + PCO2
65 atm = PN2 + 12 atm + 18 atm
PN2 = 65 atm - 12 atm - 18 atm
PN2 = 35 atm
Therefore, the partial pressure of the nitrogen in the vessel is 35 atm, which corresponds to option c.