Final answer:
The partial pressure of oxygen in the gas mixture, calculated using Dalton's Law of partial pressures, is 430 mmHg.
Step-by-step explanation:
To find the partial pressure of oxygen in a mixture of helium, nitrogen, and oxygen, we can use Dalton's Law of partial pressures. This law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas in the mixture. Since we know the total pressure and the moles of each gas, we can calculate the mole fraction of each gas and then find the partial pressures.
Calculation
Total moles of gas = moles of He + moles of N2 + moles of O2
= 0.500 + 0.500 + 1.00
= 2.00 moles
Mole fraction of O2 (XO2) = moles of O2 / Total moles of gas
= 1.00 / 2.00 = 0.50
Partial pressure of O2 (PO2) = Total pressure × Mole fraction of O2
= 860 mmHg × 0.50
= 430 mmHg