Final answer:
To find the partial pressure of hydrogen gas in a mixture, first calculate the number of moles of each gas. Apply Dalton's Law of Partial Pressures using the total pressure and the mole ratios, and solve for the hydrogen gas's partial pressure.
Step-by-step explanation:
To determine the partial pressure of hydrogen gas in a 10 L steel vessel containing 15g of oxygen gas, 20g of nitrogen gas, and 5g of hydrogen gas, with a total pressure of 4.22 atm, we can apply 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 the individual gases.
To calculate the partial pressure of hydrogen gas, we must first determine the number of moles of each gas using the ideal gas law. The molar masses of oxygen (O2), nitrogen (N2), and hydrogen (H2) are approximately 32 g/mol, 28 g/mol, and 2 g/mol, respectively.
The moles of oxygen (nO2) = 15 g / 32 g/mol, moles of nitrogen (nN2) = 20 g / 28 g/mol, and moles of hydrogen (nH2) = 5 g / 2 g/mol.
Using the mole ratios and the total pressure, we can find the partial pressure of hydrogen:
Ptotal = PO2 + PN2 + PH2
PH2 = Ptotal x (nH2 / (nO2 + nN2 + nH2))
After calculating the moles and substituting the values into the equation, we solve for the partial pressure of hydrogen (PH2).