A sealed vessel contains 8.58 moles of oxygen, 1.27moles of carbon dioxide, and 3.65 moles of nitrogen gas. The total pressure of the gas mixture is 2.94 atmospheres. What is the partial pressure of the carbon dioxide?
Question
A sealed vessel contains 8.58 moles of oxygen, 1.27moles of carbon dioxide, and 3.65 moles of nitrogen gas. The total pressure of the gas mixture is 2.94 atmospheres. What is the partial pressure of the carbon dioxide?
Solution
To solve this problem, we need to use Dalton's Law of Partial Pressures. This law states that the total pressure exerted by a mixture of gases is equal to the sum of the pressures that each gas would exert if it were alone.
Step 1: Calculate the total number of moles in the vessel.
Total moles = moles of oxygen + moles of carbon dioxide + moles of nitrogen Total moles = 8.58 moles + 1.27 moles + 3.65 moles = 13.5 moles
Step 2: Calculate the mole fraction of carbon dioxide.
Mole fraction = moles of carbon dioxide / total moles Mole fraction = 1.27 moles / 13.5 moles = 0.094
Step 3: Calculate the partial pressure of carbon dioxide.
Partial pressure = mole fraction * total pressure Partial pressure = 0.094 * 2.94 atm = 0.276 atm
So, the partial pressure of the carbon dioxide is 0.276 atmospheres.
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