A 10.0 L cannister contains a mixture of nitrogen, oxygen and argon at 4.30 atm. If the abundance of nitrogen and oxygen are 37.76 % and 17 % respectively, then determine the partial pressure of the argon in kPa.
Question
A 10.0 L cannister contains a mixture of nitrogen, oxygen and argon at 4.30 atm. If the abundance of nitrogen and oxygen are 37.76 % and 17 % respectively, then determine the partial pressure of the argon in kPa.
Solution
Sure, here are the steps to solve this problem:
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First, we need to understand that the total pressure in the canister is the sum of the partial pressures of each gas (nitrogen, oxygen, and argon). This is known as Dalton's Law of Partial Pressures.
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The total pressure is given as 4.30 atm. We know the percentage abundance of nitrogen and oxygen, so we can calculate their partial pressures.
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The partial pressure of nitrogen is 37.76% of the total pressure. So, we multiply 4.30 atm by 0.3776 (37.76/100) to get the partial pressure of nitrogen.
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Similarly, the partial pressure of oxygen is 17% of the total pressure. So, we multiply 4.30 atm by 0.17 (17/100) to get the partial pressure of oxygen.
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To find the partial pressure of argon, we subtract the partial pressures of nitrogen and oxygen from the total pressure.
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Finally, to convert the pressure from atm to kPa, we use the conversion factor 1 atm = 101.325 kPa.
Let's do the calculations:
Partial pressure of Nitrogen = 4.30 atm * 0.3776 = 1.62 atm Partial pressure of Oxygen = 4.30 atm * 0.17 = 0.73 atm Partial pressure of Argon = Total pressure - (Partial pressure of Nitrogen + Partial pressure of Oxygen) = 4.30 atm - (1.62 atm + 0.73 atm) = 1.95 atm
Now, convert this to kPa:
Partial pressure of Argon = 1.95 atm * 101.325 kPa/atm = 197.58 kPa
So, the partial pressure of argon in the canister is approximately 197.58 kPa.
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