A mixture of Nitrogen and Argon gases in a balloon exerted a pressure of 2.55 atm. Given that there were 1.0 g nitrogen gas and 3.2 g argon gas in the balloon, calculate the partial pressure of argon gas.
Calculate moles Ar and moles N2, find total moles, and calculate mole fraction of each.
Then XAr x total P = partial pressure Ar
To calculate the partial pressure of argon gas, we need to use the concept of Dalton's Law of Partial Pressure. According to this law, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases.
In this case, we are given the total pressure exerted by the gas mixture, which is 2.55 atm. We are also given the masses of nitrogen gas and argon gas in the balloon, 1.0 g and 3.2 g respectively.
First, let's convert these masses into moles. To do this, we need to know the molar masses of nitrogen (N₂, diatomic) and argon (Ar). The molar masses are as follows:
- Molar mass of nitrogen (N₂): 2 * atomic mass of nitrogen (N) = 2 * 14.01 g/mol = 28.02 g/mol
- Molar mass of argon (Ar): 39.95 g/mol
Next, we can use the molar masses and the given masses to calculate the number of moles of nitrogen and argon gases:
Number of moles of nitrogen = mass of nitrogen / molar mass of nitrogen
= 1.0 g / 28.02 g/mol
≈ 0.036 moles
Number of moles of argon = mass of argon / molar mass of argon
= 3.2 g / 39.95 g/mol
≈ 0.0801 moles
Now that we have the number of moles of nitrogen and argon, we can calculate the partial pressure of argon gas using Dalton's Law of Partial Pressure.
Partial pressure of argon = Total pressure - Partial pressure of nitrogen
= 2.55 atm - (moles of nitrogen / total moles) * total pressure
Substituting the values:
Partial pressure of argon = 2.55 atm - (0.036 moles / (0.036 moles + 0.0801 moles)) * 2.55 atm
Simplifying the expression:
Partial pressure of argon = 2.55 atm - (0.036 / 0.1161) * 2.55 atm
= 2.55 atm - 0.311 * 2.55 atm
≈ 2.55 atm - 0.82 atm
≈ 1.73 atm
Therefore, the partial pressure of argon gas in the mixture is approximately 1.73 atm.