A gas mixture contains 75.2% nitrogen and 24.8% krypton by mass. What is the partial pressure of krypton in the mixture if the total pressure is 853mmHg ?
Take a 100 g sample which gives you 75.2g N2 and 24.8g Kr.
mols N2 = grams/molar mass
mols Kr = grams/molar mass
Then X = mol fraction
XN2 = nH2/total mols
XKr = nKr/total mols
pN2 = XN2*total P
pKr = XKr*total P
Well, it seems like this gas mixture is full of some real gas-tly elements!
To find the partial pressure of krypton, we first need to calculate the mole fraction of krypton in the mixture. Do you know why krypton never gets invited to parties? Because it's always a real noble gas, never reacting with anyone!
To find the mole fraction of krypton, we need to convert the mass percentages into mole percentages. So grab your calculator and let's do some number crunching!
The mole fraction of krypton can be calculated using the equation:
Mole fraction of krypton = (mass of krypton / molar mass of krypton) / (mass of nitrogen / molar mass of nitrogen + mass of krypton / molar mass of krypton)
Now, let's plug in the numbers and calculate the mole fraction of krypton. Remember, nitrogen is N₂ and krypton is Kr.
Mole fraction of krypton = (0.248 / 83.798) / (0.752 / 28.014 + 0.248 / 83.798)
Now get your thinking cap on and calculate that mole fraction!
Once you have the mole fraction, you can find the partial pressure of krypton by multiplying the mole fraction by the total pressure of the mixture. Don't let the calculations be a gas-ter!
To find the partial pressure of krypton in the gas mixture, we need to calculate the partial pressure using Dalton's Law of partial pressures.
First, let's convert the percentages to decimal form:
- Nitrogen: 75.2% = 0.752
- Krypton: 24.8% = 0.248
According to Dalton's Law, the partial pressure of a gas in a mixture is equal to its mole fraction multiplied by the total pressure.
Step 1: Calculate the mole fractions.
The mole fraction is the ratio of moles of a gas to the total moles of all the gases in the mixture.
- Moles of nitrogen:
Moles of nitrogen = (mass of nitrogen / molar mass of nitrogen)
The molar mass of nitrogen (N2) is approximately 28 g/mol.
Assuming we have 100 grams of the gas mixture, the mass of nitrogen would be:
Mass of nitrogen = 0.752 * 100 g = 75.2 g
Moles of nitrogen = 75.2 g / 28 g/mol = 2.686 mol
- Moles of krypton:
Moles of krypton = (mass of krypton / molar mass of krypton)
The molar mass of krypton (Kr) is approximately 84 g/mol.
The mass of krypton would be:
Mass of krypton = 0.248 * 100 g = 24.8 g
Moles of krypton = 24.8 g / 84 g/mol = 0.295 mol
Step 2: Calculate the partial pressure of krypton.
Partial pressure of krypton = Moles of krypton / Total moles of the gas mixture * Total pressure
Total moles of the gas mixture = Moles of nitrogen + Moles of krypton
Total moles of the gas mixture = 2.686 mol + 0.295 mol = 2.981 mol
Partial pressure of krypton = 0.295 mol / 2.981 mol * 853 mmHg
Partial pressure of krypton = 8.39 mmHg
Therefore, the partial pressure of krypton in the gas mixture is approximately 8.39 mmHg.
To find the partial pressure of krypton in the gas mixture, we need to use the mole fraction of krypton and the total pressure.
To calculate the mole fraction of krypton, we need to convert the mass percentages to molar percentages. First, we'll assume we have 100g of the gas mixture.
Given that the gas mixture contains 75.2% nitrogen and 24.8% krypton by mass, we can calculate the mass of nitrogen and krypton in the mixture:
Mass of nitrogen = (75.2/100) * 100g = 75.2g
Mass of krypton = (24.8/100) * 100g = 24.8g
Next, we'll calculate the moles of nitrogen and krypton using their molar masses:
Molar mass of nitrogen (N2) = 28.02 g/mol
Molar mass of krypton (Kr) = 83.80 g/mol
Moles of nitrogen = Mass of nitrogen / Molar mass of nitrogen = 75.2g / 28.02 g/mol ≈ 2.68 mol
Moles of krypton = Mass of krypton / Molar mass of krypton = 24.8g / 83.80 g/mol ≈ 0.296 mol
Now, we can calculate the mole fraction of krypton:
Mole fraction of krypton = Moles of krypton / Total moles of the mixture = 0.296 mol / (2.68 mol + 0.296 mol) ≈ 0.0997
Finally, we can calculate the partial pressure of krypton using the mole fraction and the total pressure:
Partial pressure of krypton = Mole fraction of krypton * Total pressure
Partial pressure of krypton = 0.0997 * 853 mmHg ≈ 85 mmHg
Therefore, the partial pressure of krypton in the gas mixture is approximately 85 mmHg.