The diving atmosphere used by the U.S. Navy in its undersea Sea-Lab experiments consisted of 0.036 mole fraction O2 and 0.058 mole fraction N2, with helium (He) making up the remainder. What are the masses of nitrogen, oxygen, and helium in a 7.22-g sample of this atmosphere?
multipy the mole fraction by molmass of each gass. Total them up.
divide each by the total, to give a weighted fraction.
Nitrogen mass calc= molefraction*MolmassN2
then do that for all three, to get total.
massnitrogen= (nitrogenmasscalc)/total * 7.22g
To find the masses of nitrogen, oxygen, and helium in the given sample of atmosphere, we first need to calculate the moles of each gas using their mole fractions.
Given:
Total mass of the sample (m) = 7.22 g
Mole fraction of oxygen (X_O2) = 0.036
Mole fraction of nitrogen (X_N2) = 0.058
To calculate the moles of each gas, we can use the following formula:
Moles (n) = Mole fraction (X) * Total mass (m) / Molar mass (M)
Let's calculate the moles of each gas step-by-step:
1. Moles of Oxygen:
Molar mass of oxygen (M_O2) = 32 g/mol (approximate)
Moles of oxygen (n_O2) = X_O2 * m / M_O2
2. Moles of Nitrogen:
Molar mass of nitrogen (M_N2) = 28 g/mol (approximate)
Moles of nitrogen (n_N2) = X_N2 * m / M_N2
3. Moles of Helium:
Moles of helium (n_He) = 1 - (n_O2 + n_N2)
Once we have the moles of each gas, we can calculate their respective masses using their molar masses:
1. Mass of Oxygen:
Mass of oxygen = n_O2 * M_O2
2. Mass of Nitrogen:
Mass of nitrogen = n_N2 * M_N2
3. Mass of Helium:
Mass of helium = n_He * M_He
Note: The molar mass of helium (M_He) is 4 g/mol.
Let's plug in the values and solve the problem:
1. Moles of Oxygen:
n_O2 = 0.036 * 7.22 / 32
2. Moles of Nitrogen:
n_N2 = 0.058 * 7.22 / 28
3. Moles of Helium:
n_He = 1 - (n_O2 + n_N2)
After calculating the moles, we can find the masses:
1. Mass of Oxygen:
Mass of oxygen = n_O2 * M_O2
2. Mass of Nitrogen:
Mass of nitrogen = n_N2 * M_N2
3. Mass of Helium:
Mass of helium = n_He * M_He
By substituting the values into these formulas, you'll be able to calculate the masses of nitrogen, oxygen, and helium in the given sample of the atmosphere.