A gas mixture contains 4.00 grams of O2 and 4.00 grams of He. If the total pressure of the gas sample is 4.67 atm, what is the partial pressure of each component?

mols O2 = grams/molar mass

mols He = grams/molar mass
XO2 = n O2/total mols.
XHe = n He/total mols.
pO2 = XO2*Ptotal
pHe = XHe*Ptotal

To find the partial pressure of each component, we need to use Dalton's Law of Partial Pressures. According to Dalton's law, the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual component.

First, we need to calculate the number of moles of each component. To do this, we divide the mass of each component by its molar mass.

The molar mass of O2 is 32.00 g/mol and the molar mass of He is 4.00 g/mol.

For O2:
Number of moles = Mass of O2 / Molar mass of O2
= 4.00 g / 32.00 g/mol
= 0.125 mol

For He:
Number of moles = Mass of He / Molar mass of He
= 4.00 g / 4.00 g/mol
= 1.00 mol

Now we can calculate the partial pressure of each component using the ideal gas law equation:

PV = nRT

Since we know the total pressure (P), number of moles (n), and gas constant (R = 0.0821 atm·L/mol·K), we can rearrange the equation as follows:

P = nRT / V

The total pressure of the gas sample is 4.67 atm.

To find the partial pressure of O2:
Partial pressure of O2 = (Number of moles of O2 / Total number of moles) x Total pressure
= (0.125 mol / (0.125 mol + 1.00 mol)) x 4.67 atm
= (0.125 / 1.125) x 4.67 atm
= 0.111 x 4.67 atm
= 0.519 atm (rounded to three decimal places)

To find the partial pressure of He:
Partial pressure of He = (Number of moles of He / Total number of moles) x Total pressure
= (1.00 mol / (0.125 mol + 1.00 mol)) x 4.67 atm
= (1.00 / 1.125) x 4.67 atm
= 0.889 x 4.67 atm
= 4.143 atm (rounded to three decimal places)

Therefore, the partial pressure of O2 is 0.519 atm and the partial pressure of He is 4.143 atm.