d. 418 mmHg
The ideal gas law is
PV = nRT
where
P = Pressure
V = Volume
n = number of moles
R = Ideal gas constant (62.363577 L Torr/(K*mol) )
T = Absolute temperature
We are going to first need to calculate how many moles of gas particles we have, so solve for n
PV = nRT
PV/RT = n
Now we need to calculate what values to plug into the formula. mmHg is equal to torr for 6 significant figures, so we'll use that unchanged. 39.3C needs to be converted to Kelvin by adding 273.15, giving 312.45, and now to plug in the values and calculate.
(882.7 Torr)(17.2 L)/((62.363577 L Torr/(K*mol)) 312.45K) = n
(15182.44 Torr*L)/( 19485.49963 L Torr/mol ) = n
0.779166061 mol = n
So we now know that we have 0.779166061 moles of gas particles. The average molar mass of the gas particles will be the mass of the gas divided by the moles of particles. So:
28.3 g / 0.779166061 mol = 36.32088384 g/mol
Now we need to solve this equation:
x*Mo + (1-x)*Ma = A
where
x = percentage of the gas that's oxygen
Mo = Molar mass of oxygen gas
Ma = Molar mass of argon gas
A = average molar mass of unknown gas
Let's solve for x:
x*Mo + (1-x)*Ma = A
x*Mo + Ma - xMa = A
x*Mo - xMa = A - Ma
x(Mo - Ma) = A - Ma
x = (A - Ma)/(Mo - Ma)
Now let's calculate the molar mass of argon and oxygen to determine the percentage of oxygen.
Atomic weight argon = 39.948
Atomic weight oxygen = 15.999
Molar mass oxygen = 2*15.999 = 31.998 g/mol
And plug in the numbers we have to get x.
x = (A - Ma)/(Mo - Ma)
x = (36.32088384 - 39.948)/(31.998 - 39.948)
x = -3.62711616 / -7.95
x = 0.456241026
So 45.62% of gas is oxygen. And the partial pressure of oxygen will be 45.62% of 882.7 mmHg = 403 mmHg
The value of 403 mmHg does not match any of the available choices. The most likely cause for the discrepancy is the use of lower precision constants. For instance, the ideal gas constant I used was selected from a table of available choices expressed in different units. I chose the value that most closely matches the units available in the problem of 62.363577 L Torr/(K*mol) instead of the more common 8.3144598 L*kPa/(K*mol) value so I wouldn't need to convert from mmHg to kPa. Looking closely at the data, I suspect a problem with the original problem. If the temperature is off by as little as 1.2 degrees (perhaps by accidentally using 272 K instead of 273.15 K as the conversion offset), the calculated answer would be 418 mmHg. In any case, option d. 418 mmHg is the closest available choice with an error of less than 4%. All the other options have errors exceeding 8%.
