Three of the primary components of air are carbon dioxide, nitrogen, and oxygen. In a sample containing a mixture of only these gases at exactly one atmosphere pressure, the partial pressures of carbon dioxide and ni- trogen are given as PCO2 = 0.285 torr and PN2 = 593.297 torr. What is the partial pres- sure of oxygen?
Answer in units of torr
Ptotal = pO2 + pCO2 + pN2
Ptotal must be in torr if the others are in torr. 1 atm = 760 torr.
To find the partial pressure of oxygen in the mixture, we first need to understand the concept of partial pressure.
Partial pressure is the pressure that a gas would exert if it occupied the same volume as the mixture at the same temperature. It is equal to the mole fraction of the gas multiplied by the total pressure of the mixture.
In this case, since the total pressure is given as exactly one atmosphere, which is equivalent to 760 torr, we can use this value in our calculations.
To find the partial pressure of oxygen, we need to know the mole fraction of oxygen in the mixture. The mole fraction of a gas is calculated by dividing the number of moles of a gas by the total number of moles of all the gases in the mixture.
The mole fraction of oxygen (PO2) can be calculated using the following formula:
PO2 = (number of moles of oxygen) / (total number of moles of all gases)
We already know the partial pressures of carbon dioxide (PCO2) and nitrogen (PN2) in the mixture. The mole fraction of each gas can be calculated as follows:
Mole fraction of CO2 (XCO2) = PCO2 / Ptotal
Mole fraction of N2 (XN2) = PN2 / Ptotal
Now, since we know that the total pressure (Ptotal) is equal to one atmosphere (760 torr), we can calculate the mole fraction of CO2 and N2:
XCO2 = 0.285 torr / 760 torr
XN2 = 593.297 torr / 760 torr
Next, we need to find the mole fraction of oxygen (XO2). Since the mixture contains only carbon dioxide, nitrogen, and oxygen, the sum of the mole fractions of all three gases must equal 1. Therefore, we can calculate the mole fraction of oxygen as:
XO2 = 1 - (XCO2 + XN2)
Substituting the values calculated above, we get:
XO2 = 1 - (0.285 torr / 760 torr + 593.297 torr / 760 torr)
Simplifying this expression gives:
XO2 = 1 - (0.000375 + 0.7801)
Finally, we can calculate the partial pressure of oxygen (PO2) by multiplying the mole fraction of oxygen by the total pressure:
PO2 = XO2 * Ptotal
Substituting the values calculated above, we get:
PO2 = (1 - 0.000375 - 0.7801) * 760 torr
Simplifying this expression gives:
PO2 = 0.219525 * 760 torr
Therefore, the partial pressure of oxygen in the mixture is approximately 166.8 torr.