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How to Calculate Concentration at 7% Oxygen

Finding the concentration of a gas in a volume containing two gases requires application of the "ideal gas law," which relates the physical variables of any gas under conditions of low pressure and temperature. This law is expressed by the following equation: PV = NRT. In this equation, "P" is pressure in atmospheres, "V" is volume in liters, "N" is molar mass and "T" is temperature in degrees Kelvin. "R" is the "ideal gas constant" and has the value O.082. Since only one gas is known, another, such as nitrogen, must be selected to illustrate the method of calculation. Further, assume that the gases are under standard conditions of temperature and pressure, where pressure is one atmosphere and temperature is 273.15 degrees Kelvin, or 0 degrees Celsius.

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- 1
  Assume the total weight of gas is 100 grams: therefore, the volume contains 7 grams of oxygen (O2) and 93 grams of N2. Divide the weight of each gas by its molecular weight to find the molar mass as follows: 7 grams O2/(16 grams O2/mole O2) = 0.438 moles O2; 93 grams N2/(14 grams N2/mole N2) = 6.64 moles N2.
- 2
  Add the molar masses to find the total molar mass, as follows: 0.438 + 6.64 = 7.08 moles of gas. Substitute the appropriate values into the ideal gas equation to find the volume of the gas mixture, as follows: V = NRT/P = (7.08 x 0.082 x 273)/1 = 160 liters.
- 3
  Divide the molar mass of O2 by the volume to find "molar concentration" of O2, as follows: O.438 moles O2/160 liters = 0.003 moles O2/liter. The answer can be expressed in grams per liter by multiplying the molar concentration of O2 by the "gram molecular weight" of O2: 0.003 x 16 = 0.048 grams O2/liter.

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