Using the Ideal Gas Law to determine the molecular weight of an unknown compound
Suppose you have a gas that you can reliably assume is an ideal gas, and that there is only one species present. You know the mass of the sample, and you have it confined at a known pressure, volume, and temperature. What is the molecular weight of the unknown gas?
An ideal gas kept at 1.000 atm, 24.85 Celsius, and 4.000 Liters weighs 4.5824 grams. What is the molar mass of the gas?
Since we are given the information that the gas is ideal, we can use the ideal gas law (PV = nRT). We are given P, V, and T, but T is in celsius. We need to convert this to kelvin: 24.85 + 273.15 = 298.00K.
We can now rearrange to solve for n, the number of moles:
n = PV/RT = (1 atm)*(4L)/((0.08206 L*atm/mol*k)*(298.00K)) = about 0.1636 moles.
So we now have the mass, and the number of moles of gas. Molar mass is moles/mass, so the molecular weight of the gas is 4.5824 grams / 0.1636 moles, or 28.01 grams/mole.
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