I posted a question and the answer was given and I cannot get my math to add up correct?
THE QUESTION:
If 4.83mL of an unknown gas effuses through a hole in a plate in the same time it takes 9.23mL of Argon, Ar, to effuse through the same hole under the same conditions, what is the molecular mass of the unknown gas? (146amu)
THE RESPONSE:
Graham's law of effusion states that the rate of effusion of a gas through a small orifice is inversely proportional to the square root of its molecular mass. The relative effusion rates of two gases R1 and R2 is therefor given by:
R1/R2 = sqrt(m1/m2)
where R1 and R2 are the effusion rates of gases with masses m1 and m2, respectively.
Argon gas has a molecular mass of 39.948 gm/mol (the same as its atomic mass because Ar (g) is monoatomic).
In this question, the unknown gas effuses 4.83ml/9.23ml = 0.524 times as fast as the Ar, so we have:
THE SPOT I GOT LOST:
R1/R2 = 0.524 = sqrt((39.948gm/mol)/m)
m = (39.938 gm/mol)/(0524^2)
where m is the molecular mass of the unknown gas.
m = 145.88 gm/mol, which, when rounded to 3 significant figures (the number of significant figures used in the data given in the question) is 146 gm/mol.
THE QUESTION:
If 4.83mL of an unknown gas effuses through a hole in a plate in the same time it takes 9.23mL of Argon, Ar, to effuse through the same hole under the same conditions, what is the molecular mass of the unknown gas? (146amu)
THE RESPONSE:
Graham's law of effusion states that the rate of effusion of a gas through a small orifice is inversely proportional to the square root of its molecular mass. The relative effusion rates of two gases R1 and R2 is therefor given by:
R1/R2 = sqrt(m1/m2)
where R1 and R2 are the effusion rates of gases with masses m1 and m2, respectively.
Argon gas has a molecular mass of 39.948 gm/mol (the same as its atomic mass because Ar (g) is monoatomic).
In this question, the unknown gas effuses 4.83ml/9.23ml = 0.524 times as fast as the Ar, so we have:
THE SPOT I GOT LOST:
R1/R2 = 0.524 = sqrt((39.948gm/mol)/m)
m = (39.938 gm/mol)/(0524^2)
where m is the molecular mass of the unknown gas.
m = 145.88 gm/mol, which, when rounded to 3 significant figures (the number of significant figures used in the data given in the question) is 146 gm/mol.