It took 20 seconds for a certain
volume of oxygen to effuse
through an orifice(small opening) at
298K. How long will it take the
same volume of each of the
following gases to effuse through the same orifice at the same
temperature?. The gases are
hydrogen, helium, and chlorine.
(H=1, He=4, O=16 and Cl=35.5).
(rate 1/rate 2) = sqrt(M2/M1) where M2 and M1 are molar masses.
Make up a number for the "certain volume". I would use a convenient number like 100 L. Then
rate1 for oxygen = 100 L/20 = 5 L/s
rate 2 = ?
M2 = 2 for H
M1 = 32 for O
Substitute into the above and solve for rate 2. Then rate 2 = 100/seconds. You know rate 2 and 100L, solve for seconds.
The others are done the same way. Post your work if you get stuck.
To determine the time it takes for each gas to effuse through the orifice, we can use Graham's law of effusion. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Mathematically, the relationship can be expressed as follows:
Rate1/Rate2 = √(Molar mass2/Molar mass1)
Let's calculate the rate of effusion for each gas relative to oxygen.
For hydrogen (H2):
Rate(H2)/Rate(O2) = √(Molar mass(O2)/Molar mass(H2))
Molar mass of O2 = 32 g/mol
Molar mass of H2 = 2 g/mol
Rate(H2)/Rate(O2) = √(32/2) = √16 = 4
This means that hydrogen will effuse 4 times faster than oxygen.
For helium (He):
Rate(He)/Rate(O2) = √(Molar mass(O2)/Molar mass(He))
Molar mass of He = 4 g/mol
Rate(He)/Rate(O2) = √(32/4) = √8 ≈ 2.83
This means that helium will effuse approximately 2.83 times faster than oxygen.
For chlorine (Cl2):
Rate(Cl2)/Rate(O2) = √(Molar mass(O2)/Molar mass(Cl2))
Molar mass of Cl2 = 70.5 g/mol
Rate(Cl2)/Rate(O2) = √(32/70.5) ≈ 0.594
This means that chlorine will effuse approximately 0.594 times slower than oxygen.
Now, using the ratio of rates, we can determine the time it takes for each gas to effuse the same volume through the same orifice at the same temperature. Since we know it took 20 seconds for oxygen, we can multiply that time by the ratios calculated earlier:
Time(H2) = 20 seconds * (1/4) = 5 seconds
Time(He) = 20 seconds * (1/2.83) ≈ 7.07 seconds
Time(Cl2) = 20 seconds * (1/0.594) ≈ 33.67 seconds
Therefore, it will take approximately 5 seconds for hydrogen, 7.07 seconds for helium, and 33.67 seconds for chlorine to effuse the same volume through the same orifice at the same temperature.