To determine the time it will take to force out the hydrogen bromide (HBr) gas, we need to compare it with the helium gas.
Assuming the conditions are the same, the rate at which gas flows through a small aperture is directly proportional to the square root of the molar mass of the gas.
So, we can use Graham's Law of Effusion to find the ratio of the effusion rates:
Rate of effusion 1 / Rate of effusion 2 = √(Molar mass 2 / Molar mass 1)
For helium (He), the molar mass is approximately 4 g/mol, and for hydrogen bromide (HBr), the molar mass is approximately 81 g/mol.
Plugging the values into the equation:
Rate of effusion helium / Rate of effusion hydrogen bromide = √(molar mass hydrogen bromide / molar mass helium)
Rate of effusion helium / Rate of effusion hydrogen bromide = √(81 g/mol / 4 g/mol)
Rate of effusion helium / Rate of effusion hydrogen bromide ≈ √20.25
Rate of effusion helium / Rate of effusion hydrogen bromide ≈ 4.5
This means the rate of effusion for hydrogen bromide is approximately 4.5 times slower than that of helium.
Since it took 2 seconds to force out the helium gas, it will take approximately 4.5 times longer to force out the hydrogen bromide gas.
Therefore, it will take approximately 2 seconds x 4.5 ≈ 9 seconds to force out the hydrogen bromide gas.