A small bicycle pump is filled with helium (He) gas. With constant
pressure, the gas is forced out through a small aperture in two
seconds. The same pump is filled with hydrogen bromide (HBr) gas.
Using the same pressure, how long will it take to force out this gas?
Using the same pressure and the same tire we know the volume for He is the same as the volume for HBr gas. Use Graham's Law. Let's use a volume of 2 L.
So rate for He is 1 L/2 sec = 0.5 L/s. rate HBr = 1 L/seconds. I've let mm stand for molar mass. Then
(rate He/rate HBr) = sqrt (mm HBr/mm He)
Substitute the numbers and solve. Post your work if you get stuck.
9 second
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.
To determine how long it will take to force out the hydrogen bromide (HBr) gas from the pump using the same pressure, we need to apply Boyle's Law. Boyle's Law states that at constant temperature, the volume of a gas is inversely proportional to its pressure.
Here's how we can use Boyle's Law to solve the problem:
1. Define the variables:
- V1: Initial volume of the gas (unknown)
- P1: Initial pressure of the gas (constant)
- T1: Initial time taken to force out helium gas = 2 seconds
- T2: Time taken to force out hydrogen bromide gas (unknown)
- P2: Pressure of hydrogen bromide gas (unknown)
2. Formulate Boyle's Law equation:
According to Boyle's Law, P1 * V1 = P2 * V2 (where V2 is the final volume of the gas)
3. Since we are keeping the pressure constant, P1 = P2. Therefore, the equation simplifies to V1 = V2.
4. Since the initial volume (V1) of the gas is the same as the final volume (V2), we can conclude that the time required to force out the hydrogen bromide gas (T2) will also be 2 seconds, the same as it was for the helium gas.
In summary, using Boyle's Law, we determine that it will take 2 seconds to force out the hydrogen bromide gas from the pump using the same pressure.