Under constant pressure, a small basketball pump is filled with helium, He,
gas; the helium is then forced out of a small aperture in 2 seconds. The same
pump is filled with hydrogen bromide, HBr, gas. Under the same pressure,
how long will it take to force this gas out?
No volume is listed; let's make up a volume, say 2 L for He, then the rate is (2L/2sec) = 1 L/s. Then
rate1/rate2 = sqrt(M2/M1)
1/rate 2 = sqrt(80.9/4)
solve for rate 2, then rate = 2L/sec and solve for sec. Post your work if get stuck.
4505
To determine how long it will take to force hydrogen bromide (HBr) gas out of the small aperture under the same pressure, we need to consider the principles of gas flow and the ideal gas law.
The ideal gas law, PV = nRT, relates the pressure (P), volume (V), number of moles of gas (n), universal gas constant (R), and temperature (T) of a gas. In this case, the pressure (P) and volume (V) are constant, so we can ignore those variables.
Assuming the temperature (T) remains constant, and since we are comparing two gases (helium and hydrogen bromide) at the same pressure, we can equate their number of moles (n) to determine the relationship between the two gases.
n1 = n2
From the ideal gas law equation, we can rearrange it to solve for n:
n = PV / RT
Since the pressure (P), volume (V), and temperature (T) are constant, we can ignore those variables in the equation. Therefore, the equation becomes:
n1 / n2 = V1 / V2
Since the pump size and aperture size are the same for both gases, we can assume the volumes (V1 and V2) are equal. Therefore:
n1 / n2 = 1
This means that the number of moles of helium (n1) is equal to the number of moles of hydrogen bromide (n2).
Now, let's consider the gas flow rate. The rate of gas flow (Q) through a small aperture is given by the equation:
Q = A * v
Where A is the cross-sectional area of the aperture and v is the velocity of the gas flowing through it.
Since the aperture size is the same for both gases, we can assume the cross-sectional area (A) is equal. Therefore, we can compare the velocities (v) of the gases.
Since both gases are under the same pressure and have the same number of moles, we can assume they have the same average kinetic energy per molecule. According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the square of the root mean square (RMS) velocity.
v1 / v2 = sqrt(m2 / m1)
Where m1 and m2 are the molar masses of helium and hydrogen bromide, respectively.
The molar mass of helium (He) is approximately 4 g/mol, and the molar mass of hydrogen bromide (HBr) is approximately 81 g/mol.
Substituting these values into the equation, we get:
v1 / v2 = sqrt(81 / 4) = sqrt(20.25)
v1 / v2 ≈ 4.5
This means that the velocity of hydrogen bromide gas (v2) will be approximately 4.5 times slower than the velocity of helium gas (v1).
Given that it took 2 seconds to force helium gas out, we can determine the time it will take to force hydrogen bromide gas out by using the inverse of the velocity ratio:
t2 = t1 * (v1 / v2)
t2 = 2 * (4.5)
t2 ≈ 9 seconds
Therefore, it will take approximately 9 seconds to force hydrogen bromide gas out under the same pressure.