How to Calculate the Effusion Rate of Oxygen from a Balloon?

In summary, to calculate the initial rate of oxygen escaping through a 2 millimeter hole in a balloon at 0° C, one must use the equation 1/4 n*A*v, where n is the number of molecules per cubic meter (calculated using the density at STP), A is the area of the hole (calculated using the radius), and v is the velocity (calculated using the Boltzmann constant, temperature at STP, and mass of one oxygen molecule). The result would be approximately 657 oxygen atoms leaving the balloon per second.
  • #1
Zvaigzdute
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Homework Statement



Suppose we make a circular hole 2 millimeter in diameter in a balloon. Calculate the initial rate at which oxygen escapes through the hole (at 0° C), in number of oxygen atoms leaving the balloon per second.

Homework Equations



1/4 n*A*v


The Attempt at a Solution



1/4 n*A*v

n = N/V at # of molecules/m^3 (density)
n = 6.022e23/.0224 = 2.68839286E25
This is at STP so 22.4 L volume at one mol of gas

A = area
Pi*.0002^2*1/4 = 3.14159265 × 10-8

V = velocity
= sqrt(3*k*T/m)
=
k = boltzman constant 1.4e-23
T = 273K at STP
m = 2.65780731e-26 kg for one molecule of hydrogen

Atoms/second = 656.816755


What am I doing wrong?
 
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  • #2


Area is of the order of 10^(-6) and not 10^(-8).
Radius, R=1mm=10^(-3)m
A=pi*10^(-6)
 
  • #3


There are a few issues with your attempt at a solution:

1. The given information does not specify the gas being used in the balloon, so it is unclear where you are getting the values for the mass of one molecule and the Boltzmann constant. Additionally, the units for the mass of one molecule are incorrect. It should be in kilograms, not grams.

2. The equation you are using, 1/4nAv, is not the correct equation for calculating the rate of effusion. The correct equation is given by Graham's Law of Effusion: r1/r2 = sqrt(M2/M1), where r1 and r2 are the rates of effusion for two different gases and M1 and M2 are their respective molar masses. In this case, we are only dealing with one gas, so the equation would simplify to r = sqrt(M/2), where M is the molar mass of the gas.

3. You are using the wrong units for the area. The area should be in square meters, not square centimeters.

4. Lastly, the given information does not specify the pressure inside the balloon, so it is difficult to accurately calculate the effusion rate without this information. The rate of effusion is directly proportional to the pressure, so without knowing the pressure, we cannot accurately calculate the effusion rate.

In conclusion, without knowing the specific gas and pressure inside the balloon, it is difficult to accurately calculate the rate of effusion. It is also important to use the correct equation and units in order to obtain an accurate answer.
 

Related to How to Calculate the Effusion Rate of Oxygen from a Balloon?

What is effusion of gas from a balloon?

Effusion of gas from a balloon is the process of gas molecules escaping from a pressurized balloon into the surrounding environment.

What causes effusion of gas from a balloon?

Effusion of gas from a balloon is caused by the difference in pressure between the inside and outside of the balloon. The gas molecules inside the balloon are under higher pressure and will naturally escape through any openings, such as the balloon's neck, into the lower pressure environment outside.

How does the size of the balloon affect effusion?

The size of the balloon can affect effusion as a larger balloon will contain more gas molecules and therefore have a higher pressure inside, leading to a faster rate of effusion. However, the size of the opening or neck of the balloon also plays a role in effusion as a smaller opening will cause the gas to escape at a slower rate.

What factors can affect the rate of effusion?

The rate of effusion can be affected by several factors, including the pressure inside the balloon, the size of the opening or neck of the balloon, the temperature of the gas, and the type of gas inside the balloon. Higher pressure, larger openings, and higher temperatures will result in a faster rate of effusion, while heavier gases will effuse more slowly than lighter gases.

How is effusion of gas from a balloon related to the kinetic molecular theory?

Effusion of gas from a balloon is related to the kinetic molecular theory, which states that all particles are in constant motion and collide with each other and their container. In the case of effusion, the gas molecules inside the balloon are constantly colliding with each other and the walls of the balloon, causing some molecules to escape through the opening and into the surrounding environment.

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