Effusion of Gas from a Balloon

[Zvaigzdute]

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?

 

[nasu]

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

 

[kerimek]

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.