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

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SUMMARY

The discussion focuses on calculating the effusion rate of oxygen from a balloon with a 2 millimeter diameter hole at 0° C. The formula used is 1/4 n*A*v, where 'n' represents the number density of oxygen molecules, 'A' is the area of the hole, and 'v' is the velocity of the escaping gas. The correct area calculation should yield A = π*(0.001 m)^2, resulting in an area of approximately 3.14 × 10^(-6) m². The final calculation indicates that approximately 656.82 oxygen atoms escape per second.

PREREQUISITES
  • Understanding of gas laws and effusion principles
  • Familiarity with the Boltzmann constant and its application
  • Basic knowledge of molecular density calculations
  • Ability to perform area calculations for circular shapes
NEXT STEPS
  • Study the kinetic theory of gases and its implications for effusion rates
  • Learn about the ideal gas law and its applications in real-world scenarios
  • Explore advanced calculations involving the Boltzmann constant in thermodynamics
  • Investigate the effects of temperature and pressure on gas effusion rates
USEFUL FOR

This discussion is beneficial for students studying physics or chemistry, particularly those focusing on gas behavior, effusion processes, and thermodynamic principles.

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

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