Related to Kinetic Molecular theory

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The ideal gas equation is derived under the assumption of a large number of molecules, allowing for average force calculations from numerous collisions. While it holds true at low pressures, its accuracy diminishes as pressure increases, raising questions about its consistency. At normal atmospheric pressure, the ideal gas law remains effective for practical applications at everyday temperatures. Calculating the number of molecules in a 1 cm³ container at 1 atm and 20°C reveals a substantial quantity, challenging the notion of "small." Additionally, using kinetic theory to assess molecular collisions against a wall of the container indicates a significant number, reinforcing the effectiveness of the ideal gas law under these conditions.
Himanshu_6174
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The derivation of the ideal-gas equation included the assumption that the number of molecules is very latge, so that we could compute the average force due to many collisions. However, the ideal-gas equation holds accurately only at low pressures, where the molecules are few and far between. Isn't this inconsistent?
 
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Experimentally, normal atmospheric pressure is low enough that the ideal gas law works well for many practical purposes at everyday temperatures.

Using the ideal gas law, calculate the number of molecules in a 1 cm3 container at P = 1 atm and T = 20°C. Would you consider that to be a small number?

Going further, if you assume a specific gas (e.g. nitrogen) you can use kinetic theory to calculate the number of molecular collisions against one wall of that container (1 cm2 assuming it's cubical). Again, would you consider that to be a small number?
 

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