Avogadro's law and molecular sizes As Avogadro's law states that equal volume of gases contain equal numbers of molecules at same temperature and pressure, then does it mean that all gases have same molecular size?
 A: Avogadro's law assumes that the volumes of the molecules are negligible compared to the total volume of the gas i.e. the molecules behave like point particles with zero volume. So yes it does assume the molecules are all the same size in the sense that it assumes that size is zero.
Avogadro's law is based on the ideal gas equation:
$$ PV = nRT $$
A quick rearrangement of this gives:
$$ n = \frac{P}{RT}\,V $$
so at constant temperature and pressure the number of moles of gas $n$ is proportional to the volume $V$. This means equal volumes must contain equal numbers of moles of gas.
For real gases the volume occupied by the gas molecules does affect the behaviour. For example a simple correction to the ideal gas law is the Van der Waals equation:
$$ \left(P + \frac{an^2}{V^2}\right)\left(V - nb\right) = nRT $$
In this equation $b$ is effectively the molar volume of the gas molecules, so the volume term, $V-nb$, is the total gas volume minus the volume actually occupied by the molecules within it. This means that for a real gas Avogadro's law is violated. However under normal conditions the volume of the gas molecules is very small compared to the volume of the gas, i.e. $V - nb \approx V$, and Avogadro's law is an excellent approximation.
The parameter $a$ is related to long range interactions between molecules, and under normal conditions this is also negligible. If we set $a=b=0$ then we recover the usual ideal gas equation.
