Q.Give the mathematical expression that relates gas volume and moles.

Avogadro's hypothesis states that equal volumes of any gas, measured under the same temperature and pressure, contain equal numbers of molecules -- regardless of what the gas actually is. Equivalently, at constant temperature and pressure, the volume of a gas sample is directly proportional to the number of moles present:

This is the third pairwise relationship -- alongside Boyle's law ($V\propto1/P$) and Charles's law ($V\propto T$) -- that combine into the single ideal gas equation. It is also the principle that lets volume ratios stand in directly for mole ratios in problems about gas mixtures or gas-producing reactions carried out at the same temperature and pressure: for instance, if a fixed mass of gas occupies less volume in one container than another at the same temperature (both open to the same pressure), the smaller-volume sample must correspond to fewer moles, in exactly the same ratio as the volumes -- so halving the accessible volume while holding T and P fixed means only about half as many moles of gas are present.