Why is enthalpy an extensive property?

First, an extensive property is one that depends on the amount of material present. For example, mass is an extensive property because if you double the amount of material, the mass doubles. An intensive property is one that does not depend on the amount of material present. Examples of intensive properties are temperature ##T## and pressure ##P##.

Enthalpy is a measure of heat content, so the greater the mass of any substance, the greater the amount of heat that it can hold at any particular temperature and pressure.

Technically, enthalpy is defined as the integral of the heat capacity at constant pressure from absolute zero to the temperature of interest, including any phase changes. For example,

##DeltaH = int_(T_(0K))^(T_"goal") C_PdT##

##= int_(T_(0K))^(T_"fus") C_PdT + DeltaH_"fus" + int_(T_"fus")^(T_"vap") C_PdT + DeltaH_"vap" + int_(T_"vap")^(T_"goal") C_PdT##

if we suppose that the temperature of interest is above the boiling point. Then, we go through ##T_(0K) -> T_"fus" -> T_"vap" -> T_"goal"##.

If two samples are identical at the same temperature and pressure, except that Sample B has twice the mass of Sample A, then the enthalpy of Sample B is twice that of Sample A.

That's why enthalpy values are usually quoted as J/mol or kJ/mol. If you multiply the quoted value by the number of moles of substance, you get the enthalpy in J or kJ.