What equations must be used to calculate the heat associated with a phase change?

The equations must be used to calculate the heat associated with phase change is,

        Q=m×∆H(vap)

    or Q=m×∆H(fus)

here;

∆H= heat required for one gram of the substance to undergo the phase change.

*If you're going from solid to liquid, you use ∆H-heat of fusion (called the heat of fusion), which represents the heat required for 1 gram of a substance to change from solid to liquid at the melting point.

*If you're going from liquid to gas, you use ∆H-heat of vaporization (called the heat of vaporization), which represents the heat required for 1 gram of the substance to change from liquid to gas at boiling point.

For water, the values are usually given to be

ΔHfus = 334 J/g  and  

ΔHvap=2257 J/g.

the old alchemists made significant contributions to science even though there starting premises were off a bit. their conclusions after failure would steer them into better directions for investigation. science is no more than close observation and the initial mistakes result in rethinking and retrying experiments.