How many joules of heat energy are required to change 64 grams of methane from a liquid to a gas at constant temperature and pressure?

The key to this problem is the enthalpy of vaporization, #DeltaH_"vap"#, for methane.

In essence, the enthalpy change of vaporization tells you how much heat is needed in order to convert one mole of a substance from liquid at its boiling point to vapor at its boiling point.

The enthalpy change of vaporization expresses the amount of heat needed for one mole of a substance to undergo a liquid #-># vapor phase change.

In this case, you know that

#DeltaH_"vap" = "9.2 kJ mol"^(-1)#

This tells you that one mole of liquid methane at its boiling point must absorb #"9.2 kJ"# of heat to go to vapor at the same temperature.

Use methane's molar mass to determine how many moles of methane you have in that #"64-g"# sample

#64 color(red)(cancel(color(black)("g"))) * "1 mole CH"_4/(16.04color(red)(cancel(color(black)("g")))) = "3.99 moles CH"_4#

So, if one mole requires #"9.2 kJ"# of heat, it follows that this many moles would require

#3.99color(red)(cancel(color(black)("moles CH"_4))) * overbrace("9.2 kJ"/(1color(red)(cancel(color(black)("mole CH"_4)))))^(color(purple)(DeltaH_text(vap)color(white)(a) "for methane")) = "36.708 kJ"#

Rounded to two sig figs, the answer will be

#"heat required" = color(green)(|bar(ul(color(white)(a/a)"37 kJ"color(white)(a/a)|)))#