Before doing any calculations, make sure that you understand what a substance's enthalpy of condensation,
For a given substance, the enthalpy of condensation expresses the amount of heat that must be given off to convert a specific sample of that substance from vapor to liquid at constant temperature (and pressure).
Usually, that specific sample is a mole of that substance. Since heat is given off when a vapor
This is why the enthalpy of condensation, which tells you how much heat is given off when one mole of a substance undergoes condensation, carries a negative sign.
You can thus say that
#color(blue)(DeltaH_"vap" = -DeltaH_"cond")#
This means that you can use
#DeltaH_"vap" = color(red)(+)"8.17 kJ/mol" ->#enthalpy of vaporization
#DeltaH_"vap" = color(red)(-)"8.17 kJ/mol" ->#enthalpy of condensation
Now, phase changes always take place at constant temperature, so don't worry about the given value for the boiling point of methane.
This means that the enthalpy change of vaporization will be equal to
#DeltaH_"vap" = - (-"8.17 kJ/mol")#
#DeltaH_"vap" = +"8.17 kJ/mol"#
All you have to do now is figure out how many moles are contained in that
#16.5 color(red)(cancel(color(black)("g"))) * ("1 mole CH"_4)/(16.04color(red)(cancel(color(black)("g")))) = "1.0287 moles CH"_4#
Well, if one mole must absorb
#1.0287 color(red)(cancel(color(black)("moles CH"_4))) * "8.17 kJ"/(1color(red)(cancel(color(black)("mole CH"_4)))) = color(green)("8.40 kJ")#
The answer is rounded to three sig figs.
Therefore, you can say that in order to convert