Start by making sure that you have clear understanding of what heat capacity means.
As you can se from the units used to express it, heat capacity tells you what the ratio between the amount of heat added, in your case, to the bomb calorimeter, and the subsequent increase in temperature.
SImply put, a heat capacity of
Mathematically, this is expressed as
#color(blue)(q = C * DeltaT)" "#, where
Plug in your values and find
#q = 2.47"kJ"/color(red)(cancel(color(black)("K"))) * 2.22color(red)(cancel(color(black)("K"))) = "5.4834 kJ"#
Now, the idea here is that the heat released by the combustion reaction will be equal to the heat absorbed by the calorimeter.
#-q_"released" = q_"absorbed"#
The minus sign is used here because heat given off carries a negative sign.
So, you know that the combustion of
Use ethylene's molar mass to determine how many moles you would get in the sample
#0.109color(red)(cancel(color(black)("g"))) * ("1 mole C"_2"H"_4)/(28.053color(red)(cancel(color(black)("g")))) = "0.003886 moles C"_2"H"_4#
#1color(red)(cancel(color(black)("mole"))) * "5.4834 kJ"/(0.003886color(red)(cancel(color(black)("moles")))) = "1141.1 kJ/mol"#
This means that the enthalpy change of combustion for ethylene will be
#DeltaH_"comb" = -color(green)("1140 kJ/mol") ->#rounded to three sig figs
The minus sign here symbolizes that this much heat is being released when one mole of ethylene undergoes combustion.