Question

How many kilojoules are given off when 17.8 mol of `CH_4` react?

Answer 1

`DeltaH =-15860" kJ"`

Explanation:

By "react" I assume that you mean combusts with `O_2`. This reference for Methane tells us that heat given off by combustion is `DeltaH =-891" kJ/mol"`

The heat for `17.8" mol"` is

`DeltaH =(-891" kJ/mol")(17.8" mol")`

`DeltaH =-15860" kJ"`

Answer 2

`"15800 kJ"` are given off when `"17.8 mol CH"_4"` react.

Explanation:

`"CH"_4("g") + "2O"_2("g")"` `rarr` `"CO"_2("g") + "2H"_2"O("l")"` `DeltaH_c"=` `-890.7` `"kJ/mol"`.
https://webbook.nist.gov/cgi/cbook.cgi?Name=methane&Units=SI&cTG=on#Thermo-Gas

Multiply the given moles `"CH"_4"` by `DeltaH_c"` for `"CH"_4"`.

`17.8color(red)cancel(color(black)("mol CH"_4))xx(-890.7"kJ")/(1color(red)cancel(color(black)("mol CH"_4)))"="-15800` `"kJ"` (rounded to three significant figures)

`"15800 kJ"` are given off when `"17.8 mol CH"_4"` react.