How many liters of methane gas (ch4) need to be combusted to produce 12.4 liters of water vapor, if all measurements are taken at the same temperature and pressure? show all of the work used to solve this problem.
ch4 (g) + 2o2 (g) yields co2 (g) + 2h2o (g)

Since litres is the subject of the question, molar mass will be considered in litres. 
Since the question didn't specify if it was a complete combustion or incomplete combustion, we assume that it is a complete combustion. 
Mr(CH4) =16
Mr (O2)= 32 
Mr(H20)=18 
so, 16 litres of methane will produce 36 litres of water vapour. How many litres of methane will combust to produce 12.4 litres of H20? 
Cross multiply. 
(12.4 x 16) / 36 = 5.51 litres. 

Yes, endothermic means it turns cold. and some chemical changes include change of tempature.