Assuming your tea cup holds10.0 mol of water (It actually does! 10 mol water is approximate 6 fl. oz.) How much heat is required to raise the temperature of your tea water from room temperature to 100 °C? The specific heat of water is 4.184 J g-1 K-1.

If you are going to work in moles you need to know the molar heat capacity

q = n Cmol dT

q = (10.0 mol)(75.318 J mol-1 K-1)(100 °C - 23 °C)

q = 57,990 J

How much methane would have to be burned to heat the water?

Since the water absorbs 57.990 J of heat, the reaction must release 57,990 J of heat. So,

qrxn = - 57,990 J

Since you know that DHcombustion = -890 kJ/mol (because you looked it up in a book) use factor label and stoichiometry to solve the problem.

(-890 kJ was converted to -890,00 J)