Specific heat?

Question

Hi,

A gas stove generates heat from the combustion of methane:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) ΔH = -802 kJ

How many moles of methane would need to be reacted in order to heat 4.00 kg (~ 1 gallon) of water (Cs = 4.18 J/g-K) from room temperature (25° C) to boiling (100° C)?

I know you use the formula q=c*m*deltaT. How would you go about doing it though?


Thanks!

Answer 1

q=c*m*deltaT
q=(4.18 J/gK)*(4000g)*(75K)
q=1254000 J = 1254 kJ

This is the amount of heat required to raise the temperature of 4000g of water from 25 C to 100 C (a total of 75 C or 75 K).

Burning one mole of methane nets us 802 kJ so we need to burn 1254/802 = 1.56 mole to obtain the required amount of heat.