Question

Natural gas burns in air to form carbon dioxide and water, releasing heat. CH4(g)+2O2(g)→CO2(g)+2H2O(g) ΔHrxn = -802.3 kJ.What minimum mass of CH4 is required to heat 45.0 g of water by 21.0 ∘C? (Assume 100% heating efficiency.) (For water,Cs= 4.18 J/g∘C).

Answer 1

CH4(g)+2O2(g)-------------------->CO2(g)+2H2O(g)

Each gram of water requires 4.18J of heat to increase by 1C

45g * 21C = 945 Joules of heat needed

One mole of CH4 weighs 16.04 grams/mole and burning one mole supplies 802.3kJ of heat

Specific heat Q = m Cp dT

Heat added = specific heat x mass x (tfinal - tinitial)

Heat added = 4.18 J/g∘C * 45g * (21C - 0C)

Heat added = 3950 Joules = 3.950 kJ

3.950 kJ / 802.3kJ = 4.9234 x 10^-3 moles of methane needed

mass = 4.9234 x 10^-3 mol x 16.04 g/mol = 0.079

mass of methane needed = 0.079 grams