Answer to Question #91684 in Organic Chemistry for Jamad

Question

burning methan releases 890.4kj/mol-1 of methane burned in a hot water tank, natural gas is burned to release heat and warm up the water. what mass of methane would need to be burned to warm up 60.0 us gallons of water from 12.0c to 75.0 c?

Answer 1

SI: 1 US gallon=3.785 l; 60 gallons=227.1 l; 

definitions: m(water)=227.1 kg, weight of water;

c=4183 J/(kg*C), Specific heat capacity of water;

t2=75C

t1=12C

q=890.4 kJ/mol, heat of methane burning

M=0.016 kg/mol, molar weight of methane

Q1=c*m(water)*(t2-t1) (energy for heating of water)

Q2=q*n(CH4) (energy releases by methane burning)

Q1=Q2, thus

m(CH4)=(M(CH4)*c*m(water)*(t2-t1))/q=((0.016 kg/mol)*(4183 J/(kg*mol))*(227 kg)*(63C))/(890.4*10^3 (J/mol))=1.08 kg of methane