Question

The complete combustion of acetylene, C2H2(g), produces 1300. kJ of energy per mole of acetylene consumed. How many grams of acetylene must be burned to produce enough heat to raise the temperature of 1.00 gal of water by 14.8

Answer 1

we know that

1 gallon = 3.78541 L

also

1 L = 1000 cm3

so

1 gallon = 3785.41 cm3

so

volume of water given = 3785.41 cm3

given

density of water = 1 g /cm3

mass = density x volume

so

mass of water = 1 x 3785.41

so

mass of water = 3785.41 g

now

heat required to raise temperature = mass x specific heat x temp change

Q = m x s x dT

Q = 3785.41 x 4.184 x 14.8

Q = 234404.7 J

so

234404.7 J of heat is required to raise the temp of water

but given the efficiency is 73.5

so

efficiency = ( heat output / heat input ) x 100

73.5 = 234404.7 x 100 / heat input

heat input = 318917.95988 J

heat input = 318.9179 kJ

given 1 mole of C2H2 on burning gives 1300 kJ

so

moles of C2H2 required = heat required / 1300 kJ

moles of C2H2 required = 318.9179 / 1300

moles of C2H2 required = 0.245

now

mass of C2H2 required = moles x molar mass

molar mass of C2H2 = 26

so

mass of C2H2 required = 0.245 x 26

mass of C2H2 required = 6.378 g

so

6.378 g of C2H2 must be burned to produce enought heat