Question

A swimming pool, 10.0 m by 4.0 m, is filled with water to a depth of 3.0 m at a temperature of 20.2°C. If the energy needed to raise the temperature of the water to 26.1°C is obtained from the combustion of methane (CH4), what volume of methane, measured at STP, must be burned? ∆Hcombustion for CH4 = -891 kJ/mol volume CH4 needed

Answer 1

Volume of water = 10 X 4 X 3 = 120 m³ = 120000 L = 120000000 ml

density of water = 1g/ml

mass of water = 1.2 x 10⁸ g

q = msT

   = 1.2 X 10⁸ X 4.184 X(26.1-20.2)

   = 2.96 X 10⁹ J = 2.96 X 10⁶ KJ

891 KJ energy comes from ----> one mole of methae

2.96 X 10⁶ KJ energy from ----> 2.96 X 10⁶ KJ /891 KJ/mol

                                            = 3.32 X 10³ moles of methane

At STP

one mole of methane occupying volume             = 22.4 L

3.32 X 10³ moles of methane occupying volume = 22.4 X 3.32 X 10³

                                                                            = 7.44 X 10⁴ L