Question

Calculate the mass of methane that must be burned to provide enough heat to convert 203.0 g of water at 31.0°C into steam at 116.0°C. (Assume that the H₂O produced in the combustion reaction is steam rather than liquid water.)

Answer 1

We know that,

Enthalpy of combustion of Methane = - 890 kJ / mol

Heat required to convert 203.0 g of water at 31.0°C into steam at 116.0°C = Heat required to raise the temp. of water from 31 C to 100 C + Heat required to convert water to steam at 100 C + Heat required to raise the temp. of steam from 100 C to 116 C

Heat required to raise the temp. of water from 31 C to 100 C = m c (100 - 31) = 203 x 4.18 x 69 = 58549.3 J

Heat required to convert water to steam at 100 C = m L = 203 x 2257 = 458171 J

Heat required to raise the temp. of steam from 100 C to 116 C = m c (116 - 100) = 203 x 2 x 16 = 6496 J

=> Heat required to convert 203.0 g of water at 31.0°C into steam at 116.0°C = 58549.3 + 458171 + 6496 = 523216.3 J = 523.22 kJ

We need 523.22 kJ of Heat

If we burn 1 mole of methan we get 890 kJ of heat

Therefore moles of methane that we need to burn = 523.22 / 890 = 0.588 moles of CH4

=> Mass of Methane that needs to be burnt = 0.588 x 16 = 9.41 g