Question

Calculate the mass of methane that must be burned to provide enough heat to convert 300.0 g of water at 30.0°C into steam at 106.0°C.

Answer 1

the enthapy of combustiondata of methane and the enthapy of vaporisation of water should be given.

these data are missing so i am taking them from my side .....  

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O (l)    ΔH combustion   = - 890Kj/mol

H2O(l) -------->   H2O (g)      ΔHvap = 40.66 kj/mol

Specific heat of water = 4.184 j/g         Specific heat of steam = -1.996 j/g

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Heat needed for Water = Heating from 30^o to 100^o + heat for vaporisation at 100^o +

                                                 heat for heating steam from 100^o to 106^o

           = (msΔT)_water    +    n x ΔHvap +   (msΔT )_steam

          = 300x4.184x (100-30)   + 1000x (300/18) x40.66 + 300x(-1.996) (106-100)

          = 24864 + 677666.67 - 3592.8 =698.937 Kj

Heat needed = heat supplied by methane

let m be the mass of the methane , so moles = m/16

698.937 Kj = (m/16) (890)

m = mass of methane = 14.921 grams