if entropy of methane ,oxygen, carbon dioxide, and water are 186,205,214,70 respectively and enthalpy of fusion of methane, carbon dioxide and water are -74.8,-393.5,-285.8 respectively, find the free energy change for the combustion of methane at 300K.

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Solution

$T h e c o m b u s t i o n r e a c t i o n o f m e t h a n e i s C H_{4} + 2 O_{2} \to C O_{2} + 2 H_{2} O T h e c h a n g e i n e n t h a l p y i s ∆ H = H_{P r o d u c t} - H_{R e a c \tan t} = [H_{C O_{2}} + 2 H_{H_{2} O}] - [H_{C H_{4}} + 2 H_{O_{2}}] = [- 393.5 + 2 (- 285.8)] - [- 74.8 + 0] (e n t h a l p y o f o x y g e n i s z e r o \sin c e i t i s a n e l e m e n t a l f o r m) = - 890.3 K J / m o l T h e c h a n g e i n e n t r o p y i s ∆ S = S_{P r o d u c t} - S_{R e a c t a n t} = [S_{C O_{2}} + 2 S_{H_{2} O}] - [S_{C H_{4}} + 2 S_{O_{2}}] = [214 + 2 (70)] - [186 + 2 (205)] = - 242 J / m o l / K T h e r e l a t i o n b e t w e e n e n t h a l p y, e n t r o p y a n d f r e e e n e r g y i s ∆ G = ∆ H - T ∆ S = - 890.3 \times 10^{3} - (300 \times - 242) = - 817700 J / m o l = - 817.7 K J / m o l$

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Similar questions

Q. The enthalpy of combustion of methane, graphite and dihydrogen at

298 K

are

- 890.3

k J {m o l}^{- 1}, - 393.5

k J {m o l}^{- 1}, - 285.8

k J {m o l}^{- 1}

respectively. Enthalpy of formation of

{C H}_{4 (g)}

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