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Hess' Law

Calculate fre...

Question

Calculate free energy change for the reaction at $27^{o} C$
$H_{2 (g)} + C l_{2 (g)} \to 2 H - C l_{(g)}$
by using the bond energy and energy data.
Bond energies of $H - H, C l - C l$ and $H - C l$ bonds are $435 k J m o l^{- 1}, 240 k J m o l^{- 1}$ and $430 k J m o l^{- 1}$ respectively. Standard entropies of $H_{2}, C l_{2}$ and $H C l$ are $131, 223$ and $187 J K^{- 1} m o l^{- 1}$ respectively.

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Solution

Calculating $△ H_{r e a c t i o n}$
$H_{2} (g) + C l_{2} (g) \to 2 H - C l (g); T = 300 K$
$△ H_{r e a c t i o n} = \sum △ H_{p r o d u c t}^{f} - \sum △ H_{r e a c t a n t}^{f}$
$△ H_{H_{2}}^{f} = 435 k J m o l^{- 1}; △ H_{C l_{2}}^{f} = 240 k J m o l^{-}; △ H_{H - C l}^{f} = 430 k J m o l^{-}$
$△ H_{r e a c t i o n} = 2 \times 430435 - 240 = 185 k J m o l^{-}$
Calculating $△ S_{r e a c t i o n}$
$△ S_{r e a c t i o n} = \sum △ S_{p r o d u c t} - \sum △ S_{r e a c t a n t}$
$△ S_{H_{2}} = 131 J K^{- 1}; △ S_{C l_{2}} = 223 J K^{- 1}; △ S_{H - C l} = 187 J K^{- 1}$
$△ S_{r e a c t i o n} = 2 \times 187223 - 131 = 20 J K^{- 1}$
Now, $△ G_{r e a c t i o n} = △ H_{r x n} - T △ S_{r e a c t i o n}$
$= 185 - \frac{20 (300)}{1000}$
$= 185 - 6$
$- 179 k J m o l^{- 1}$
$∴ △ G_{r x n} = 179 k J m o l^{- 1}$

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