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Spontaneity

For the react...

Question

For the reaction,
$4 C (g r a p h i t e) + 5 H_{2} ⟶ n C_{4} H_{10}; Δ H^{o} = - 124.73 k J {m o l}^{- 1}$
$4 C (g r a p h i t e) + 5 H_{2} ⟶ i s o - C_{4} H_{10}; Δ S^{o} = - 365.8 J K^{- 1} {m o l}^{- 1}$
$Δ H^{o} = - 131.6 k J {m o l}^{- 1}$
$Δ S^{o} = - 381.079 J K^{- 1} {m o l}^{- 1}$
Indicate whether normal butane can be spontaneously converted to iso-butane or not.

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Solution

Yes, $Δ G^{o} = - 2.32 k J$
For $n C_{4} H_{10}$
$Δ G^{o} = Δ H^{o} - T Δ S^{o}$
$= - 15.72 k J$
For $i s o - C_{4} H_{10}$
$Δ G^{o} = - 18.04 k J$
For conversion
$Δ G^{o} = - 18.04 - (- 15.72) = - 2.32 k J$

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