Gibbs will get steamed

Chemistry Level 3

Consider the conversion of water to steam at p = 1 bar p=\SI{1}{\bar} and T = 393 K T = \SI{393}{\kelvin} . Find the change in Gibbs Free Energy (in J / mol \si[per-mode=symbol]{\joule\per\mole} ) for this reaction.

Details and Assumptions

  • Standard molar enthalpy of vaporisation of water at T = 373 K T = \SI{373}{\kelvin} is 40.657 kJ / mol \SI[per-mode=symbol]{40.657}{\kilo\joule\per\mole} .
  • Isobaric Molar heat capacity of steam (assume constant) = 37.47 J / ( mol K ) \SI[per-mode=symbol]{37.47}{\joule\per\mole\per\kelvin} .
  • Isobaric Molar heat capacity of water (assume constant) = 75.327 J / ( mol K ) \SI[per-mode=symbol]{75.327}{\joule\per\mole\per\kelvin} .

Round off your answer to nearest integer


The answer is -2160.

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1 solution

Neelesh Vij
Oct 27, 2016

To solve these kind of questions , it is better to define a energy reference level , from where all energies are to be measured.

For this particular one it will be water at 373 K 373K

Let C p C_p for water be C p 2 C_{p2} and steam be C p 1 C_{p1} The reaction is:

H X 2 O ( l ) H X 2 O ( g ) \ce{H_2O}_{(l)} \to \ce{H_2O}_{(g)}

We know that:

Δ G = Δ H T Δ S \Delta G = \Delta H - T \Delta S

Δ H reaction = Δ H products Δ H reactants \Delta H_{\text{reaction} } = \Delta H_{\text{products}} - \Delta H_{\text{reactants}}

Δ H reaction = ( H v + Δ T C p 1 ) ( Δ T C p 2 ) \Delta H_{\text{reaction}} = ( H_{v} + \Delta T C_{p1} ) - ( \Delta T C_{p2} )

Δ H reaction = 39899.86 J/mol \Delta H_{\text{reaction}} = 39899.86 \text{J/mol}

Now similarly:

Δ S reaction = Δ S products Δ S reactants \Delta S_{\text{reaction} } = \Delta S_{\text{products}} - \Delta S_{\text{reactants}}

Δ S reaction = ( H v T + C p 1 ln T 2 T 1 ) ( C p 2 ln T 2 T 1 ) \Delta S_{\text{reaction} } = ( \dfrac{ H_v }{T} + C_{p1} \ln{\dfrac{T_2}{T_1} } ) - ( C_{p2} \ln{ \dfrac{T_2}{T_1} } )

Δ S reaction = ( 40657 373 + C p 1 ln 393 373 ) ( C p 2 ln 393 373 ) \Delta S_{\text{reaction} } = ( \dfrac{40657}{373} + C_{p1} \ln{ \dfrac{393}{373} } ) - ( C_{p2} \ln{\dfrac{393}{373} } )

Δ S reaction = 107.023 \Delta S_{\text{reaction} } = 107.023

Putting values

Δ G = 2106.17 \Delta G = -2106.17

@neelesh vij typo error at the end 2160:2106

Gauri shankar Mishra - 4 years, 7 months ago

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Yeah , @neelesh vij ; Correct your typo!

Aniket Sanghi - 4 years, 6 months ago

Nice solution ! 👍

Aniket Sanghi - 4 years, 6 months ago

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