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Sodium carbonate can be made by heating sodium bicarbonate: 2NaHCO3(s) → Na2CO3(s) + CO2(g) + H2O(g) At 25°C, for this reaction, ΔH°rxn = 128.9 kJ/mol and ΔG°rxn = 33.1 kJ/mol. Above what minimum temperature will the reaction become spontaneous under standard state conditions?

User Cethint
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1 Answer

5 votes

Answer:

401.17 K is the minimum temperature at which the reaction will become spontaneous under standard state conditions.

Step-by-step explanation:

The expression for the standard change in free energy is:


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

Where,


\Delta G is the change in the Gibbs free energy.

T is the absolute temperature. (T in kelvins)


\Delta H is the enthalpy change of the reaction.


\Delta S is the change in entropy.

Given at:-

Temperature = 25.0 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15

So,

T₁ = (25.0 + 273.15) K = 298.15 K


\Delta H = 128.9 kJ/mol


\Delta G = 33.1 kJ/mol

Applying in the above equation, we get as:-


33.1=128.9-298.15* \Delta S


-29815\Delta S=-9580


\Delta S=-9580 = 0.32131 kJ/Kmol

So, For reaction to be spontaneous,
\Delta G<0

Thus, For minimum temperature:-


\Delta H-T* \Delta S=0


128.9-T* 0.32131=0


T=(128.9)/(0.32131)=401.17\ K

Hence, 401.17 K is the minimum temperature at which the reaction will become spontaneous under standard state conditions.

User Exilit
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