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djverab [1.8K]
3 years ago
13

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?
Chemistry
1 answer:
insens350 [35]3 years ago
6 0

Answer:

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

Explanation:

The expression for the standard change in free energy is:

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

-29815\Delta S=-9580

\Delta S=-9580 = 0.32131 kJ/Kmol

So, For reaction to be spontaneous, \Delta G

Thus, For minimum temperature:-

\Delta H-T\times \Delta S=0

128.9-T\times 0.32131=0

T=\frac{128.9}{0.32131}=401.17\ K

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

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