Use standard free energies of formation to calculate ΔG^∘ at 25^∘ C for each reaction in Problem

step 1 In this question we've been given some systems. Four systems I've been asked to determine the st

Use standard free energies of formation to calculate ΔG^∘ at...

Use standard free energies of formation to calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each reaction in Problem $57 .$ How do the values of $\Delta G^{\circ}$ calculated this way compare to those calculated from $\Delta H^{\circ}$ and $\Delta S^{\circ} ?$ Which of the two methods could be used to determine how $\Delta G^{\circ}$ changes with temperature?

Key Concepts

Standard Free Energy of Formation

This concept involves tabulated values for the Gibbs free energy change when one mole of a compound is formed from its elements in their standard states. It is the baseline data used to compute the overall free energy change for reactions by combining the formation energies of products and reactants.

Calculation of Reaction Free Energy

The free energy change for a reaction (?G°) can be computed by subtracting the sum of the standard free energies of formation of the reactants from that of the products. This method directly uses formation data and provides the ?G° at a specified temperature, such as 25°C.

Enthalpy and Entropy Relationship

An alternative approach to calculate ?G° is based on the thermodynamic relation ?G° = ?H° - T?S°. Here, ?H° represents the enthalpy change and ?S° the entropy change for the reaction, highlighting the interplay between heat exchange and disorder in determining reaction spontaneity.

Temperature Dependence of Gibbs Free Energy

While both methods yield ?G° at a given temperature, the ?H° - T?S° formulation is particularly useful for predicting how ?G° changes with temperature. This approach, often further refined by the Gibbs-Helmholtz equation, explicitly shows the temperature dependence by incorporating the T?S° term.

Transcript

00:01 In this question we've been given some systems.

00:02 Four systems i've been asked to determine the standard gives energy change.

00:09 And we know the gibbs energy change is a state function, so we can calculate it as the sum of the gives energy change, standard gives energy change of the products minus the sum of the standard gives energy change of the reactants.

00:32 And we always have to remember to include the stoichiometric coefficients.

00:38 We also know that this can be calculated from the standard gives energy change being equal to the standard enthalpy change minus the temperature multiplied by the standard entropy change.

00:49 So we have to use these two methods in order to determine our gibbs energy change.

00:55 So looking at the first system, we can tell that dota g standard is going to be equal to 2 multiplied by 5.

01:02 1 .3 minus 1 multiplied by 97 .8.

01:07 What we are doing here we're just looking at the products minus the reactants.

01:12 So at the end of the day using this approach this is going to be equal to 4 .8 and this is in kilo -tops.

01:21 And if we use this formula again, we can tell that our delta standard is equal to the enthalpy change of that reaction which is 57 .2 to 4, multiplied by 10 to the power 3 minus the temperature of 298 .15 kelvinry number.

01:40 This is 25 degrees celsius multiplied by the standard entropy change, which is 175 .8...

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