Calculate ΔG^∘ and K at 25^∘ C for the reactions in Exercises 36 and 40 .

Name: Problem 72, Chapter 18: Chemistry
Uploaded: 2021-02-13T17:27:48-08:00
Duration: 6 min 58 s
Channel: David Collins
Description: Calculate ΔG^∘ and K at 25^∘ C for the reactions in Exercises 36 and 40 .

Calculate ΔG^∘ and K at 25^∘ C for the reactions in...

Key Concepts

Temperature Conversion to Kelvin

In thermodynamic calculations, temperature must be expressed in Kelvin. For instance, 25°C is converted to 298 K. This conversion is critical because the thermodynamic equations, such as those relating ?G° and K, require the absolute temperature scale to ensure consistency and correctness of the results.

Relationship Between ?G° and K

The fundamental thermodynamic relationship between ?G° and the equilibrium constant is given by the equation ?G° = -RT ln K. This equation connects the spontaneity of a reaction (through ?G°) with the equilibrium position (through K), where R is the universal gas constant and T is the temperature in Kelvin. It allows for the calculation of one parameter when the other is known.

Standard Gibbs Free Energy Change (?G°)

This concept refers to the change in Gibbs free energy when a reaction occurs under standard conditions. It provides an indication of the spontaneity of a reaction; a negative ?G° suggests that the reaction is spontaneous, while a positive ?G° indicates non-spontaneity under standard conditions.

Equilibrium Constant (K)

The equilibrium constant is a dimensionless number that quantifies the ratio of the concentrations (or activities) of products to reactants when a chemical reaction has reached equilibrium. It serves as a measure of the extent to which a reaction proceeds and is critical in predicting the composition of reaction mixtures at equilibrium.

Transcript

00:01 In order to calculate delta g and e cell for the chemical reactions that are found in questions 38 and 42, we need to know the equations that allow us to calculate delta g and k, those being delta g standard is equal to negative nfe standard, where n is the number of moles of electrons that are transferred in the balanced chemical reaction.

00:33 Reaction, and e standard is the cell potential for the balanced chemical reaction, and f is faraday's constant.

00:42 So that means to calculate delta g, knowing this equation, we need to know the balanced chemical reaction, so we can get n, the moles of electrons that are transferred in the balanced chemical reaction, and we need to know the cell potential for the balanced chemical reaction, which will require us to know the standard reduction potentials for the two half -reactions, reactions that comprise the entire reaction.

01:08 Then once we know delta g standard, we can calculate the equilibrium constant, where the equilibrium constant is equal to e to the negative delta g standard divided by r, which is universal gas constant as 8 .314 joules per kelvin mole, and then t is the kelvin temperature.

01:31 So for 38a, this is the chemical reaction.

01:38 It's not balanced as is, but if you look up the two half reactions that give us this overall reaction, you'll notice that five electrons are involved in order to get one -half i -2.

01:54 So in order to get a full i -2, we're going to need to have 10 electrons involved.

01:59 We'll take the two half reactions that comprise this reaction, and e -cell will be equal to what is being reduced, so the cathode potential minus what is being oxidized, the anode potential, and we get a cell potential of 0 .43 volts.

02:19 So the delta g standard will be equal to, as i mentioned, once this is balanced, we will get 10 electrons for the balanced chemical reaction is equal to negative 10, multiplied by 96 ,485, multiplied by the cell potential we just determined up here.

02:38 And we get negative 415 ,000 joules or negative 415 kilojoules.

02:46 So for the equilibrium constant, k is going to be equal to e to the negative, negative 415 ,000 jules, knowing that we need to have g in units of joules up here, not kilojoules when solving for k, divided by r, 8 .314 divided by t, 25 degrees celsius or 298 kelvin.

03:12 Now we get 5 .3 times 10 to the 72 for our equilibrium constant.

03:18 For the next one, we have z metal plus ag plus goes to zinc 2 plus plus a g.

03:25 This one is easy to balance.

03:27 We need a 2 in front of the silvers, so we have a total 2 plus charge and a 2 plus charge on both sides.

03:36 E standard then is going to be equal to what is being reduced, the silver potential minus what is being oxidized, the zinc potential, and we get a cell potential of 1 .56 volts.

03:49 Delta g standard then is going to be equal to the number of electrons transferred...

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