Using data from Appendix C, calculate the change in Gibbs free energy for each of the following

Using data from Appendix C, calculate the change in Gibbs...

Using data from Appendix $\mathrm{C},$ calculate the change in Gibbs free energy for each of the following reactions. In each case indicate whether the reaction is spontaneous at $298 \mathrm{~K}$ under standard conditions. (a) $2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)$ (b) $\mathrm{P}_{4} \mathrm{O}_{6}(s)+12 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$

Using data from Appendix $\mathrm{C},$ calculate the change in Gibbs free energy for each of the following reactions. In each case indicate whether the reaction is spontaneous at $298 \mathrm{~K}$ under standard conditions.
(a) $2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)$
(b) $\mathrm{P}_{4} \mathrm{O}_{6}(s)+12 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
(c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$
(d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$

Key Concepts

Gibbs Free Energy Change

Gibbs free energy change (?G) is a thermodynamic quantity that indicates the amount of reversible work obtainable from a chemical reaction at constant temperature and pressure. It is calculated by summing the standard free energies of formation for the products and subtracting that of the reactants, and it provides insight into whether a reaction will proceed spontaneously or require an input of energy.

Standard Gibbs Free Energy of Formation

The standard Gibbs free energy of formation is the change in free energy when one mole of a compound is formed from its elements in their standard states. These tabulated values, usually found in reference data like Appendix C, are essential for calculating the overall ?G for a reaction using the stoichiometric coefficients of the balanced chemical equation.

Standard Conditions

Standard conditions refer to a set of predefined conditions under which thermodynamic measurements are made, typically 298 K (25°C) for temperature, 1 atm for pressure, and 1 M concentration for solutions. Using these conditions allows for consistency in comparing thermodynamic data and calculating Gibbs free energy changes.

Reaction Spontaneity

Reaction spontaneity is determined by the sign of the Gibbs free energy change. A negative ?G indicates that the reaction is spontaneous under standard conditions, while a positive ?G means the reaction is non-spontaneous. This concept is fundamental in predicting whether a reaction will occur without external energy input.

Transcript

00:01 Let's see if we can determine whether a reaction is spontaneous or not at 298 kelvin using the gibbs free energy.

00:10 A reaction will be spontaneous if the change in gibbs free energy of a reaction winds up being negative.

00:22 And so we're going to have to use the equation that the gibbs free energy of reaction under standard conditions or delta g not of reaction.

00:31 Is equal to the sum of the number of moles times the gives energy of formation for the products minus the sum of the number of moles times the gibbs free energy of the reactants.

00:47 So the n and the m here mean number of moles and this mathematical symbol sigma means to sum it up.

00:57 So if we have more than one product, we'll have to add them up if there's more than one reactants.

01:01 We'll have to add them up.

01:04 So let's take a look at a couple examples of chemical reactions and see whether we can figure out whether they're spontaneous or not.

01:13 So the first reaction we'll look at is taking a look at silver and chlorine gas and making silver chloride.

01:29 Again, these are being done at standard conditions, 298 kelvin, so you can look up the values for the gibbs.

01:37 Formation.

01:39 So to do our calculation, we look at the product side first.

01:45 There's one product.

01:47 We take the number of moles and multiply it by the gibbs energy of formation.

01:52 So we have two moles.

01:55 And we go and take a look at what the gibbs free energy is for this reaction.

02:00 It's negative 109 .7 kilojoules per mole.

02:06 And that is the only product.

02:08 So there's nothing to sum up.

02:10 We have our subtraction sign in our equation.

02:14 Now for our reactants, we have two reactants.

02:19 Recall that the gibbs free energy of elements in their natural state is zero, and both of these elements are in their natural state.

02:26 But just to show you how the equation works, we have a number of moles.

02:32 So for silver, we have two moles.

02:34 We would multiply that by the gibbs energy of formation, which in this case is zero.

02:40 But this sigma in the equation says that we have to add any other substances as well.

02:49 And so cl2 is another substance.

02:52 We have one mole of that.

02:55 And the gibbs free energy that is also zero kilojoules per mole.

03:02 If there were any other substances, we'd add those in as well.

03:05 And then we would go do the math and figure out that the gibbs energy of reaction for this particular reaction is negative two.

03:14 219 .4 kilojoules.

03:17 And since it is negative, it is spontaneous.

03:25 Now we can do this for several other reactions too.

03:31 So for instance, we can take a look at p4 .010 as a solid and 16 hydrogens, hydrogen is a gas, forming four ph -3s, and 10 waters...

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