Reactions in which a substance decomposes by losing CO are...

Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds as follows: $$ \mathrm{CH}_{3} \mathrm{COOH}(l) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{CO}(g) $$ By using data from Appendix $\mathrm{C},$ calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not vary with temberature.

Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds as follows:
$$
\mathrm{CH}_{3} \mathrm{COOH}(l) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{CO}(g)
$$
By using data from Appendix $\mathrm{C},$ calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not vary with temberature.

Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that combines enthalpy and entropy to determine the spontaneity of a reaction. The equation ?G = ?H - T?S shows how the balance of these properties affects whether a process will occur naturally, with a negative ?G indicating spontaneity under given conditions.

Temperature Dependence of Reaction Spontaneity

The spontaneity of a reaction is influenced by temperature because of its role in the Gibbs free energy equation. By setting ?G = 0, one can determine the threshold temperature (T = ?H/?S) at which a reaction changes from non-spontaneous to spontaneous, assuming the enthalpy and entropy are constant over the temperature range considered.

Thermodynamic Spontaneity Criteria

The criteria for spontaneity in thermodynamics are based on the sign of the Gibbs free energy change. A reaction is spontaneous if ?G is negative, requires equilibrium when ?G is zero, and is non-spontaneous when ?G is positive. This concept is fundamental when predicting the behavior of chemical reactions under different conditions.

Standard Thermodynamic Conditions

Standard thermodynamic conditions refer to a set of baseline conditions (typically 1 atm pressure and a specified temperature, often 298 K, though temperature can vary in different contexts) used to simplify the reporting and calculation of thermodynamic data. Under these conditions, standard enthalpy (?H°) and entropy (?S°) values are used to evaluate the feasibility and spontaneity of reactions.

Transcript

00:01 A reaction is spontaneous when the gibbs free energy for that particular reaction is negative.

00:08 And so we can figure out what temperatures at which a reaction will be spontaneous or not spontaneous.

00:17 And specifically, we can use the equation for gibbs free energy at standard conditions to be able to figure out the minimum temperature at which a reaction will take place.

00:30 So what we do know is that the value of delta g is going to have to be negative for a reaction to be spontaneous.

00:41 And so if that is the case, that must mean that the t delta s term here must wind up being greater than the delta h term.

00:57 And if that is true, that must mean that what we're looking for for this to wind up being negative.

01:04 Is for t to wind up being greater than the ratio of the enthalpy to the entropy.

01:17 So we're going to have to use this equation to be able to find that minimum temperature at which the reaction will be spontaneous.

01:26 Well, how are we going to do that? we're going to have to go and calculate the delta h of reaction and the delta s of reaction, for this decarbonolation reaction of acetic acid into methanol and carbon monoxide.

01:42 So we're going to have to use the equation where the delta h of reaction is equal to the sum of the products minus the sum of the reactants.

01:55 And then go look up those values and solve.

02:08 Let's do the same thing in a moment for the entropy as well.

02:13 So if you take a look at the reaction, they're all one mole of each substance.

02:20 And we do products minus reactants.

02:24 So the delta h of reaction here, since there's only one mole of each, we're going to take the products.

02:37 So we have negative 201 .2 kilojoules because we have times one mole.

02:46 And we're going to add to that our negative 110 .5 kilojoules because we have only one mole.

02:55 We would multiply by the number of moles if we had more than one...

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