Consider the reaction: CaCO3(s) ⟶CaO(s)+CO2(g) Estimate ΔG^∘ for this reaction at each temperatu

Consider the reaction: CaCO3(s) ⟶CaO(s)+CO2(g) Estimate ΔG^∘...

Consider the reaction: $$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$ Estimate $\Delta G^{\circ}$ for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change too much within the given temperature range.) a. $298 \mathrm{~K}$ b. $1055 \mathrm{~K}$ c. $1455 \mathrm{~K}$

Consider the reaction:
$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$
Estimate $\Delta G^{\circ}$ for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change too much within the given temperature range.)
a. $298 \mathrm{~K}$
b. $1055 \mathrm{~K}$
c. $1455 \mathrm{~K}$

Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic quantity defined as ?G = ?H - T?S that predicts whether a reaction occurs spontaneously under constant temperature and pressure. A negative ?G indicates that the reaction proceeds spontaneously, while a positive ?G suggests non-spontaneity.

Reaction Spontaneity

Reaction spontaneity is determined by the sign of the ?G value. A spontaneous reaction has a negative ?G, meaning that the overall free energy of the system decreases. This concept is crucial for predicting the direction in which a chemical process will favorably proceed.

Temperature Dependence

The temperature dependence of free energy arises from the T?S term in the equation ?G = ?H - T?S. As temperature increases, the entropy contribution becomes more significant; thus, even reactions with positive ?H may become spontaneous if the T?S term is large enough to make ?G negative.

Enthalpy Change

Enthalpy change, ?H, represents the heat absorbed or released during a reaction at constant pressure. It is an essential term in the free energy equation and influences reaction spontaneity, as endothermic reactions (positive ?H) require a sufficiently positive entropy change and high temperature to become spontaneous.

Entropy Change

Entropy change, ?S, measures the disorder or randomness of a system during a reaction. In the Gibbs free energy equation, an increase in entropy (positive ?S) can drive a reaction toward spontaneity, especially at higher temperatures where the T?S term becomes more influential.

Transcript

00:01 So for this problem, we're given the reaction of calcium carbonate, c .a .c .o .3, as a solid, decomposing to calcium oxide and carbon dioxide as a gas.

00:20 And what they want us to do is calculate delta g, not, or at least predict it, at varying temperatures, at 298, 1055, and 1455 kelvin.

00:38 And so to do that, we first need to calculate, well, think back to this formula.

00:43 Delta g equals delta h minus t delta s.

00:49 So we need to go back and find out what delta h delta s are.

00:54 And so we can find those out by doing this, or delta h equals h not of products minus the enthalpy formation of the reactants.

01:12 And normally you have to account for the stoichiometry.

01:15 But it's all one to one, so there's no molar coefficients you need to consider.

01:20 So you can find these numbers.

01:22 Same thing for delta s.

01:27 And so you can find these values in your textbook and an appendix.

01:32 And so i've already looked them up.

01:34 So delta h not equals negative 634 .9 minus 393.

01:46 0 .5.

01:47 So these are your products minus your reactant, which is negative 1 -207 .6 so that gets you 179 .2 kilojoules.

02:01 Delta s can be found similarly, delta s -0...

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