Consider the thermal decomposition of calcium carbonate: CaCO3(s) ⟶CaO(s)+CO2(g) (a) Use the dat

Consider the thermal decomposition of calcium carbonate:...

Consider the thermal decomposition of calcium carbonate: $$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(g)$$ (a) Use the data in Appendix B to calculate the standard free-energy change for this reaction at $25^{\circ} \mathrm{C}$. (b) Will a mixture of solid $\mathrm{CaCO}_{3}$, solid $\mathrm{CaO}$, and gaseous $\mathrm{CO}_{2}$ at 1 atm pressure react spontaneously at $25^{\circ} \mathrm{C}$ to produce more $\mathrm{CaO}$ and $\mathrm{CO}_{2}$? (c) Assuming that and are independent of temperature, estimate the temperature at which the reaction becomes spontaneous.

Consider the thermal decomposition of calcium carbonate:
$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(g)$$
(a) Use the data in Appendix B to calculate the standard free-energy change for this reaction at $25^{\circ} \mathrm{C}$.
(b) Will a mixture of solid $\mathrm{CaCO}_{3}$, solid $\mathrm{CaO}$, and gaseous $\mathrm{CO}_{2}$ at 1 atm pressure react spontaneously at $25^{\circ} \mathrm{C}$ to produce more $\mathrm{CaO}$ and $\mathrm{CO}_{2}$?
(c) Assuming that and are independent of temperature, estimate the temperature at which the reaction becomes spontaneous.

Key Concepts

Standard Free Energy Change

This concept involves calculating the overall change in Gibbs free energy (?G°) for a reaction under standard conditions. It is computed using the standard free energies of formation of the reactants and products. A negative ?G° indicates that the reaction is thermodynamically favored, while a positive value suggests non-spontaneity under standard conditions.

Reaction Spontaneity

Spontaneity refers to whether a reaction can proceed without needing an external input of energy. In thermodynamic terms, a reaction is spontaneous if the Gibbs free energy change (?G) is negative. This assessment can be made under standard conditions or under the actual conditions of the reaction, including considerations of pressure and temperature.

Thermal Decomposition Reaction

Thermal decomposition reactions are chemical processes where a single compound breaks down into two or more simpler substances when heated. Understanding the energy dynamics of these reactions is crucial, as the decomposition depends on the conditions under which the sample is heated and the thermodynamic stability of the resultant products.

Temperature Dependence of Reaction Spontaneity

The spontaneity of a reaction is temperature-dependent as described by the Gibbs free energy equation, ?G = ?H - T?S, where ?H is the change in enthalpy and ?S is the change in entropy. This relationship explains why a reaction that is non-spontaneous at one temperature can become spontaneous at another if the temperature change sufficiently influences the T?S term.

Equilibrium Temperature Calculation

This concept involves determining the specific temperature at which a reaction reaches equilibrium—that is, when ?G is equal to zero. By setting ?G = 0 in the equation ?G = ?H - T?S and solving for T, one can estimate the temperature at which a reaction transitions from non-spontaneous to spontaneous under the assumption that ?H and ?S remain constant.

Transcript

00:01 So we're going to look at a reaction and kind of talk about the gibbs free energy, how we can calculate that.

00:07 And then what does that mean, talking about the spontaneity of a reaction? so when we look over here, we have our equation for our gibbs free energy.

00:16 And then another way we can do it is we can do the gibbs free energy of our product minus the sum of it of our reactants to find it for our.

00:32 Our reaction total.

00:34 And so that's what we're going to do.

00:35 We're also going to use this one i just starred and then talk about spontaneity.

00:39 So let's look at this example.

00:41 Our calcium carbonate solid is going to decompose to calcium oxide, which is a solid and then our carbon dioxide, which is gas.

00:48 This equation is balanced as written.

00:51 So let's go ahead and try to find our gibbs free energy for our reaction as a total.

00:57 When you look in different appendixes, it will give you the information, making sure that we are looking out that delta g.

01:03 So for calcium carbonate, you'll see that it is 11 to 9 .1.

01:08 This is kilojoules per mole.

01:10 Calcium oxide is negative 603 .3 kilojoules per mole.

01:20 And then our carbon dioxide is negative 394 .4 kilojoules per mole.

01:27 So what we're going to do is we're going to take this into account.

01:32 And so we're going to do these sum of the products.

01:40 And we notice that we have this mole unit here.

01:43 So we are going to need to cancel that out.

01:46 And so we will multiply this times one mole because we have one mole of each of those.

01:53 And then add it with our 394 negative 394 .4.

02:01 Mull times one mole so that is the sum of our products and now let's subtract the reactants so we just have one negative 11 to 9 .1 and i'm bringing out of space kilojules per mole and once we have one mole here okay so this will give us the delta g for our reaction and so this is going to be 131 .4 kilojoules.

02:40 So that is going to be our delta g.

02:45 So looking at this, what is that delta g going to tell us? well, now we can look over here at these three things.

02:53 Is this reaction going to be spontaneous or not? does it happen automatically? so delta g in this case is greater than zero.

03:02 And so no, this one is going to be non -spontaneous.

03:05 It does not happen automatically.

03:08 It's going to need some help with that...

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