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# 20.6: Temperature and Free Energy

Difficulty Level: At Grade Created by: CK-12
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Practice Temperature and Free Energy
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#### How is steel produced?

Iron ore (Fe2O3) and coke (an impure form of carbon) are heated together to make iron and carbon dioxide. The reaction is non-spontaneous at room temperature, but becomes spontaneous at temperature above 842 K. The iron can then be treated with small amounts of other materials to make a variety of steel products.

### Temperature and Free Energy

Consider the reversible reaction in which calcium carbonate decomposes into calcium oxide and carbon dioxide gas. The production of CaO (called quicklime) has been an important reaction for centuries.

CaCO3(s)CaO(s)+CO2(g)\begin{align*}\text{CaCO}_3(s) \rightleftarrows \text{CaO}(s) +\text{CO}_2(g)\end{align*}

The ΔH\begin{align*}\Delta H^\circ\end{align*} for the reaction is 177.8 kJ/mol, while the ΔS\begin{align*}\Delta S^\circ\end{align*} is 160.5 J/K • mol. The reaction is endothermic with an increase in entropy due to the production of a gas. We can first calculate the ΔG\begin{align*}\Delta G^\circ\end{align*} at 25°C in order to determine if the reaction is spontaneous at room temperature.

ΔG=ΔHTΔS=177.8 kJ/mol298 K(0.1605 kJ/Kmol)=130.0 kJ/mol\begin{align*}\Delta G^\circ=\Delta H^\circ -T \Delta S^\circ=177.8 \ \text{kJ}/ \text{mol} - 298 \ K (0.1605 \ \text{kJ} / \text{K} \cdot \text{mol})=130.0 \ \text{kJ} / \text{mol}\end{align*}

Since the ΔG\begin{align*}\Delta G^\circ\end{align*} is a large positive quantity, the reaction strongly favors the reactants and very little products would be formed. In order to determine a temperature at which ΔG\begin{align*}\Delta G^\circ\end{align*} will become negative, we can first solve the equation for the temperature when ΔG\begin{align*}\Delta G^\circ\end{align*} is equal to zero.

0T=ΔHTΔS=ΔHΔS=177.8 kJ/mol0.1605 kJ/Kmol=1108 K=835 C\begin{align*}0 &=\Delta H^\circ - T \Delta S^\circ \\ T &=\frac{\Delta H^\circ}{\Delta S^\circ}= \frac{177.8 \ \text{kJ} / \text{mol}}{0.1605 \ \text{kJ} / \text{K} \cdot \text{mol}}=1108 \text{ K}=835^\circ \text{ C}\end{align*}

So at any temperature higher than 835°C, the value of ΔG\begin{align*}\Delta G^\circ\end{align*} will be negative and the decomposition reaction will be spontaneous.

This lime kiln in Cornwall was used to produce quicklime (calcium oxide), an important ingredient in mortar and cement.

Recall that the assumption that ΔH\begin{align*}\Delta H^\circ\end{align*} and ΔS\begin{align*}\Delta S^\circ\end{align*} are independent of temperature means that the temperature at which the sign of ΔG\begin{align*}\Delta G^\circ\end{align*} switches from being positive to negative (835°C) is an approximation. It is also important to point out that one should not assume that absolutely no products are formed below 835°C and that at that temperature decomposition suddenly begins. Rather, at lower temperatures, the amount of products formed is simply not great enough to say that the products are favored. When this reaction is performed, the amount of products can be detected by monitoring the pressure of the CO2 gas that is produced. Above about 700°C, measurable amounts of CO2 are produced. The pressure of CO2 at equilibrium gradually increases with increasing temperature. Above 835°C, the pressure of CO2 at equilibrium begins to exceed 1 atm, the standard-state pressure. This is an indication that the products of the reaction are now favored above that temperature. When quicklime is manufactured, the CO2 is constantly removed from the reaction mixture as it is produced. This causes the reaction to be driven towards the products according to LeChâtelier’s principle.

### Summary

• The influence of temperature on free energy is described.

### Review

1. If you increased the pressure of CO2 in the quicklime reaction, what would happen to the equilibrium?
2. Why do we calculate the situation where ΔG\begin{align*}\Delta G\end{align*} is zero?
3. At temperatures below 835°C, is any product formed?

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