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### The molecular scene depicts a gaseous equilibrium…

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Problem 102

Write equations for the oxidation of Fe and of Al. Use $\Delta G_{\mathrm{f}}^{\circ}$ to determine whether either process is spontaneous at $25^{\circ} \mathrm{C} .$

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## Video Transcript

The first step in this problem is to write out the oxidation reactions of both iron and aluminum metals into their respective metal oxides, starting with the oxidation of iron. When iron and oxygen form a metal oxide, it's usually between iron three plus and oxygen, which is always has a charge of pew minus. So when we combine those into compound, it's Effie to 03 or aluminum. We also use three plus as a charge. So this is a L 203 and both of these air solid metal oxides that are forming oxygen is bonded to these metals. Informed an oxide. And now we need to balance each one of these equations. If we begin by looking at the number of oxygen oxygen's on each side, we see that we have to oxygen's on the reactant and three on the products. In order to use whole numbers, we need to balance out 30 twos to get six oxygen's and two F E 203 to get six oxygen's, which leaves or iron solid on the react inside. In these end up being the same story key metric coefficients who used for the oxidation of aluminum. And now we want to determine using delta G of formation values. Which one of these processes is spontaneous at that standard conditions of 298 Kelvin And so since easier. Both formation reactions. The changing Gibbs free energy of formation. It's danger conditions or the solid medals and die atomic oxygen or both. Zero, because they occur naturally and there's no change in energy required to form them. So for each one of these were only going to be examining the tomb two moles of the metal oxide that form in each case, because we're taking the total change in Gibbs free energy of the products and subtracting the total change in Gibbs Free Energy, the reactant. But we know that since this is a formacion reaction, delta G information and senior conditions for the reactant zero. So we are only concerned with the products. In starting with the oxidation of iron, we formed two moles of f E 203 We can look up that Delta G information value for that compound and because Delta G A formation for the reactant zero information reaction, we can see that this comes out to this negative value or Delta G information of that metal oxide. Similarly, for the oxidation of aluminum, we formed two moles of a L 203 which has its own value for its change in Gibbs free energy of formation. It's standard conditions and again, due to the formation reaction, the Delta G information of the reactant zero and so Delta G of formation is equal to that value that we just calculated. Remember that were a reaction to be spontaneous. Delta G has to be less than zero. It has to be negative. And in each one of the Delta G information values that we calculated, we see that both of them are negative, so we can conclude that both the oxidation reactions of F e and A L or spontaneous spontaneous reactions do not require any input of energy in order to form the products. And this is what we should expect because these equations represent the rusting of metals over time, and we know that we have metals like iron and aluminum exposed to oxygen Over time. Rust will form in the form of these metal oxides, and that occurs naturally, does not require any input of energy so we we should expect both of these processes to be spontaneous and we can verify that with these negative values of Delta G.