# Video: Ionic Equations for the Formation of Iron(III) Hydroxide during Rusting

Iron(III) hydroxide is a key product of rusting in humid conditions. This solid material forms from dissolved Fe³⁺ ions, which in turn are formed from solid iron. The reactions involve water, hydrogen ions (H⁺), and oxygen molecules. Each step of the reaction can be represented using a net ionic equation, which is balanced based on the total charge of the two sides of the equation being equal. a) Including state symbols, give a balanced net ionic equation for the formation of Fe³⁺ ions from metallic iron and dissolved hydrogen ions and oxygen molecules. b) Including state symbols, give a balanced net ionic equation for the formation of iron(III) hydroxide from Fe³⁺ ions and water molecules. c) How many hydrogen ions are consumed in total when an atom of iron is converted to iron(III) hydroxide? d) Iron(III) hydroxide can be dehydrated to produce a material containing no hydrogen atoms. How many water molecules are removed for every atom of iron in the material?

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### Video Transcript

Iron(III) hydroxide is a key product of rusting in humid conditions. The solid material forms from dissolved Fe³⁺ ions, which in turn are formed from solid iron. The reactions involve water, hydrogen ions H⁺, and oxygen molecules. Each step of the reaction can be represented using a net ionic equation, which is balanced based on the total charge of the two sides of the equation being equal. Including state symbols, give a balanced net ionic equation for the formation of Fe³⁺ ions from metallic iron and dissolved hydrogen ions and oxygen molecules.

This question has been very generous. Nearly, all the components of the equation have been provided. Metallic iron, dissolved hydrogen ions, and dissolved oxygen molecules are all reactants. Well, one of the products is Fe³⁺. The formula for metallic iron as in neutral iron is Fe. And the question asks us to include state symbols. So we include s for iron, meaning solid. The next reactant in our equation is dissolved hydrogen ions.

The introduction gives us a hint that this reaction occurs under humid conditions. So the solvent the hydrogen ions are dissolved in is water. And the state symbol for an ion dissolved in water is aq, meaning aqueous. Our final reactant is molecular oxygen O₂. You might be tempted to write O₂ gas. But in this case, the O₂ molecules are dissolved in water. That’s got our reactants sorted. Now, we can move on to the products.

Our first product is Fe³⁺ ions, which the introduction indicates are dissolved in water. This leaves a question. We have iron, hydrogen, and oxygen atoms on the reactant side, but only iron on the product side. Therefore, we must have another product. The most plausible product is water, H₂O, given we have a reaction involving H⁺ and O₂ and the question mentions that the reactions involve water. And the state symbol for water under these conditions is L, standing for liquid.

Now, we can move on to balancing the net ionic equation. There’s one equivalent of iron on both sides of the equation. There’s one equivalent of hydrogen on the reactant side. And there are two equivalents of hydrogen on the product side. And the reverse is true for oxygen as we have two equivalents on the left-hand side and only one on the right. As this is an ionic equation, we also need to balance the charge. So we have one plus from the hydrogen ion on the reactant side and three plus from the iron ion on the product side. Now let’s get balancing.

We can balance up the oxygen atoms by doubling the amount of water produced. And we can balance the hydrogens by adding three more equivalents of H⁺. If you’re not careful, you could trip up at this point and think that the equation is balanced. After all, all the elements are balanced, but the charge is not. We have a charge of 4+ on the reactant side and only a charge of 3+ on the product side. There’s a little trick that will help you solve this.

If you look back at the equation, you’ll see that Fe and Fe³⁺ balance as a pair, while independently, H⁺ and O₂ balance H₂O. So we can change the coefficient for the iron pair without affecting anything else. By multiplying the iron pair through by 𝑥, we can scale up the charge. And we can do the same with the other set multiplying through by 𝑦. All we need to do is find values of 𝑥 and 𝑦 that give us a common charge. The smallest number that can be divided by three and four is 12. So 𝑥 is four and 𝑦 is three.

So we multiply through the iron set by four, producing four equivalents of iron on both sides and a charge for the products of 12+. And we multiply through the second set by three, giving us 12H⁺ ions, three oxygen molecules, and six molecules of water producing 12 equivalents of hydrogen on both sides, six equivalents of oxygen on both sides, and a combined charge of 12+ on both sides.

So we finally have a balanced net ionic equation. Including state symbols, our balanced net ionic equation for the formation of Fe³⁺ ions from metallic iron dissolve hydrogen ions and oxygen molecules is 4Fe(s) H⁺ 12H⁺(aq) H⁺ 3O₂(aq) react to form 4Fe³⁺(aq) plus 6H₂O(L).

Including state symbols, give a balanced net ionic equation for the formation of iron(III) hydroxide from Fe³⁺ ions and water molecules.

Again, the question has provided us nearly all the information we need in order to construct the net ionic equation. The reactants are Fe³⁺ ions and water molecules and iron(III) hydroxide is one of the products. Fe³⁺ is our first reactant. And we’ve included state symbols as asked for in the question. And our other reactant is water which as the solvent will be in liquid form. These are reacting together to form iron(III) hydroxide which has the formula Fe(OH)₃, where we have three hydroxide ions with single negative charges counterbalancing the Fe³⁺ ion with a three plus charge. Since for an ionic compound, it needs to be neutral overall.

The question tells us that iron(III) hydroxide is a solid under these conditions. Therefore, the state symbol for iron(III) hydroxide in our equation is s for solid. The question remains as to whether there is another product. Well, we know the source of the hydroxide ions is water and that water has this structure. If this is the source of the hydroxide ions, then what’s left behind is H⁺. So our other product is H⁺. The state symbol for H⁺ in these circumstances will be aqueous.

Now that we have the net ionic equation, we can move on to balancing. This is the current state of affairs. We have one equivalent of iron on both sides of the equation. That’s balanced. But hydrogen is imbalanced, having only two equivalents on the left-hand side and four equivalents on the right. Meanwhile, oxygen has one equivalent on the left and three equivalents on the right. And the charge is imbalanced with 3+ on the reactant side and 1+ on the product side. Since iron is already balanced, it would be best to start balancing either hydrogen or oxygen.

Hydrogen appears in one reactant and two products, while oxygen appears in only one product. So it’ll be easier to balance this first. Adding a couple of extra water molecules to the reactant side gives us three equivalents of oxygen on both sides. Balancing hydrogen is easiest if we modify the number of protons produced. An extra two gives us those extra two protons we’re missing on the reactant side and also balances the charges.

This gives us our balanced net ionic equation. So including state symbols, our balanced net ionic equation for the formation of iron(III) hydroxide from Fe³⁺ ions and water molecules is Fe³⁺(aq) plus 3H₂O(L) react to form FeOH₃(s) plus 3H⁺(aq).

How many hydrogen ions are consumed in total when an atom of iron is converted to iron(III) hydroxide?

To answer this question, we’re going to need to revisit the equations we derived in parts a and b. This is the equation from part a with the state symbols removed. Taking the equation from part a and dividing it by four gives the ratio between iron atoms and H⁺. Converting between iron atoms and Fe³⁺ ions consumes three protons. And here is the equation from part b, the conversion of Fe³ ions to iron(III) hydroxide. The conversion of one Fe³⁺ ion to iron(III) hydroxide generates three protons. This means in the conversion of iron to iron(III) hydroxide, there is no net consumption or production of H⁺ ions. So our answer is zero.

Iron(III) hydroxide can be dehydrated to produce a material containing no hydrogen atoms. How many water molecules are removed for every atom of iron in the material?

Let’s start by figuring out the first part: how iron(III) hydroxide is dehydrated? The equation will go something like this: iron (III) hydroxide will decompose to some material and water molecules. We know the product will contain iron and will need a negative ion to counterbalance the Fe³⁺. Oxygen in the form of an oxide is the most likely candidate. The combination of these charges gives an ionic formula of Fe₂O₃. That’s two equivalents of Fe³⁺ counteracting three equivalents of oxygen two minus. Now, we can move on to balancing.

We have one equivalent of iron on the left-hand side and two equivalents on the right, three equivalents of oxygen on the left and four on the right, three equivalents of hydrogen on the left and two equivalents on the right. None of the species in this equation are charged. So we don’t need to worry about balancing charge. Doubling up the amount of iron(III) hydroxide we’re reacting in the first place balances the ions. And adding two more equivalents of water on the product side balances the oxygens and the hydrogens. This gives us our balanced equation.

Now, all we need to do is work out how many water molecules are removed for every atom of iron in iron(III) oxide. We work this out by taking the number of water molecules in our equation and dividing it by the number of iron atoms in our other product. This is equal to three divided by two which is equal to 1.5. So for every iron atom in our product, iron(III) oxide produced by dehydrating iron(III) hydroxide, we produce 1.5 water molecules.

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