Question

Nickel-Iron Battery In \(1901,\) Thomas Edison inventt the nickel-iron battery. The following reaction takes place in the battery. $$\mathrm{Fe}(\mathrm{s})+2 \mathrm{NiO}(\mathrm{OH})(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow\( \)\mathrm{Fe}(\mathrm{OH})_{2}(\mathrm{s})+2 \mathrm{Ni}(\mathrm{OH})_{2}(\mathrm{aq})$$ How many mol of Fe(OH), is produced when 5.00 \(\mathrm{mol}\) of Fe and 8.00 \(\mathrm{mol}\) of \(\mathrm{NiO}(\mathrm{OH})\) react?

Short answer

Given the reaction: \[ \mathrm{Fe(s)} + 2 \mathrm{NiO(OH)(s)} + 2 \mathrm{H_{2}O(l)} \rightarrow \mathrm{Fe(OH)_{2}(s)} + 2 \mathrm{Ni(OH)_{2}(aq)} \] and the amount of reactants (5.00 mol of Fe and 8.00 mol of NiO(OH)), the limiting reactant is Fe. Therefore, 5.00 mol of Fe(OH)₂ is produced.

Step-by-step solution

Examine the stoichiometry of the reaction

First, examine the stoichiometry of the redox reaction. In the balanced equation given, you will observe that one mol of Fe reacts with two mols of NiO(OH) to produce one mol of Fe(OH)2 and 2 mols of Ni(OH)2.

Determine the limiting reactant

To compute how much Fe(OH)2 is produced, it's crucial to first establish if there's a limiting reactant in the reaction. By comparing the actual mole ratio of Fe to NiO(OH) given the problem (5.00 mol Fe : 8.00 mol NiO(OH)) with the desired stoichiometric ratio from the balanced equation (1 mol Fe: 2 mol NiO(OH)), this reveals that Fe is the limiting reactant. As a result, the reaction will stop when all 5.00 moles of Fe have reacted.

Calculate moles of Fe(OH)2 produced

Now that the limiting reactant (Fe) is determined, utilize the balanced equation to calculate the amount of Fe(OH)2 produced. According to the balanced chemical equation, 1 mol of Fe produces 1 mol of Fe(OH)2. So for 5.00 mol of Fe used, 5.00 mol of Fe(OH)2 will be produced. So, the answer to the question "How many mol of Fe(OH)2 is produced when 5.00 mol of Fe and 8.00 mol of NiO(OH) react?" is that 5.00 mol of Fe(OH)2 is produced given the amounts of reactants provided.

Key concepts

Limiting Reactant

In chemical reactions, the limiting reactant is the substance that is totally consumed first and thus determines the amount of products that can be formed. This is because the chemical reaction cannot continue without all the necessary reactants. Identifying the limiting reactant is like figuring out which ingredient will run out first when cooking a recipe: once it's gone, you can't make any more food, or in this case, product.

To find the limiting reactant, we compare the number of moles of each reactant with the ratios needed according to the balanced equation. In our exercise with the nickel-iron battery, the balanced reaction requires 1 mole of Fe for every 2 moles of NiO(OH). Given 5.00 moles of Fe and 8.00 moles of NiO(OH), the iron (Fe) is used up first since it's in a lesser amount relative to its need in the reaction. Thus, Fe is the limiting reactant, and it dictates how much Fe(OH)2 can be produced. Once all of the Fe has been used, the reaction stops, even if there is still some NiO(OH) left over.

Chemical Reactions

A chemical reaction is a process that converts one or more substances, called reactants, into different substances, called products. It involves breaking bonds within reactants and forming new bonds to create the products. To fully understand a chemical reaction, like the one occurring in a nickel-iron battery, we must first look at the reaction's balanced equation. This equation shows the exact ratio in which the reactants combine and the products form, based on the law of conservation of mass which states that matter cannot be created or destroyed in a chemical reaction.

The balanced equation for our reaction is:
Fe(s) + 2 NiO(OH)(s) + 2 H2O(l) → Fe(OH)2(s) + 2 Ni(OH)2(aq).
This equation tells us that solid iron reacts with nickel oxyhydroxide in the presence of water to produce iron hydroxide and nickel hydroxide in solution. Every coefficient in the balanced equation indicates the molar ratio of each substance involved, which is essential when determining how much product is made when given amounts of reactants are used.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a way for chemists to count atoms, molecules, and ions by relating the mass of substances to their number of particles. One mole represents Avogadro's number, which is approximately 6.022 × 10²³ particles. This concept is crucial when dealing with chemical reactions because it allows us to use the balanced chemical equation to relate moles of reactants to moles of products.

In the context of our problem, using the mole concept, we can see that 1 mole of Fe produces 1 mole of Fe(OH)2. With 5.00 moles of Fe as the limiting reactant, and applying the 1:1 ratio from the balanced equation, it directly results in 5.00 moles of Fe(OH)2 being created. By understanding the mole concept, students can solve stoichiometric problems effectively, predicting the outcomes of reactions and the amounts of substances involved.