Question

The ferrate ion, \(\mathrm{FeO}_{4}^{2-}\) , is such a powerful oxidizing agent that in acidic solution, aqueous ammonia is reduced to elemental nitrogen along with the formation of the iron(III) ion. a. What is the oxidation state of iron in FeO \(_{4}^{2-},\) and what is the electron configuration of iron in this polyatomic ion? b. If 25.0 \(\mathrm{mL}\) of a 0.243 \(\mathrm{M} \mathrm{FeO}_{4}^{2-}\) solution is allowed to react with 55.0 \(\mathrm{mL}\) of 1.45 \(\mathrm{M}\) aqueous ammonia, what volume of nitrogen gas can form at \(25^{\circ} \mathrm{C}\) and 1.50 \(\mathrm{atm}\) ?

Short answer

The oxidation state of iron in the ferrate ion is +6, and the electron configuration of iron in this ion is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁰. When 25.0 mL of 0.243 M FeO_{4}^{2-} solution reacts with 55.0 mL of 1.45 M aqueous ammonia, approximately 0.011 L of nitrogen gas can form at 25°C and 1.50 atm.

Step-by-step solution

a) Oxidation State of Iron and its Electron Configuration

To find the oxidation state of iron in the ferrate ion, FeO_4^{2-}, let's consider the oxidation states of both oxygen and iron in this polyatomic ion. 1. Oxygen always has an oxidation state of -2, except in peroxides and superoxides. 2. Let x be the oxidation state of iron. The overall electric charge of the ion is -2. Considering both iron and oxygen atoms in the ion, the equation is: \(Fe + 4(O) = -2\) \(x + 4(-2) = -2\) Now, the oxidation state of iron can be found by solving for x: \(x= -2 + 4(2)\) \(x = 6\) So, the oxidation state of iron in the ferrate ion is +6. Now let's look at the electron configuration of an iron: The atomic number of iron (Fe) is 26, so its electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ in the neutral state. Because the iron (III) ion has a +6 oxidation state, we have to remove 6 electrons. The removal priority is 4s first, then 3d. After removing 6 electrons, the electron configuration of iron in the ferrate ion is: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁰.

b) Volume of Nitrogen Gas Formed

First, write the balanced chemical equation for the reaction of ferrate ion solution with aqueous ammonia and formation of nitrogen gas: \(3FeO_{4}^{2-} + 12NH_3 -> N_2 + 6H_2O + 3Fe^{3+} + 12OH^-\) Now, we will use stoichiometry to find the amount of nitrogen gas formed: 1. We can calculate the amount of substance (mol) of the ferrate ion solution and aqueous ammonia using their volume and concentration. Amount of ferrate ion solution in moles = Volume × Concentration = 0.025 L × 0.243 mol/L = 0.006075 mol Amount of aqueous ammonia in moles = Volume × Concentration = 0.055 L × 1.45 mol/L = 0.07975 mol 2. Next, we will determine the limiting reactant by comparing the mole ratio of the ferrate ion to ammonia in the balanced chemical equation. The mole ratio of ferrate ion to ammonia: 3:12 (or 1:4) Divide moles of each reactant by its respective coefficient in the balanced equation: FeO_4^{2-} ratio = 0.006075 mol / 3 = 0.002025 NH_3 ratio = 0.07975 mol / 12 = 0.006646 The reactant with the smallest ratio is the limiting reactant, which in this case is the ferrate ion (FeO_4^{2-}). Calculate the amount of nitrogen gas formed using the stoichiometric coefficients and the limiting reactant: Amount of nitrogen gas formed (mol) = 0.002025 / 3 × 1 = 0.000675 mol Now, using ideal gas law to find the volume of nitrogen gas under given conditions (Temperature = 25°C = 298 K and Pressure = 1.50 atm): \(PV = nRT\) where P is pressure, V is volume, n is the amount of nitrogen gas in moles, R is the ideal gas constant (0.0821 L atm/mol K), and T is the temperature in Kelvin. Now we can solve for the volume (V): \(V = nRT/P\) \( V = (0.000675 mol)(0.0821 \frac{L\cdot atm}{mol \cdot K})(298 K) / (1.50 atm)\) \(V \approx 0.011 L\) Hence, the volume of nitrogen gas that can form at 25°C and 1.50 atm is approximately 0.011 L.

Key concepts

Ferrate Ion

The ferrate ion, denoted as \( ext{FeO}_4^{2-}\), is a polyatomic ion where iron is found in a relatively high oxidation state. Understanding the oxidation state is crucial in chemistry as it helps predict the behavior of elements in a reaction.
- In the ferrate ion, iron is bonded to four oxygen atoms. Oxygen generally has an oxidation state of -2.- To determine the oxidation state of iron in the ferrate ion, you set up the equation: \(x + 4(-2) = -2\) where \(x\) is the oxidation state of iron.
- Solving this equation yields \(x = +6\). Therefore, iron in the ferrate ion has an oxidation state of +6, indicating it has lost six electrons compared to its elemental form.This high oxidation state makes the ferrate ion a powerful oxidizing agent, useful in various chemical reactions, including those involving ammonia.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It allows chemists to predict how much of a product will form based on the quantities of starting materials.
- In reactions like the one involving the ferrate ion and ammonia, balanced chemical equations provide the mole ratio of reactants and products.- For example, the balanced equation: \(3 ext{FeO}_4^{2-} + 12 ext{NH}_3 \to ext{N}_2 + 6 ext{H}_2 ext{O} + 3 ext{Fe}^{3+} + 12 ext{OH}^-\) indicates that three moles of ferrate react with twelve moles of ammonia to produce nitrogen gas and other products.
- By examining these ratios, you can determine the limiting reactant, that is, the reactant that will be completely consumed first, limiting the amount of product.- For this reaction, ferrate is determined to be the limiting reactant by comparing its mole ratio to ammonia's. This information is crucial to calculating yields and efficiencies of chemical reactions.

Ideal Gas Law

The ideal gas law is an equation of state for a gas that describes the relationship between its pressure, volume, temperature, and amount in moles. The formula is expressed as: \[PV = nRT\] - Here, \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles of gas, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin.
- In the example of nitrogen gas formed from the reaction between ferrate ions and ammonia, the ideal gas law is used to calculate the volume of nitrogen gas produced under certain conditions.- This involves substituting known values into the formula: \(V = \frac{nRT}{P}\). Given \(n\), the number of moles of nitrogen gas formed, \(T\), and \(P\), we can solve for \(V\), the gas volume.
- The ideal gas constant \(R\) is typically \(0.0821 \text{ L atm/mol K}\), making calculations straightforward when pressure is in atmospheres and volume in liters.Although no gas behaves perfectly as an ideal gas, this equation provides a good approximation under many conditions.

Electron Configuration

Electron configuration is a notation describing the distribution of electrons among the energy levels of an atom or ion. It provides insight into an element’s chemical behavior and reactivity.
- For iron in the ferrate ion, the oxidation state of +6 means that six electrons have been removed from the neutral iron atom. In its ground state, iron has the electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6\).- Removing six electrons from iron involves first taking the two from the \(4s\) subshell and then four from the \(3d\) subshell, resulting in a final configuration of \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^0\) for the ferrate ion.
- Understanding how electrons are arranged helps predict how atoms interact in chemical reactions. High oxidation states, involving the removal of many electrons, often lead to stronger oxidizing capabilities, as seen with the ferrate ion.