Problem 98 - Chemistry An Atoms First Approach

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 \(\mathrm{FeO}_{4}^{2-},\) 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 atm?

Step-by-Step Solution

Answer

The oxidation state of iron is +6, and the electron configuration of iron in the ferrate ion is \([Ar] 3d^0 4s^2\). The volume of nitrogen gas formed at 25°C and 1.50 atm is V = nRT/P, where n is the moles of nitrogen gas formed, R is the ideal gas constant (0.0821 \(L\cdot atm /(mol\cdot K)\)), T is the temperature in Kelvin (298 K), and P is the pressure (1.50 atm).

Step 1: Identify the charges of elements in \(\mathrm{FeO}_{4}^{2-}\)

First, find the charges of each element in \(\mathrm{FeO}_{4}^{2-}\). Oxygen has a charge of -2. Since there are 4 oxygen atoms, the total charge represented by oxygen in the compound is -8. As the overall charge of the ion \(\mathrm{FeO}_{4}^{2-}\) is -2, we can find the charge of iron (Fe).

Step 2: Calculate the charge of iron

To find the charge of iron, balance the charges of oxygen and iron. It can be formulated as: \[x + (-8) = -2\] \[x = -2 + 8\] \[x= 6\] The charge of iron is thus +6.

Step 3: Determine the electron configuration of iron

To obtain the electron configuration of iron in \(\mathrm{FeO}_{4}^{2-}\), remove 6 electrons from the ground state electron configuration of iron, since it has an oxidation state of +6. The ground state electron configuration of iron is: \([Ar] 3d^6 4s^2\). Removing 6 electrons gives the electron configuration of iron in \(\mathrm{FeO}_{4}^{2-}\): \([Ar] 3d^0 4s^2\) #a. Answer:# The oxidation state of iron is +6, and the electron configuration of iron in the ferrate ion is \([Ar] 3d^0 4s^2\). #b. Calculating the volume of nitrogen gas:#

Step 4: Find the limiting reactant

First, find the limiting reactant between \(\mathrm{FeO}_{4}^{2-}\) and \(\mathrm{NH}_{3}\). The balanced chemical equation of this reaction is: \[2\mathrm{NH}_3 (aq) + \mathrm{FeO}_4^{2-} (aq) \rightarrow N_2 (g) + \mathrm{Fe}^{3+} + 4 \mathrm{OH}^{-}\] Using the molarity and volume, calculate the moles of \(\mathrm{FeO}_{4}^{2-}\) and \(\mathrm{NH}_{3}\) as follows: Moles of \(\mathrm{FeO}_{4}^{2-} = 0.243 \mathrm{M} \times 0.025 L\) Moles of \(\mathrm{NH}_{3} = 1.45 \mathrm{M} \times 0.055 L\)

Step 5: Compare the mole ratio

Compare the mole ratio with the balanced equation to find the limiting reactant. Mole ratio of \(\mathrm{FeO}_{4}^{2-}\) and \(\mathrm{NH}_{3}\): \(1 : 2\)

Step 6: Determine the moles of nitrogen gas formed

The moles of nitrogen gas formed will be limited by the moles of the limiting reactant (which was found in the other note). Calculate the moles of nitrogen gas formed through the mole ratio of reactants and products. \(N_{2}\) moles \(=\frac{1}{2}\) * moles of the limiting reactant

Step 7: Apply the ideal gas law

Use the ideal gas law (PV = nRT) to determine the volume of nitrogen gas formed at the given conditions (1.50 atm, 25°C). R = 0.0821 \(L\cdot atm /(mol\cdot K)\) T = 298 K Calculate the volume of nitrogen gas: V = nRT/P #b. Answer# The volume of nitrogen gas formed at 25°C and 1.50 atm is V.

Key Concepts

Ferrate Ion

The ferrate ion, symbolized as \(\mathrm{FeO}_{4}^{2-}\), is known for its remarkable oxidative strength. This polyatomic ion consists of one iron atom and four oxygen atoms. Oxygen, typically a divalent anion, holds a -2 charge. Since there are four oxygen atoms, their total contribution sums up to -8. Given the entire ferrate ion holds a charge of -2, the oxidation state of iron must be adjusted to balance these charges.
To determine the oxidation state of iron, we use the equation:\[x + (-8) = -2\]Solving this yields:\[x = 6\]
Thus, iron has a +6 oxidation state within the ferrate ion. This high oxidation state is crucial to its ability to act as an oxidizing agent.

• Iron in ferrate ion: Oxidation State +6
• Composition: 1 Iron and 4 Oxygen atoms

Electron Configuration

The electron configuration of an element describes the distribution of its electrons across different energy levels and orbitals. For iron in its neutral state, the electron configuration is given by \([Ar] 3d^6 4s^2\). However, when considering iron in the ferrate ion \(\mathrm{FeO}_{4}^{2-}\), the electrons need to be adjusted according to its oxidation state.
Since iron has an oxidation state of +6 here, it loses 6 of its electrons. Starting with the neutral ground state configuration:

• Remove 4 electrons from the 3d orbital (\(3d^6 \to 3d^2\))
• Then remove 2 electrons from the 4s orbital (\(4s^2 \to 4s^0\))

This means, after losing these 6 electrons, iron's electron configuration in the ferrate ion becomes \([Ar] 3d^0 4s^0\), although typically simplified as \([Ar]\). This indicates iron has no valence electrons left, which aligns well with its role in oxidation reactions.

Limiting Reactant

In any chemical reaction, the limiting reactant is the substance that is totally consumed when the chemical reaction is complete. This reactant determines the amount of product formed. To find the limiting reactant, we compare the mole ratio of each reactant used to the ratio in the balanced chemical equation.
In the reaction between \(\mathrm{FeO}_{4}^{2-}\) and \(\mathrm{NH}_3\), we follow these steps:

• Calculate moles based on provided volume and concentration:
• Moles of \(\mathrm{FeO}_{4}^{2-} = 0.243 \times 0.025 = 0.006075 \) moles
• Moles of \(\mathrm{NH}_3 = 1.45 \times 0.055 = 0.07975 \) moles

The reaction \[2\mathrm{NH}_3 (aq) + \mathrm{FeO}_4^{2-} (aq) \rightarrow N_2 (g) + \mathrm{Fe}^{3+} + 4 \mathrm{OH}^{-}\] indicates a 1:2 mole ratio. With fewer moles of \(\mathrm{FeO}_{4}^{2-}\) than needed to react with \(\mathrm{NH}_3\), \(\mathrm{FeO}_{4}^{2-}\) is the limiting reactant.
This dictates the maximum amount of nitrogen gas produced.

Ideal Gas Law

The ideal gas law is an equation of state for an ideal gas. It is a useful approximation for the behavior of many gases under various conditions. The law is presented as \(PV = nRT\), where:

• \(P\) is the pressure
• \(V\) is the volume
• \(n\) is the number of moles
• \(R\) is the gas constant (0.0821 \(L\cdot atm /(mol\cdot K)\))
• \(T\) is the temperature in Kelvin

In the scenario presented, we need to calculate the volume of nitrogen gas formed using the ideal gas law at a given pressure of 1.50 atm and a temperature of 25°C (which is 298 K). After determining \(n\), the moles of nitrogen gas (from previous limiting reactant calculations), use the equation:\[V = \frac{nRT}{P}\]
This will yield the volume of nitrogen gas created under the described conditions. It's crucial to convert temperature to Kelvin and ensure pressure units match those in the gas constant to get accurate results.