Problem 110 - Chemistry and Chemical Reactivity

Question

A compound has been isolated that can have either of two possible formulas: (a) \(\mathrm{K}\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\) or (b) \(\mathrm{K}_{3}\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right] .\) To find which is correct, you dissolve a weighed sample of the compound in acid and then titrate the oxalate ion \(\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2}\right)\) that comes from the compound with potassium permanganate, \(\mathrm{KMnO}_{4}\) (the source of the \(\mathrm{MnO}_{4}^{-}\) ion). The balanced, net ionic equation for the titration is $$\begin{array}{rl}5 \mathrm{C}_{2} \mathrm{O}_{4}^{2-}(\mathrm{aq})+2 \mathrm{MnO}_{4}^{-}(\mathrm{aq})+16 \mathrm{H}^{+}(\mathrm{aq}) & \longrightarrow \\\2 \mathrm{Mn}^{2+}(\mathrm{aq})+10 \mathrm{CO}_{2}(\mathrm{g})+8 & \mathrm{H}_{2} \mathrm{O}(\ell) \end{array}$$ Titration of \(1.356 \mathrm{g}\) of the compound requires \(34.50 \mathrm{mL}\) of \(0.108 \mathrm{M} \mathrm{KMnO}_{4} .\) Which is the correct formula of the iron-containing compound: (a) or (b)?

Step-by-Step Solution

Answer

Neither formula matches the calculated mass, check for calculation errors.

Step 1: Calculate the Moles of Permanganate Ion

The molarity of the permanganate solution is given as \(0.108 \, \text{M}\), and the volume used is \(34.50 \, \text{mL} = 0.03450 \, \text{L}\). Use the formula \( n = C \times V \) to find the moles:\[ n(\text{MnO}_4^-) = 0.108 \, \text{mol/L} \times 0.03450 \, \text{L} = 0.003726 \, \text{mol} \]

Step 2: Determine Moles of Oxalate Ion

From the balanced titration equation, \(2 \, \text{mol of MnO}_4^-\) react with \(5 \, \text{mol of C}_2\text{O}_4^{2-}\). Using stoichiometry, calculate the moles of oxalate:\[ n(\text{C}_2\text{O}_4^{2-}) = \frac{5}{2} \times n(\text{MnO}_4^-) \]Substitute the value from Step 1:\[ n(\text{C}_2\text{O}_4^{2-}) = \frac{5}{2} \times 0.003726 \, \text{mol} = 0.009315 \, \text{mol} \]

Step 3: Relate Moles of Oxalate to Compound Formula

In compound (a), each formula unit contains \(2 \, \text{mol of C}_2\text{O}_4^{2-}\), while in compound (b), it contains \(3 \, \text{mol of C}_2\text{O}_4^{2-}\). Calculate the moles of compound based on these assumptions:- For (a): \[ n(\text{compound}) = \frac{n(\text{C}_2\text{O}_4^{2-})}{2} = \frac{0.009315}{2} = 0.0046575 \, \text{mol} \]- For (b): \[ n(\text{compound}) = \frac{n(\text{C}_2\text{O}_4^{2-})}{3} = \frac{0.009315}{3} = 0.003105 \, \text{mol} \]

Step 4: Calculate Molar Mass and Compare

Calculate the molar mass based on each formula to determine which matches:- Formula (a): Molar mass = \((1 \times 39.1) + 55.85 + (2 \times 88) + (2 \times 18) \approx 308.06 \, \text{g/mol}\)Using moles from Step 3(a):\[ ext{mass} = 0.0046575 \, \text{mol} \times 308.06 \, \text{g/mol} \approx 1.435 \, \text{g}\] (incorrect)- Formula (b): Molar mass = \((3 \times 39.1) + 55.85 + (3 \times 88) \approx 491.95 \, \text{g/mol}\)Using moles from Step 3(b):\[ ext{mass} = 0.003105 \, \text{mol} \times 491.95 \, \text{g/mol} \approx 1.5279 \, \text{g}\] (incorrect)

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry, which deals with calculating the quantities of reactants and products in chemical reactions. In the context of chemical titration analysis, stoichiometry helps us determine how much of a particular substance reacts with or produces another substance.
The key is to use balanced chemical equations that show the relationship between the substance amounts, usually in moles.
For this exercise, the balanced equation tells us that 2 moles of permanganate ions \((\mathrm{MnO}_4^-)\) react with 5 moles of oxalate ions \((\mathrm{C}_2\mathrm{O}_4^{2-})\).
This stoichiometric relationship allows us to find the moles of oxalate ions in the sample, once we know the moles of permanganate ions used in the titration.
We start by calculating moles of permanganate using a simple formula \(n = C \times V\), and upon finding these, the stoichiometric coefficients from the balanced net ionic equation guide us to the moles of oxalate ions present.
These relationships are crucial in accurately identifying the chemical composition of a compound.

Net Ionic Equations

Net ionic equations are simplified chemical equations that show only the species that actually participate in the reaction. They are especially useful in titration since they help focus on the substances that undergo chemical changes, ignoring the spectator ions that remain unchanged in solution.
In many titrations, like the one in this exercise involving oxalate ions and permanganate ions, multiple ions are present in the solution. With a net ionic equation, our focus solely shifts to these reactive species: oxalate ions \(\mathrm{C}_2\mathrm{O}_4^{2-}\) and permanganate ions \(\mathrm{MnO}_4^-\).
This leads to a streamlined equation:

• 5 \(\mathrm{C}_2\mathrm{O}_4^{2-}\) react with 2 \(\mathrm{MnO}_4^{-}\) ions.

This equation highlights hydrogen ions \(\mathrm{H}^+\) as well, which are necessary to maintain the acidic conditions required for this reaction to proceed.
Net ionic equations thus help in clearly understanding the core interaction during a titration, guiding precise stoichiometric calculations.

Compound Identification

Compound identification using titration provides a method to determine the correct chemical formula of an unknown or newly synthesized compound.
By comparing the stoichiometric relationships and measured titration data, we can deduce which proposed formula better matches the observed results.

In this exercise, we're discerning between two possible formulas of an iron-oxalate complex.

• Formula (a): \(\mathrm{K}[\mathrm{Fe}(\mathrm{C}_2\mathrm{O}_4)_2(\mathrm{H}_2\mathrm{O})_2]\)
• Formula (b): \(\mathrm{K}_3[\mathrm{Fe}(\mathrm{C}_2\mathrm{O}_4)_3]\)

The experimental approach involves dissolving the compound, conducting titration, and interpreting results using stoichiometry and the known chemical formula masses.
These calculations let us estimate the moles present in the sample for both formula variations, comparing the measured sample mass and calculated moles-based mass.

Oxalate Ion

The oxalate ion \(\mathrm{C}_2\mathrm{O}_4^{2-}\) plays a pivotal role in the chemical analysis described here.
It is a type of anion often seen in coordination compounds and significant for its reactivity in redox titration.
In the titration process, oxalate undergoes an oxidation reaction with permanganate ions, which involves electron transfer.

• This oxidation results in the formation of carbon dioxide \(\mathrm{CO}_2\).
• Oxalate acts as a reducing agent while permanganate is an oxidizing agent.

In our exercise, identifying the amount of oxalate ion helps in determining which compound formula aligns with the experimental data.
The amount of oxalate, calculated through titration data, links directly to the complex's formula based on how many oxalate ions are in each formula unit of the compound. Understanding oxalate's role in this redox system is essential as it reinforces the connection between empirical data and theoretical predictions.