Question

A useful application of oxalic acid is the removal of rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\) from, say, bathtub rings according to the reaction $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+6 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \longrightarrow_{2 \mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}^{3-}(a q)+3 \mathrm{H}_{2} \mathrm{O}+6 \mathrm{H}^{+}(a q)} $$ Calculate the number of grams of rust that can be removed by \(5.00 \times 10^{2} \mathrm{~mL}\) of a \(0.100-M\) solution of oxalic acid.

Short answer

1.33 g of rust can be removed.

Step-by-step solution

Calculate Moles of Oxalic Acid

First, we need to find the number of moles of oxalic acid in the solution. The volume of the solution is given as \(500 \text{ mL} = 0.500 \text{ L}\), and the molarity is \(0.100 \text{ M}\). Use the formula for moles: \( \text{moles} = \text{Molarity} \times \text{Volume in liters}\). \[n \text{moles of oxalic acid} = 0.100 \frac{\text{mol}}{\text{L}} \times 0.500 \text{ L} = 0.050 \text{ mol}\]

Find the Mole Ratio

According to the balanced chemical equation, 6 moles of oxalic acid react with 1 mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). So, the mole ratio is 6:1. We need to find the moles of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) that can be reacted with 0.050 moles of oxalic acid. \[ \frac{\text{moles of Fe}_2\text{O}_3}{0.050 \text{ mol of oxalic acid}} = \frac{1}{6} \]Thus, \[n\text{moles of Fe}_2\text{O}_3 = \frac{0.050}{6} = 0.00833 \text{ mol}\]

Calculate the Mass of Rust

Calculate the mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) using its molar mass. The molar mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is approximately \(159.7 \text{ g/mol}\). Use the formula: \( \text{mass} = \text{moles} \times \text{molar mass} \). \[ \text{mass of Fe}_2\text{O}_3 = 0.00833 \text{ mol} \times 159.7 \text{ g/mol} = 1.33 \text{ g} \]

Key concepts

Oxalic Acid

Oxalic acid is a chemical compound that takes on a crucial role in rust removal, among other applications. It is a relatively strong organic acid that tends to form colorless crystals and is water-soluble.

In the context of rust removal, oxalic acid reacts with the rust (\( \mathrm{Fe}_2\mathrm{O}_3\) or iron(III) oxide). This reaction leverages the acidic nature of oxalic acid to break down the rust, allowing it to be removed from surfaces like bathtub rings.

The compound is often used in diluted solutions for household cleaning tasks because, in higher concentrations, it can be quite caustic. When handling oxalic acid, it's important to follow proper safety precautions, such as wearing gloves and working in a well-ventilated area.

Balanced Chemical Equations

Balanced chemical equations are fundamental tools in chemistry that describe how reactants transform into products in a chemical reaction. They ensure that the same number of each type of atom appears on both sides of the equation, reflecting the Law of Conservation of Mass.

In the oxalic acid and rust removal reaction:
\[\mathrm{Fe}_{2} \mathrm{O}_{3}(s) + 6 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(aq) \rightarrow 2 \mathrm{Fe}(\mathrm{C}_{2} \mathrm{O}_{4})_{3}^{3-}(aq) + 3 \mathrm{H}_{2} \mathrm{O} + 6 \mathrm{H}^{+}(aq)\] Every element is accounted for, and no atoms are lost.

Balancing chemical equations involves determining the correct coefficients that will balance all atoms present in reactants and products. This is a crucial step for calculating the quantities of reactants or products involved in any chemical reaction.

Mole Calculations

Mole calculations are an essential concept in chemistry, allowing scientists to measure out exact amounts of a substance for reactions. A "mole" is a unit that represents approximately \(6.022 \times 10^{23}\) particles (atoms, molecules).

Using moles helps in relating macroscopic quantities of substances to the molecules they contain. In the solution provided, we calculated the number of moles of oxalic acid using its molarity and the volume of solution:

The formula used is: \[\text{moles} = \text{Molarity} \times \text{Volume in liters} \]. Using this formula, we find that the solution contains \(0.050\) moles of oxalic acid.

Understanding the mole ratio from the equation informs us how many moles of rust will react with the oxalic acid, providing a crucial connection between reactants.

Molar Mass

Molar mass is defined as the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). It is calculated by adding the atomic masses of all atoms in a molecule.

For example, in determining the rust's mass removal, we used the molar mass of iron(III) oxide (\( \mathrm{Fe}_2\mathrm{O}_3\)). Its approximate molar mass is calculated as: \[\text{Fe} = 55.85\ \rightarrow 2 \times 55.85 = 111.7\ \]\[\text{O} = 16.00\ \rightarrow 3 \times 16.00 = 48.00\ \]\[\text{Total } = 159.7\ \mathrm{g/mol}\].

Utilizing molar mass, we can accurately convert moles of a compound to grams, which is crucial for practical laboratory work and industrial processes. In this example, multiplying the moles of Fe₂O₃ by its molar mass gives the total mass of iron oxide removed, completing the link from mole concepts to physical mass.