Question

Oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), is a toxic substance found in spinach leaves. What is the molarity of a solution made by dissolving \(12.0 \mathrm{~g}\) of oxalic acid in enough water to give \(400.0 \mathrm{~mL}\) of solution? How many milliliters of \(0.100 \mathrm{M}\) KOH would you need to titrate \(25.0 \mathrm{~mL}\) of the oxalic acid solution according to the following equation? $$ \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q)+2 \mathrm{KOH}(a q) \longrightarrow \mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

The molarity of the oxalic acid solution is 0.333 M, and 167 mL of 0.100 M KOH is required for titration.

Step-by-step solution

Calculate molar mass of oxalic acid

To find the molar mass of oxalic acid (\(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\)), we add the atomic masses of all atoms in the formula: H (2x1.01 g/mol) + C (2x12.01 g/mol) + O (4x16.00 g/mol) = 2.02 + 24.02 + 64.00 = 90.04 g/mol.

Convert grams to moles

To find the number of moles of oxalic acid, divide the mass by its molar mass. \( 12.0 \text{ g} \div 90.04 \text{ g/mol} = 0.133 \text{ mol} \).

Calculate molarity of the solution

Molarity (M) is defined as moles of solute per liter of solution. Convert the solution volume from mL to L: \(400.0 \text{ mL} = 0.400 \text{ L}\). Then, divide the moles of oxalic acid by the volume in liters: \(0.133 \text{ mol} \div 0.400 \text{ L} = 0.333 \text{ M} \).

Write the balanced chemical equation

Given reaction: \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(aq) + 2\mathrm{KOH}(aq) \to \mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(aq) + 2\mathrm{H}_{2} \mathrm{O}(l)\). This indicates that 1 mole of oxalic acid reacts with 2 moles of KOH.

Calculate moles of oxalic acid in 25 mL

Use the molarity from Step 3 to find moles of oxalic acid in 25.0 mL (0.025 L) of solution: \(0.333 \text{ M} \times 0.025 \text{ L} = 0.00833 \text{ mol}\).

Determine moles of KOH needed

According to the balanced equation, 2 moles of KOH react with 1 mole of oxalic acid. Thus, \(0.00833 \text{ mol} \times 2 = 0.0167 \text{ mol KOH}\) is needed.

Calculate volume of KOH required

Using the molarity of the KOH solution (0.100 M), the volume needed is moles of KOH divided by the molarity: \(0.0167 \text{ mol} \div 0.100 \text{ M} = 0.167 \text{ L} = 167 \text{ mL}\).

Key concepts

Oxalic Acid

Oxalic acid is a naturally occurring organic compound with the chemical formula \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \). It's found in plants like spinach and rhubarb and is known for its toxic properties. The presence of oxalic acid in food can lead to a sharp taste and can sometimes interfere with calcium absorption when consumed in large quantities.
It contains two carboxylic acid groups which makes it a dicarboxylic acid. This structure contributes to its ability to act as a reducing agent, making it useful in various industrial applications, such as rust removal and bleaching.
In laboratories, oxalic acid is often used to standardize solutions in titration processes due to its strong acidic properties.

Titration Chemistry

Titration is an important analytical technique often employed in chemistry to determine the concentration of an unknown solution. It involves adding a solution of known concentration (titrant) to a solution of unknown concentration until the reaction between them is complete.
The endpoint of a titration is usually marked by a visible change, often indicated by a color change due to an indicator or a change in pH. This allows for precise determination of the amount of substance present in the original solution.
In the case of oxalic acid, titration with a base like KOH (potassium hydroxide) can be used to find its concentration. Oxalic acid reacts with KOH in a 1:2 molar ratio. This means one mole of oxalic acid will neutralize two moles of KOH, which is usually derived from the balanced chemical equation of the reaction.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They show the reactants transforming into products with the conservation of mass. Each side of a chemical equation must balance, meaning the number of atoms for each element should be the same on both sides.
In the reaction of oxalic acid with potassium hydroxide, the balanced chemical equation is:
\[ \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(aq) + 2 \mathrm{KOH}(aq) \rightarrow \mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(aq) + 2 \mathrm{H}_{2} \mathrm{O}(l) \]
This equation clearly shows that one mole of oxalic acid reacts with two moles of KOH to produce one mole of potassium oxalate and two moles of water. Balancing chemical equations ensures the law of conservation of matter is upheld, which is crucial to predict the amounts of reactants and products for reactions accurately.