Question

What volume of \(0.125 \mathrm{M}\) oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), is required to react with \(35.2 \mathrm{mL}\) of \(0.546 \mathrm{M} \mathrm{NaOH} ?\) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \rightarrow\) $$ \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$

Short answer

76.8 mL of \(0.125 \mathrm{M}\) oxalic acid is required.

Step-by-step solution

Write the Balanced Chemical Equation

The balanced equation for the reaction between oxalic acid (\(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\)) and sodium hydroxide (\(\mathrm{NaOH}\)) is given as: \[ \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{H}_{2} \mathrm{O}\] This tells us that 2 moles of \(\mathrm{NaOH}\) react with 1 mole of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\).

Calculate Moles of NaOH

First, calculate the moles of \(\mathrm{NaOH}\) using the concentration and volume. Convert the volume from \(\mathrm{mL}\) to \(\mathrm{L}\): \[ 35.2 \mathrm{mL} = 0.0352 \mathrm{L} \]Use: \[ \text{Moles of } \mathrm{NaOH} = \mathrm{Concentration} \times \mathrm{Volume} = 0.546 \times 0.0352 = 0.0192 \text{ moles} \]

Use Mole Ratio to Find Moles of Oxalic Acid

From the balanced equation, the mole ratio of \( \mathrm{NaOH} \) to \( \mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4} \) is 2:1. Use this to find the moles of \( \mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4} \): \[ \text{Moles of } \mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4} = \frac{0.0192}{2} = 0.0096 \text{ moles} \]

Calculate Volume of Oxalic Acid Solution Required

To find the volume of \(0.125 \mathrm{M} \) oxalic acid solution required, use the formula: \[ \text{Volume} = \frac{\text{Moles}}{\text{Concentration}} = \frac{0.0096}{0.125} = 0.0768 \mathrm{L} \] Convert this to milliliters: \[ 0.0768 \mathrm{L} = 76.8 \mathrm{mL} \]

Key concepts

Molarity Calculations

Molarity is a fundamental concept in chemistry that tells us the concentration of a solution. It is represented as the number of moles of solute per liter of solution, often expressed in moles per liter (M). To perform molarity calculations, like those involved in acid-base titration, you need to know the molarity and volume of one of the reactants to find the required volume or moles of the other.

In the given problem, the molarity of NaOH is used to calculate the moles available. By converting volume from milliliters to liters and using the formula:

• Moles of solute = Molarity \(\times\) Volume (in liters)

We can determine the moles of NaOH. This value is crucial as it helps in the subsequent steps where stoichiometry will be applied. Understanding molarity in this context allows us to control and predict how substances react in a solution.

Chemical Reactions

Chemical reactions are processes where reactants transform into products through the breaking and forming of bonds. They are typically represented by balanced chemical equations, which provide moles relationships between reactants and products.

In the scenario of our exercise, the balanced equation:

• \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{H}_{2} \mathrm{O}\)

shows that two moles of NaOH are required to react completely with one mole of oxalic acid. Without this crucial information, it would be challenging to determine the quantities needed for a complete reaction. Reactants either get consumed or remaining, and products form as per this stoichiometric ratio, ensuring reactions occur as intended.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantification and measurement of reactants and products in chemical reactions. It hinges on the principles of conservation of mass and energy, allowing you to calculate the necessary amounts of substances.

In an acid-base titration, stoichiometry tells us how the amounts of acid and base relate through their balanced equation. For the problem at hand, the mole ratio obtained from the balanced chemical equation is 2:1, meaning two moles of NaOH react with one mole of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\). Using this ratio, the moles of oxalic acid are calculated from the moles of NaOH. This is a critical step, as stoichiometry ensures that we can titrate precisely, predicting and achieving the desired endpoint where reactants are exhausted, leaving only the desired products.