Problem 68 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

76.8 mL of 0.125 M oxalic acid is required.

Step 1: Write the balanced chemical equation

The given chemical reaction is already balanced: \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \). This equation tells us that 1 mole of oxalic acid reacts with 2 moles of NaOH.

Step 2: Calculate moles of NaOH

First, calculate the moles of NaOH. Use the formula: \( \text{moles} = \text{molarity} \times \text{volume (L)} \). Convert 35.2 mL to liters by dividing by 1000: \( 35.2\, \text{mL} = 0.0352\, \text{L} \). Then, calculate the moles: \( 0.546\, \text{M} \times 0.0352\, \text{L} = 0.0192\, \text{moles} \; \text{NaOH} \).

Step 3: Use stoichiometry to find moles of oxalic acid

According to the balanced equation, 1 mole of \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \) reacts with 2 moles of \( \mathrm{NaOH} \). Thus, \( 0.0192\, \text{moles NaOH} \) will require \( \frac{0.0192}{2} = 0.0096\, \text{moles of} \; \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \).

Step 4: Calculate the volume of oxalic acid needed

Use the moles of \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \) and its molarity to find the volume required. Use the formula: \( \text{volume (L)} = \frac{\text{moles}}{\text{molarity}} \). With \( 0.0096\, \text{moles} \) and \( 0.125\, \text{M} \), the volume is \( \frac{0.0096}{0.125} = 0.0768\, \text{L} \). Convert to milliliters (mL): \( 0.0768\, \text{L} \times 1000 = 76.8\, \text{mL} \).

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is crucial for stoichiometry as it provides the mole ratio of the reactants and products involved in a chemical reaction. In our exercise, the balanced equation is \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \). This tells us that one mole of oxalic acid reacts with two moles of sodium hydroxide.

• Coefficients indicate the quantity of molecules involved.
• They allow us to determine how much of each reactant is needed or how much product is formed.

Recognizing these ratios makes calculations more manageable, setting a foundation for the rest of the stoichiometric calculations.

Molarity Calculations

Molarity is a measurement of concentration expressed as moles of solute per liter of solution, denoted as \( M \). To solve our problem, we first needed to calculate the moles of \( \mathrm{NaOH} \) using its molarity and its volume in liters. The formula used is: \[\text{Moles} = \text{Molarity} \times \text{Volume (L)}\]This formula gives us the number of moles, even if the volume is initially provided in milliliters, as conversion to liters is necessary for accuracy.

• Ensure units are consistent.
• Understanding molarity allows us to quantitatively relate reactants and products.

This calculation helps establish how many moles of reactants are available to react.

Volume Conversion

In stoichiometry problems, it's often necessary to convert volumes to align with the required units. In our exercise, the volume of \( \mathrm{NaOH} \) was initially given in milliliters (mL) and needed conversion to liters (L) for use in molarity calculations. The conversion process is simple:

• 1 mL = 0.001 L, or simply divide by 1000.
• This keeps units consistent and formulas valid.

Such conversions are essential because stoichiometric calculations rely on proper unit alignment to ensure accurate results.

Chemical Reaction

A chemical reaction involves the process of substances, known as reactants, transforming into different substances, called products. In the given scenario, oxalic acid reacts with sodium hydroxide to produce sodium oxalate and water. This interaction is a reflection of chemical changes where:

• Bonds in reactants break.
• New bonds form to create products.

Understanding chemical reactions is pivotal as it helps in predicting the products and quantities formed by the interaction of different reactants. The balanced equation we started with is the road map that outlines how reactants transform into products in a precise away.