Problem 68 - Chemistry and Chemical Reactivity

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 \(0.546 \mathrm{M} \mathrm{NaOH} ?\) $$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell)$$

Step-by-Step Solution

Answer

76.88 mL of 0.125 M oxalic acid is required.

Step 1: Understand the Reaction Stoichiometry

The balanced chemical equation for the reaction between oxalic acid and sodium hydroxide is given by:\[\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq}) + 2 \mathrm{NaOH}(\mathrm{aq}) \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq}) + 2 \mathrm{H}_{2} \mathrm{O}(\ell)\]From the equation, we see that 1 mole of oxalic acid reacts with 2 moles of sodium hydroxide.

Step 2: Calculate Moles of NaOH

First, we calculate the number of moles of \(\mathrm{NaOH}\) using its concentration and volume:\[\text{Moles of } \mathrm{NaOH} = \text{Concentration} \times \text{Volume in Liters} = 0.546 \, \mathrm{M} \times 0.0352 \, \mathrm{L} = 0.0192192 \, \mathrm{mol}\]

Step 3: Determine the Required Moles of Oxalic Acid

Using the stoichiometry of the reaction, \(1\) mole of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) reacts with \(2\) moles of \(\mathrm{NaOH}\). Therefore, the moles of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) required are:\[\text{Moles of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} = \frac{0.0192192 \, \mathrm{mol}}{2} = 0.0096096 \, \mathrm{mol}\]

Step 4: Calculate the Volume of Oxalic Acid Solution Needed

Finally, calculate the volume of \(0.125 \, \mathrm{M}\) oxalic acid needed to provide \(0.0096096 \, \mathrm{mol}\):\[\text{Volume in Liters} = \frac{\text{Moles of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}}{\text{Concentration of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}} = \frac{0.0096096 \, \mathrm{mol}}{0.125 \, \mathrm{M}} = 0.0768768 \, \mathrm{L}\]To convert this volume to milliliters:\[0.0768768 \, \mathrm{L} \times 1000 = 76.88 \, \mathrm{mL}\]

Key Concepts

Reaction Stoichiometry

Understanding reaction stoichiometry is crucial in any chemical reaction. It tells us the exact ratio in which different reactants combine to form products. In our specific problem, the balanced chemical equation is given as: \[ \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq}) + 2 \mathrm{NaOH}(\mathrm{aq}) \rightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq}) + 2 \mathrm{H}_{2} \mathrm{O}(\ell) \] The equation indicates that 1 mole of oxalic acid reacts with 2 moles of sodium hydroxide. This stoichiometric relationship is key. It guides us in determining how much of one reactant is necessary to completely react with a given quantity of another. In our case, the 1:2 ratio signals that for every mole of oxalic acid, two moles of NaOH are needed. This foundational step ensures that calculations about reactants and products adhere to the laws of conservation of mass.

Moles Calculation

The next step involves calculating the moles of sodium hydroxide (NaOH) present in the given solution. Moles are a unit of measurement which quantify the amount of a substance. To find the moles, we employ the formula: \[ \text{Moles} = \text{Concentration} \times \text{Volume in Liters} \] In our exercise, the concentration provided is 0.546 M (moles per liter), and the volume is 35.2 mL. Before using the formula, it's important to convert milliliters to liters. Remember:- 1 L = 1000 mL - Therefore, 35.2 mL = 0.0352 L With these conversions in place, you can determine the moles of NaOH:\[ 0.546 \text{ M} \times 0.0352 \text{ L} = 0.0192192 \text{ mol} \] Thus, there are approximately 0.0192 moles of NaOH in the solution.

Solution Concentration

Solution concentration is a measure of how much solute is dissolved in a given volume of solvent. Usually expressed in molarity (M), concentration plays a vital role in calculating the volume required for reactions. In our problem, the concentration of oxalic acid (\(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\)) is given as 0.125 M. This means there are 0.125 moles of oxalic acid in every liter of its solution.Using our stoichiometry knowledge, we found earlier that 0.0096096 mol of oxalic acid is necessary to fully react with our sodium hydroxide. Therefore, the concentration helps us determine how much solution we need to supply this exact mole quantity.

Volume Conversion

Converting volumes between units is frequently required, especially in chemistry where solutions are often measured in liters or milliliters. Our task involves converting the final solution volume from liters back to milliliters for practicality and comprehension.In the last calculation step, you find the volume of the oxalic acid solution necessary using the relation:\[ \text{Volume in Liters} = \frac{\text{Moles of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}}{\text{Concentration of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}} = \frac{0.0096096 \text{ mol}}{0.125 \text{ M}} = 0.0768768 \text{ L} \]To convert this volume into milliliters:- Multiply the volume in liters by 1000 (since 1 L = 1000 mL)- Hence, 0.0768768 L becomes 76.88 mLThis conversion ensures the volume is presented in a unit more commonly used in laboratory settings, making it intuitively easier to measure and use.