Question

Consider separate aqueous solutions of \(\mathrm{HCl}\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}\) with the same concentrations in terms of molarity. You wish to neutralize an aqueous solution of NaOH. For which acid solution would you need to add more volume (in \(\mathrm{mL}\) ) to neutralize the base? a. The HCl solution. b. The \(\mathrm{H}_{2} \mathrm{SO}_{4}\) solution. c. You need to know the acid concentrations to answer this question. d. You need to know the volume and concentration of the NaOH solution to answer this question. e. \(\mathrm{c}\) and \(\mathrm{d}\) Explain your answer.

Short answer

a. The HCl solution.

Step-by-step solution

Determine the balanced neutralization reactions.

First, we need to write the balanced chemical equations for the neutralization reactions between NaOH and the two acids. For HCl: \[\mathrm{HCl } (aq) + \mathrm{NaOH } (aq) \rightarrow \mathrm{NaCl } (aq) + \mathrm{H}_2\mathrm{O} (l)\] For H₂SO₄: \[\mathrm{H}_2\mathrm{SO}_4 (aq) + 2\mathrm{NaOH } (aq) \rightarrow \mathrm{Na}_2\mathrm{SO}_4 (aq) + 2\mathrm{H}_2\mathrm{O} (l)\]

Understand the stoichiometry of the neutralization reactions.

From the balanced equations, we observe the following stoichiometric ratios: For HCl: 1 mole of HCl reacts with 1 mole of NaOH. For H₂SO₄: 1 mole of H₂SO₄ reacts with 2 moles of NaOH.

Determine the volume ratios from the stoichiometry.

Since the concentrations of the two acids are the same, we can reason in terms of volumes. From the stoichiometry, we can determine how the volume of each acid solution needed for complete neutralization relates to the volume of NaOH solution: For HCl: 1 mole of HCl reacts with 1 mole of NaOH, so the volume ratio will be 1:1 (volumes of acid and base solutions will be equal). For H₂SO₄: 1 mole of H₂SO₄ reacts with 2 moles of NaOH, so the volume ratio will be 1:2 (volume of acid solution will be half the volume of base solution).

Find the solution to the problem.

Comparing the volume ratios of the two acids needed to neutralize the NaOH, we can see that we would need to add more volume when using HCl as compared to H₂SO₄. Thus, the correct answer is: a. The HCl solution.

Key concepts

Stoichiometry

In chemistry, stoichiometry is crucial for understanding reactions at a molecular level. It refers to the calculation of reactants and products in chemical reactions. For a neutralization reaction, stoichiometry is key to determining how much acid is needed to completely react with a given base.

In the original exercise, consider two acids, \(\text{HCl}\) and \(\text{H}_2\text{SO}_4\), neutralizing a NaOH solution. By writing balanced chemical equations and considering the mole ratios between reactants and products, we can precisely calculate the volume of acid required. These calculations ensure the reactants will fully convert to products without leaving any excess reactants.

• For \(\text{HCl}\), the equation \(\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}\) shows that one mole of \(\text{HCl}\) reacts with one mole of NaOH.
• For \(\text{H}_2\text{SO}_4\), the equation \(\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}\) demonstrates that one mole of acid reacts with two moles of NaOH.

Understanding these stoichiometric ratios allows us to make predictions about the volumes needed, clearly shown in the exercise.

Acid-Base Chemistry

Acid-base chemistry is a fundamental part of science, focusing on the interactions between acids and bases. Acids are substances that donate protons (H⁺ ion), while bases are substances that accept protons. Neutralization reactions occur when acids and bases react to form water and a salt. This is one of the simplest forms of chemical reactions, yet highly significant in various scientific applications.

The original exercise involves neutralizing NaOH (a base) using acids \(\text{HCl}\) and \(\text{H}_2\text{SO}_4\). In both cases, the acids donate protons (H⁺) to hydroxide ions (OH⁻ from NaOH), forming water.

• \(\text{HCl}\) is a monoprotic acid, meaning it can donate only one proton per molecule.
• In contrast, \(\text{H}_2\text{SO}_4\) is a diprotic acid, effectively contributing two protons per molecule.

Given their different proton contributions, \(\text{HCl}\) and \(\text{H}_2\text{SO}_4\) participate in reactions at different volume ratios, as explained in the stoichiometry section.

Balanced Chemical Equations

Balanced chemical equations are vital in accurately representing chemical reactions. They ensure the conservation of mass by having equal numbers of each type of atom on both the reactant and product sides. Balancing equations is important for stoichiometry and is essential in laboratory chemistry and industrial applications.

The original problem required us to write balanced chemical equations to understand the neutralization reactions:

• For \(\text{HCl}\), the balanced equation is \(\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}\).
• For \(\text{H}_2\text{SO}_4\), it's \(\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}\).

By comparing these equations, it's clear why we need more of the \(\text{HCl}\) solution for neutralization. Each \(\text{HCl}\) molecule reacts with just one \(\text{NaOH}\) molecule, whereas each \(\text{H}_2\text{SO}_4\) molecule reacts with two, making use of half as many acid molecules, thus demonstrating an essential role of balanced chemical equations in understanding reaction dynamics.