Question

A \(25.00\) -mL sample of hydrochloric acid solution requires 24\. 16 mL of \(0.106 M\) sodium hydroxide for complete neutralization. What is the concentration of the original hydrochloric acid solution?

Short answer

The concentration of the original hydrochloric acid solution is approximately \(0.1024 M\).

Step-by-step solution

Write down the neutralization reaction

The neutralization reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl) can be written as: \( NaOH + HCl \rightarrow NaCl + H_2O \)

Calculate moles of sodium hydroxide

We are given the volume and concentration of sodium hydroxide (NaOH) required for complete neutralization. We can use this information to calculate the moles of sodium hydroxide. Moles of a substance are given by the product of volume and concentration: Moles of NaOH = Volume of NaOH × Concentration of NaOH Moles of NaOH = (24.16 mL) × (0.106 M) (Note that the volume is given in mL. For calculation purposes, we can use mL, as long as we're consistent with volume units.) Moles of NaOH = 2.56 mmol

Determine moles of hydrochloric acid

From the balanced equation in Step 1, we can see that one mole of NaOH reacts with one mole of HCl. Therefore, the moles of hydrochloric acid (HCl) will be equal to the moles of sodium hydroxide (NaOH). Moles of HCl = Moles of NaOH = 2.56 mmol

Calculate the concentration of hydrochloric acid

We are given the volume of the hydrochloric acid (HCl) solution and we have found the moles of HCl in Step 3. We can use this information to calculate the concentration of hydrochloric acid. Concentration is given by the ratio of moles to volume: Concentration of HCl = Moles of HCl / Volume of HCl Concentration of HCl = (2.56 mmol) / (25.00 mL) Concentration of HCl = 0.1024 M The concentration of the original hydrochloric acid solution is approximately 0.1024 M.

Key concepts

Neutralization Reaction

One of the fundamental reactions in chemistry is the neutralization reaction, an essential player in the wide field of acid-base chemistry. This reaction typically involves an acid and a base coming together to form water and a salt, characterized by the disappearance of the properties of the acid and the base. It's an essential concept that explains how titrations, used to determine unknown concentrations, operate.

For instance, when hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH), they form sodium chloride (NaCl) and water (H₂O). This can be represented by the chemical equation:
\( NaOH + HCl \rightarrow NaCl + H_2O \)

Understanding the 1:1 ratio in which these reactants combine is crucial, as it lays the groundwork for molarity and stoichiometry calculations. Remember, the key to neutralization is balance – essentially, you're bringing the pH of the solution closer to seven, which is neutral on the pH scale.

Molarity Calculation

Molarity is a term that often comes up in chemistry, especially when discussing solutions and their concentrations. It is defined as the moles of solute per liter of solution, enabling chemists to quantify how much of a chemical is present in a given volume. The formula for molarity is:
\( Molarity (M) = \frac{Moles\thinspace of\thinspace solute}{Volume\thinspace of\thinspace solution\thinspace in\thinspace liters} \)

For example, if we need to determine the molarity of a hydrochloric acid solution, using the amount of sodium hydroxide that neutralizes it in a titration gives us the data we need. By calculating the moles of the base and using the volume of the acid, we can compute its molarity. Molarity is fundamental when preparing solutions in the laboratory and forms the basis for many quantitative analyses in chemistry.

Stoichiometry

Stoichiometry is the aspect of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is based on the conservation of mass where the total mass of the reactants equals the total mass of the products. This concept is used to predict the amount of products that can be formed from a given amount of reactants or to determine the required amount of a reactant for a desired product yield.

In the context of acid-base titrations, stoichiometry comes into play to determine the unknown concentration of an acid or base. By using the known volume and molarity of one reactant and the stoichiometry of the neutralization reaction, we can find the molarity of the other reactant. In our exercise, the balanced equation illustrates a 1:1 stoichiometry, meaning the moles of hydrochloric acid and sodium hydroxide are equal. By applying stoichiometric principles, we calculate the molarity of the acid after identifying the moles required for complete neutralization.