Question

What volume of \(0.151 \mathrm{N} \mathrm{NaOH}\) is required to neutralize \(24.2 \mathrm{mL}\) of \(0.125 \mathrm{N} \mathrm{H}_{2} \mathrm{SO}_{4} ?\) What volume of 0.151 \(N\) NaOH is required to neutralize \(24.1 \mathrm{mL}\) of \(0.125 M \mathrm{H}_{2} \mathrm{SO}_{4} ?\)

Short answer

The volume of \(0.151 N\) NaOH required to neutralize \(24.1 mL\) of \(0.125 N\) \(H_{2}SO_{4}\) is approximately \(19.95 mL\).

Step-by-step solution

Identify the normalities and volumes of the acid and base

We are given the following information: - Normality of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) (\(N_{acid}\)): \(0.125\) N - Volume of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) (\(V_{acid}\)): \(24.1\) mL - Normality of \(\mathrm{NaOH}\) (\(N_{base}\)): \(0.151\) N

Set up the equivalent volumes equation

Using the given values, we can set up the equation to solve for the volume of \(\mathrm{NaOH}\) (\(V_{base}\)): \[0.125 \times 24.1 = 0.151 \times V_{base}\]

Solve for the volume of \(\mathrm{NaOH}\) required to neutralize the \(\mathrm{H}_{2}\mathrm{SO}_{4}\)

To find \(V_{base}\), we need to divide both sides of the equation by the normality of the base (\(N_{base}\)): \[V_{base} = \frac{0.125 \times 24.1}{0.151}\] Now, we can calculate the value: \[V_{base} = \frac{3.0125}{0.151} \approx 19.95 \mathrm{mL}\] So, the volume of \(0.151\) N \(\mathrm{NaOH}\) required to neutralize \(24.1\) mL of \(0.125\) N \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is approximately \(19.95\) mL.

Key concepts

Acid-Base Titration

Acid-base titration is a laboratory process used to determine the concentration of an unknown acid or base solution by neutralizing it with a base or acid of known concentration, respectively. During a titration, a titrant (the known solution) is added to the analyte (the unknown solution) until the reaction reaches the equivalence point, which is the exact point where the number of acid equivalents equals the number of base equivalents. Indicators are often used to visually signal the end of the reaction, changing color at or near the equivalence point.

Understanding acid-base titration involves a clear grasp of concepts like molarity, normality, and equivalence points, which dictate the quantitative relationships between the acid and base in the reaction.

Normality

Normality (N) is a measure of the concentration of a solution expressed in equivalents of reactive species per liter of solution. It's especially useful in redox reactions, precipitation, and acid-base titrations because it considers the stoichiometry of the reaction. In the context of the given exercise, it allows us to calculate the volume of titrant needed without needing to know the number of moles directly.

One equivalent of an acid or base is the amount that can donate or accept one mole of hydrogen ions (H+) or hydroxide ions (OH-), respectively. The normality of a substance can vary based on the reaction because one chemical might react differently with various substances, contributing different numbers of equivalents.

Stoichiometry

Stoichiometry is the portion of chemistry that deals with the quantities and proportional relationships between reactants and products in a chemical reaction. In the exercise, we apply stoichiometry to determine how much of the sodium hydroxide (NaOH) solution is needed to neutralize the sulfuric acid (H2SO4). We do this by using the stoichiometric coefficient from the balanced chemical equation and the relation of normality to the number of equivalents. An understanding of moles, molar masses, and balance reactions is crucial for accurate stoichiometric calculations.

The exact stoichiometric relationship is crucial because it ensures that the reaction will be complete, with neither reactant in excess. This is important for the precise calculation of the unknown concentration.

Equivalence Point

The equivalence point is the stage in a titration where the number of moles of the titrant added equals the number of moles of substance present in the sample. It is the ideal end point of a titration, where the reaction is stoichiometrically balanced. In our exercise, it is the point where the NaOH has completely neutralized H2SO4.

At the equivalence point in an acid-base titration, the solution will contain only the salt from the neutralization reaction and water. The volume at the equivalence point can be calculated using the stoichiometry of the chemical reaction and the normality of the reactants as shown in the provided exercise solution. Precise determination of the equivalence point is vital to accurate titrations and is often indicated by a pH meter or a visual indicator which changes color in response to pH changes in the surrounding solution.