Question

How many milliliters of \(0.150 \mathrm{M} \mathrm{NaOH}\) are required to neutralize \(50.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} ?\) The balanced neutralization reaction is: $$ \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{NaOH}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) $$.

Short answer

133.3 mL of NaOH is required.

Step-by-step solution

Write Balanced Reaction Equation

The balanced neutralization reaction is given as: \( \mathrm{H}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l) \). This tells us that one mole of \( \mathrm{H}_{2}\mathrm{SO}_{4} \) reacts with two moles of \( \mathrm{NaOH} \).

Calculate Moles of H₂SO₄

Using the formula \( n = C \times V \), where \( n \) is the number of moles, \( C \) is the concentration in moles per liter, and \( V \) is the volume in liters. For \( \mathrm{H}_{2}\mathrm{SO}_{4} \): \[ n_{\mathrm{H}_{2}\mathrm{SO}_{4}} = 0.200 \text{ M} \times 0.050 \text{ L} = 0.010 \text{ moles} \].

Determine Moles of NaOH Required

From the balanced equation, we know 1 mole of \( \mathrm{H}_{2}\mathrm{SO}_{4} \) requires 2 moles of \( \mathrm{NaOH} \). Therefore, the moles of \( \mathrm{NaOH} \) needed are: \[ n_{\mathrm{NaOH}} = 2 \times n_{\mathrm{H}_{2}\mathrm{SO}_{4}} = 2 \times 0.010 = 0.020 \text{ moles} \].

Calculate Volume of NaOH Solution

Using the equation \( V = \frac{n}{C} \), where \( V \) is the volume in liters, \( n \) is the number of moles, and \( C \) is the concentration. We calculate: \[ V_{\mathrm{NaOH}} = \frac{0.020}{0.150} \approx 0.1333 \text{ L} \].Convert liters to milliliters: \[ V_{\mathrm{NaOH}} = 0.1333 \text{ L} \times 1000 \text{ mL/L} = 133.3 \text{ mL} \].

Key concepts

Neutralization Reaction

In the world of chemistry, a neutralization reaction is a chemical reaction where an acid and a base interact to form water and a salt. This type of reaction is fundamental in titration experiments. In the given exercise, sulfuric acid (\(\text{H}_2\text{SO}_4\)) and sodium hydroxide (\(\text{NaOH}\)) are mixed. The result of their neutralization forms sodium sulfate (\(\text{Na}_2\text{SO}_4\)) and water (\(\text{H}_2\text{O}\)).

Key elements of the neutralization include:

• The combination of hydrogen ions (from the acid) and hydroxide ions (from the base) to form water.
• Every mole of sulfuric acid needs two moles of \(\text{NaOH}\) in this balanced equation.

Understanding these reactions is critical for calculating quantities in titration.

Stoichiometry

Stoichiometry offers a reliable way to quantify relationships within chemical reactions. By focusing on the proportions of reactants and products, stoichiometry is essential in determining how substances react in precise amounts. This concept applies in the neutralization example, where one mole of \(\text{H}_2\text{SO}_4\) reacts with two moles of \(\text{NaOH}\).

Stoichiometric calculations involve using:

• Balanced chemical equations to understand the ratio of reactants to products.
• Moles as a measurement to express chemical quantities.

These ratios help predict how much of each reactant is needed or how much product can form from a given amount of reactant.

Mole Calculations

Mole calculations are crucial in every chemical equation. They translate the balanced equation into actual quantities of substances. In the exercise, the number of moles of \(\text{H}_2\text{SO}_4\) was calculated using the formula \(n = C \times V\), with \(C\) as concentration and \(V\) as volume.

Here’s a step-by-step on how it works:

• Determine moles of the acid using the concentration (\(0.200\) M) and its volume (\(50.0\) mL converted to liters).
• Calculate moles of the base desired, knowing that each mole of acid needs two moles of \(\text{NaOH}\) as per the balanced reaction.

These calculations enable understanding of the quantities needed for complete neutralization.

Solution Concentration

Solution concentration denotes how much solute is dissolved in a solvent, often presented as molarity (\(\text{M}\)), which is moles per liter. This concept is pivotal when predicting how much solution is needed to cause certain reactions, such as in titrations. In this case, the concentrations of \(\text{H}_2\text{SO}_4\) and \(\text{NaOH}\) were crucial for calculation.

Key aspects of concentration include:

• The relationship between volume, concentration, and moles: a higher concentration results in more moles of solute per liter, influencing reaction outcomes.
• Concentration helps determine how much solution to use to achieve neutralization in titration experiments.

Mastering concentration concepts allows accurate formulation of chemical solutions.