Question

The concentration of a sodium hydroxide solution is to be determined. A 50.0-mL sample of 0.104 M HCl solution requires \(48.7 \mathrm{mL}\) of the sodium hydroxide solution to reach the point of neutralization. Calculate the molarity of the NaOH solution.

Short answer

The concentration of the sodium hydroxide solution can be calculated using the balanced equation \(\mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H_2O}\) and the given information about the HCl solution. The moles of HCl in the sample are calculated as \(5.2 \times 10^{-3} \mathrm{mol}\), and since the mole ratio of HCl to NaOH is 1:1, there are also \(5.2 \times 10^{-3} \mathrm{mol}\) of NaOH. The molarity of the NaOH solution is then determined as \(0.107 \frac{mol}{L}\).

Step-by-step solution

Write the balanced chemical equation for the reaction.

The balanced chemical equation for the neutralization of HCl and NaOH is: \[ \mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H_2O} \]

Determine the moles of HCl in the sample.

We are given the concentration and volume of the HCl solution. Use them to calculate the moles of HCl in the 50 mL sample. Moles of HCl = Molarity × Volume Moles of HCl = \(0.104 \frac{mol}{L} \times 50.0 \mathrm{mL} \times \frac{1 L}{1000 \mathrm{mL}}\) Moles of HCl = \(5.2 \times 10^{-3} \mathrm{mol}\)

Determine the moles of NaOH in the sample.

From the balanced chemical equation, we see that the mole ratio between HCl and NaOH is 1:1. Therefore, the moles of NaOH must be equal to the moles of HCl. Moles of NaOH = \(5.2 \times 10^{-3} \mathrm{mol}\)

Calculate the molarity of the NaOH solution.

Now that we have the moles of NaOH, we can finally calculate the molarity of the NaOH solution. We are given the volume of NaOH required for neutralization, which is 48.7 mL. Molarity of NaOH = \(\frac{moles_{\mathrm{NaOH}}}{volume_{\mathrm{NaOH}}}\) Molarity of NaOH = \(\frac{5.2 \times 10^{-3} mol}{48.7 \mathrm{mL} \times \frac{1 L}{1000 \mathrm{mL}}}\) Molarity of NaOH = \(0.107 \frac{mol}{L}\) The concentration of the sodium hydroxide solution is \(0.107 M\).

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculating the amounts of substances that are consumed and produced in a given reaction. Understanding stoichiometry is crucial for scientists and students alike, as it helps predict yields of reactions and to scale up laboratory results to industrial production.

For example, when working on molarity calculations, such as in the given exercise to determine the concentration of a sodium hydroxide solution, stoichiometry allows you to use the known concentration and volume of the HCl solution to find the moles of HCl. This is especially important because chemical reactions often happen in a defined ratio, known as the stoichiometric ratio, which in the case of a neutralization reaction like HCl reacting with NaOH, is typically 1:1.

Neutralization Reactions

Neutralization reactions are specific types of chemical reactions where an acid and a base react to form a salt and water. These reactions are of great interest in various fields such as chemistry, environmental science, and medicine. They proceed until the reacting acid and base are completely consumed, creating a neutralized solution.

In the context of our exercise, we are examining a neutralization reaction where hydrochloric acid (HCl) combines with sodium hydroxide (NaOH) to produce sodium chloride (NaCl) and water (H₂O). Having an understanding of these reactions allows you to predict that when equal moles of NaOH and HCl mix, they will completely neutralize each other, thus simplifying the task of finding the molarity of the NaOH solution.

Chemical Equation Balancing

Chemical equation balancing is the process of making sure that the number of atoms of each element is the same on both sides of a chemical equation. It's a necessary step in solving many chemistry problems because it reflects the law of conservation of mass, stating that matter cannot be created nor destroyed in a chemical reaction.

For the neutralization reaction provided in the exercise, the balanced chemical equation is \( \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \). This equation shows a one-to-one ratio between HCl and NaOH, allowing us to directly relate the moles of HCl used to the moles of NaOH required for neutralization. Accurate balancing is key to determining the correct stoichiometry and, subsequently, the precise molarity of solutions involved in the reaction.