Question

In a titration, 25.9 \(\mathrm{mL}\) of \(3.4 \times 10^{-3} \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) neutralized 16.6 \(\mathrm{mL}\) of HCl solution. What is the molarity of the HCl solution?

Short answer

0.01061 M

Step-by-step solution

Write the balanced chemical equation

The reaction between \text{Ba(OH)}_2 and HCl can be represented by the balanced equation: \[ \text{Ba(OH)}_2 + 2\text{HCl} \rightarrow \text{BaCl}_2 + 2\text{H}_2\text{O} \]

Calculate moles of \text{Ba(OH)}_2

Use the molarity and volume to find the moles of \text{Ba(OH)}_2: \[ \text{Moles of Ba(OH)}_2 = \text{Molarity} \times \text{Volume} \] \[ \text{Moles of Ba(OH)}_2 = 3.4 \times 10^{-3} \text{ M} \times 0.0259 \text{ L} \] \[ \text{Moles of Ba(OH)}_2 = 8.806 \times 10^{-5} \text{ moles} \]

Relate moles of \text{Ba(OH)}_2 to moles of HCl

From the chemical equation, 1 mole of \text{Ba(OH)}_2 reacts with 2 moles of HCl. So, the moles of HCl will be twice the moles of \text{Ba(OH)}_2: \[ \text{Moles of HCl} = 2 \times 8.806 \times 10^{-5} \] \[ \text{Moles of HCl} = 1.7612 \times 10^{-4} \text{ moles} \]

Calculate the molarity of HCl solution

Use the moles of HCl and the volume of the HCl solution to find its molarity: \[ \text{Molarity} = \frac{\text{Moles}}{\text{Volume}} \] \[ \text{Molarity of HCl} = \frac{1.7612 \times 10^{-4} \text{ moles}}{0.0166 \text{ L}} \] \[ \text{Molarity of HCl} = 0.01061 \text{ M} \]

Key concepts

Molarity

Molarity is a measure of concentration, representing the number of moles of a solute per liter of solution. It is denoted by \(\text{M}\). Understanding molarity is crucial in titration calculations because it helps determine how much of one solution is needed to react completely with another. For instance, in our exercise, we know the molarity of Ba(OH)_2, which is used to find the moles of Ba(OH)_2. This initial step is essential to eventually determine the molarity of the unknown HCl solution.

Balanced Chemical Equation

In any titration, writing the balanced chemical equation is an essential first step. This ensures that you are aware of the stoichiometry of the reaction, i.e., the ratio in which the reactants combine. For the reaction between Ba(OH)_2 and HCl, the balanced equation is: \[\text{Ba(OH)}_2 + 2\text{HCl} \rightarrow \text{BaCl}_2 + 2\text{H}_2\text{O}\]. This equation tells us that one mole of Ba(OH)_2 reacts with two moles of HCl. Without the balanced equation, one cannot accurately relate the quantities of reactants and products involved.

Neutralization Reaction

A neutralization reaction occurs between an acid and a base, producing a salt and water as the products. In our titration example, Ba(OH)_2 (a strong base) reacts with HCl (a strong acid). During this reaction, the hydroxide ions (OH^-) from Ba(OH)_2 neutralize the hydrogen ions (H^+) from HCl, resulting in water (H_2O). Essentially, such reactions allow us to determine the concentration of an unknown solution by reacting it with a solution of known concentration.

Moles Calculation

Calculating the number of moles is a fundamental step in titration calculations. Moles measure the quantity of a substance and are calculated by multiplying the molarity by the volume of the solution used. For example, the moles of Ba(OH)_2 in our exercise are computed as: \[\text{Moles of Ba(OH)}_2 = 3.4 \times 10^{-3}\text{ M} \times 0.0259\text{ L} = 8.806 \times 10^{-5}\text{ moles}\]. Knowing the moles of Ba(OH)_2 helps us determine the moles of HCl required, and ultimately, the molarity of the HCl solution.