Question

In a titration, \(23.25 \mathrm{~mL}\) of \(0.105 \mathrm{M} \mathrm{NaOH}\) was needed to react with \(21.45 \mathrm{~mL}\) of \(\mathrm{HCl}\) solution. What is the molarity of the acid?

Short answer

The molarity of the HCl solution is approximately 0.1138 M.

Step-by-step solution

Write the balanced chemical equation

The first step is to write the balanced chemical equation for the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl). The equation is: \[\mathrm{NaOH + HCl \rightarrow NaCl + H_2O}\].

Calculate moles of NaOH used

Next, calculate the number of moles of NaOH that reacted. Use the volume of NaOH solution and its molarity. \[\text{Moles of NaOH} = \text{volume} \times \text{molarity}\]\[\text{Moles of NaOH} = 23.25 \times 10^{-3} \, \text{L} \times 0.105 \, \text{mol/L} = 2.44125 \times 10^{-3} \, \text{mol}\]

Calculate moles of HCl reacted

According to the balanced equation, the mole ratio of NaOH to HCl is 1:1. Therefore, the moles of HCl that reacted will be equal to the moles of NaOH. \[\text{Moles of HCl} = \text{Moles of NaOH} = 2.44125 \times 10^{-3} \, \text{mol}\]

Calculate the molarity of the HCl solution

Finally, use the moles of HCl and the volume of HCl solution to find its molarity. \[\text{Molarity of HCl} = \frac{\text{Moles of HCl}}{\text{Volume of solution in liters}}\]\[\text{Molarity of HCl} = \frac{2.44125 \times 10^{-3} \, \text{mol}}{21.45 \times 10^{-3} \, \text{L}} \approx 0.1138 \, \text{M}\]

Key concepts

Chemical Titration

Chemical titration is an analytical method used to determine the concentration of a given substance, often an acid or a base. It involves the precise addition of a solution from a burette into a volume of the substance being tested until the reaction between the two is complete, which can be indicated through a color change by a pH indicator or by reaching an equivalence point.

In the given exercise, a strong acid (hydrochloric acid, HCl) is being titrated with a strong base (sodium hydroxide, NaOH). The point at which the amount of NaOH added neutralizes the HCl is when the number of moles of each reactant is equivalent. This endpoint can be used to calculate the unknown molarity of the acid solution, based on the known molarity and volume of the base used.

Mole Concept

The mole concept is a fundamental aspect of chemistry that provides a bridge between the atomic level and the macroscopic level. It is based on Avogadro's number, which is defined as the number of constituent particles (usually atoms or molecules) in one mole of a substance, and is approximately equal to \(6.022 \times 10^{23}\).

One mole of any substance will have the same number of entities as one mole of any other substance. This exercise employs the mole concept by converting the volume and concentration (molarity) of a solution into moles, reflecting the number of particles involved in the chemical reaction. The calculation of moles is critical in determining the exact point at which the reactants are stoichiometrically balanced in a titration.

Stoichiometry

Stoichiometry deals with the quantitative relationships between reactants and products in a chemical reaction. In a balanced chemical equation, the coefficients indicate the ratio of moles of each substance involved.

For instance, the chemical equation \(\mathrm{NaOH + HCl \rightarrow NaCl + H_2O}\) suggests that the reaction between NaOH and HCl occurs in a 1:1 molar ratio. Applying stoichiometry is crucial in titration exercises because it allows the calculation of the unknown concentration of a reactant when the other is known. In our problem, the stoichiometric relationship is used to determine that the moles of HCl (unknown concentration) that reacted will be the same as the moles of NaOH (known concentration) due to their 1:1 molar ratio.

Acid-Base Reaction

In an acid-base reaction, an acid reacts with a base to form salt and water. This type of reaction is also known as a neutralization reaction because the acid (proton donor) and base (proton acceptor) neutralize each other's properties.

The exercise provided exemplifies an acid-base reaction where sodium hydroxide (a base) reacts with hydrochloric acid (an acid) to yield sodium chloride (salt) and water. The neutralization reaction follows the Arrhenius definition of acids and bases, and it is essential to understanding the concept of titration, as it is the fundamental reaction type being analyzed.