Question

A 12.5 mL sample of vinegar, containing acetic acid, was titrated using \(0.504 \mathrm{M} \mathrm{NaOH}\) solution. The titration required \(20.65 \mathrm{~mL}\) of the base. What was the molar concentration of acetic acid in the vinegar?

Short answer

The molar concentration of acetic acid in the vinegar is 0.816 M.

Step-by-step solution

Write the balanced chemical equation

Write the balanced chemical equation for the neutralization reaction between acetic acid (CH3COOH) and sodium hydroxide (NaOH). The equation is: CH3COOH (aq) + NaOH (aq) → CH3COONa (aq) + H2O (l).

Calculate moles of NaOH

Calculate the number of moles of NaOH used in the titration using the concentration of NaOH solution and the volume of NaOH solution used. The formula to use is: moles = molarity × volume (in liters). moles NaOH= 0.504 M × 0.02065 L.

Calculate moles of acetic acid

Since acetic acid and NaOH react on a 1:1 mole ratio according to the balanced equation, the moles of acetic acid are equal to the moles of NaOH used in the titration.

Calculate the molarity of acetic acid

Calculate the molar concentration of acetic acid in the vinegar by using the formula: molarity = moles of solute / volume of solution (in liters). The volume of the vinegar sample is 12.5 mL, which needs to be converted to liters by dividing by 1000.

Key concepts

Molar Concentration

Understanding the molar concentration is crucial when tackling problems involving chemical solutions. Molar concentration, also known as molarity, represents the number of moles of a solute (a substance being dissolved) present in one liter of solution. Mathematically, it is expressed using the formula: \[\begin{equation} Molarity (M) = \frac{moles \text{ of solute}}{liters \text{ of solution}} \end{equation}\]In the context of our vinegar titration exercise, the goal is to find the molarity of acetic acid, which will reveal how concentrated the acetic acid is within the vinegar solution.

1. For practical applications, one should always start by converting the volume of solution to liters if it's not already provided in that unit, since molarity is defined per liter of solution.
2. Next, determine the number of moles of the solute present, which in a titration setup comes from the stoichiometric relationship with the titrant.
3. Finally, divide the moles of solute by the volume of solution in liters to find the molarity.

Concentration units are pivotal in predicting the extent of a reaction and for proper stoichiometric calculations, which ultimately helps in the preparation of a desired solution concentration.

Neutralization Reaction

A neutralization reaction is a type of chemical reaction in which an acid and a base react to form a salt and water. In the context of the titration we're discussing, acetic acid (a weak acid) reacts with sodium hydroxide (a strong base). The universal form of a neutralization reaction can be simplified as:\[\begin{equation} Acid (aq) + Base (aq) \rightarrow Salt (aq) + H_{2}O(l) \end{equation}\]These reactions are often exothermic, releasing heat. Titration is a practical application of neutralization, wherein an acid solution is titrated with a known concentration of a base (or vice versa) to determine the concentration of the unknown. Identifying the neutralization reaction allows us to understand the stoichiometric relationships between reactants and to properly balance the chemical equation, which is a fundamental step in stoichiometry.

Stoichiometry

Stoichiometry is the section of chemistry that involves calculating the quantities of reactants and products in a chemical reaction. It is based on the conservation of mass where the quantity of each element must be the same at the start and end of a chemical reaction.

To perform stoichiometric calculations effectively, you need:

1. A balanced chemical equation which provides the mole ratios of the reactants and products.
2. Information about the quantity of one or more reactants or products (e.g., mass, volume, moles).
3. Understanding of the molar relationships, which can be used to convert between units of mass, volume, and number of particles.

In titration exercises, stoichiometry allows for the calculation of unknown concentrations by using the known volume and molarity of one reactant to determine the amount that reacts, and subsequently find the unknown concentration of the other reactant.

Balanced Chemical Equation

A balanced chemical equation is necessary for any stoichiometric computation since it depicts the exact ratio in which reactants combine and products form. In our vinegar titration scenario, the reaction between acetic acid (CH3COOH) and sodium hydroxide (NaOH) needs to be represented with a balanced equation:\[\begin{equation} CH3COOH (aq) + NaOH (aq) \rightarrow CH3COONa (aq) + H2O (l) \end{equation}\]In this equation, the coefficients of all the molecules are '1', indicating that they react on a one-to-one basis. What this means is that one mole of acetic acid reacts with one mole of sodium hydroxide to produce one mole of sodium acetate and one mole of water. Without this knowledge, it would be impossible to determine the quantities involved in the reaction, making the balanced chemical equation an essential facet of solving titration problems and of stoichiometry in general.