Question

Acetic acid \(\left(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)\) is an important ingredient of vinegar. A sample of \(50.0 \mathrm{~mL}\) of a commercial vinegar is titrated against a \(1.00 \mathrm{M} \mathrm{NaOH}\) solution. What is the concentration (in \(M\) ) of acetic acid present in the vinegar if \(5.75 \mathrm{~mL}\) of the base is needed for the titration?

Short answer

The concentration of acetic acid is \(0.115\, M\).

Step-by-step solution

Write the Balanced Equation

The chemical reaction between acetic acid \(\left(\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\right)\) and sodium hydroxide \(\left(\mathrm{NaOH}\right)\) is \(\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} + \mathrm{NaOH} \rightarrow \mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} + \mathrm{H}_{2}\mathrm{O}\). This shows a 1:1 molar ratio between acetic acid and sodium hydroxide.

Calculate Moles of NaOH Used

Using the concentration and volume of NaOH, calculate the moles involved. Volume should be in liters: \(5.75\, \text{mL} = 0.00575\, \text{L}\). Moles of NaOH = \(1.00\, \text{M} \times 0.00575\, \text{L} = 0.00575\, \text{mol}\).

Determine Moles of Acetic Acid

Using the balanced equation, it is clear the moles of acetic acid are equal to the moles of NaOH since the reaction is 1:1. Therefore, moles of acetic acid = \(0.00575\, \text{mol}\).

Calculate Concentration of Acetic Acid

The concentration \((M)\) of acetic acid is calculated by dividing its moles by the volume of the vinegar solution in liters: \(50.0\, \text{mL} = 0.0500\, \text{L}\). Thus, \(\text{Concentration} = \frac{0.00575\, \text{mol}}{0.0500\, \text{L}} = 0.115\, \text{M}\).

Key concepts

Acetic Acid

Acetic acid, also known by its chemical formula \( \mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} \), is a weak organic acid that gives vinegar its characteristic taste and smell. It is a vital compound in various chemical reactions because of its acidic properties. Acetic acid is commonly found in household products, often in vinegar which is used in cooking and cleaning.
The acid is colorless and biodegradable, meaning it breaks down naturally and poses minimal environmental risk. Its structure consists of a carboxyl group \((\mathrm{-COOH})\), which is responsible for its acidity. Understanding its properties helps chemists use acetic acid in different applications, from food preservation to laboratory research.

Vinegar

Vinegar is a solution primarily comprised of acetic acid and water. It is not just a kitchen staple but also an important substance in chemical titration processes. The concentration of acetic acid in vinegar usually ranges between 4-8%, making it effective for both culinary and cleaning purposes.
When we talk about vinegar in the context of titration, we're looking at how much acetic acid is in the solution. Titrating vinegar helps to precisely measure its acetic acid content. This is important for quality control in the manufacturing of vinegar products, ensuring consistency in taste and effectiveness as a cleaning agent.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, are transformed into different substances, called products. In the context of this exercise, we're observing a reaction between acetic acid and sodium hydroxide (\(\mathrm{NaOH}\)).
This reaction can be represented by the formula: \(\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} + \mathrm{NaOH} \rightarrow \mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} + \mathrm{H}_{2}\mathrm{O} \).

• Reactants: Acetic acid and sodium hydroxide
• Products: Sodium acetate and water

Notice the 1:1 molar ratio, meaning each molecule of acetic acid reacts with one molecule of sodium hydroxide. Understanding these reactions allows us to calculate the concentration of unknown solutions, a fundamental concept in chemistry.

Molar Concentration

Molar concentration, often just called "molarity," is a way of expressing how many moles of a substance are present in a liter of solution. It is denoted by the symbol \(M\). Calculating molarity is essential in chemical titrations, such as determining the concentration of acetic acid in vinegar.
To find molarity, you divide the number of moles of solute by the volume of the solution in liters: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution (L)}} \]
In this exercise, we calculated the molarity of acetic acid by knowing the number of moles from the titration process and the total volume of vinegar used.

• This gives us insight into how concentrated a solution is, a critical aspect when performing precise chemical experiments or creating specific formulations in various industries.