Question

If \(16.33 \mathrm{~mL}\) of \(0.6664 \mathrm{M} \mathrm{KOH}\) was needed to titrate a sample of \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) to its equivalence point, what mass of \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) was present?

Short answer

The mass of HC₂H₃O₂ was approximately 0.653 g.

Step-by-step solution

Determine Moles of KOH

First, use the molarity and volume of the KOH solution to find the number of moles of KOH. The formula for moles is \[moles = Molarity \times Volume = 0.6664 \, \text{mol/L} \times 16.33 \, \text{mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} \approx 0.01088 \, \text{mol}.\]

Understand the Reaction

Recognize that KOH and HC₂H₃O₂ react in a 1:1 molar ratio. The balanced chemical equation is:\[\text{KOH} + \text{HC}_2\text{H}_3\text{O}_2 \rightarrow \text{KC}_2\text{H}_3\text{O}_2 + \text{H}_2\text{O}.\]So, the moles of KOH required are equal to the moles of HC₂H₃O₂.

Calculate Moles of HC₂H₃O₂

Since KOH and HC₂H₃O₂ react in a 1:1 ratio, the moles of HC₂H₃O₂ are equal to the moles of KOH calculated in Step 1: \[\text{Moles of } \mathrm{HC}_2\mathrm{H}_3\mathrm{O}_2 = 0.01088 \, \text{mol}.\]

Calculate Mass of HC₂H₃O₂

To find the mass, multiply the moles of HC₂H₃O₂ by its molar mass. The molar mass of HC₂H₃O₂ is approximately 60.05 g/mol:\[\text{Mass} = 0.01088 \, \text{mol} \times 60.05 \, \text{g/mol} \approx 0.653 \, \text{g}.\]

Key concepts

Moles Calculation

When calculating moles, it's essential to understand what a mole represents. A mole is a unit used to count atoms and molecules, similar to how a dozen counts objects. This concept is fundamental in chemistry, allowing scientists to quantify amounts of substances in a systematic way.
To calculate moles, you typically use the formula:

• Moles = Molarity × Volume

Molarity is given in moles per liter (mol/L), and the volume should be in liters for the formula to be correct.
In the exercise, you used the molarity of KOH, which is 0.6664 M, and the volume of 16.33 mL. Note that because volume must be in liters, you convert the volume from mL to L by dividing by 1000, leading to:

• 0.6664 mol/L × 0.01633 L ≈ 0.01088 mol

This calculation gives you the moles of KOH present in the solution.

Chemical Reaction

Chemical reactions describe the process in which substances interact, leading to a transformation into different products. In this exercise, the reaction involved is between potassium hydroxide (KOH) and acetic acid (HC₂H₃O₂).
The balanced chemical equation for this reaction is:

• KOH + HC₂H₃O₂ → KC₂H₃O₂ + H₂O

It shows that each molecule of KOH reacts with one molecule of HC₂H₃O₂, highlighting a 1:1 stoichiometric relationship. This means the moles of KOH required at the equivalence point are equal to the moles of HC₂H₃O₂.
By understanding this balanced equation, you can correctly determine how the substances will react and how much of each will be needed or produced.

Acetic Acid

Acetic acid, known chemically as HC₂H₃O₂, is a weak acid commonly found in vinegar. It's an important compound in chemistry due to its reactivity and various applications.
One key property of acetic acid is its ability to react with bases, such as KOH, in titration reactions. This reaction mirrors general concepts about acid-base neutralization, where an acid and a base react to form water and a salt.
In the case of acetic acid, the reaction with KOH produces potassium acetate (KC₂H₃O₂) and water (H₂O). Because the reaction occurs on a 1:1 molar basis, determining the moles of acetic acid present involves recognizing that they are equal to the moles of KOH reacted.
To find the mass of the acetic acid in the sample, you multiply the moles of HC₂H₃O₂ by its molar mass, which is approximately 60.05 g/mol. This helps calculate the mass of acetic acid that was originally present in the sample used for the reaction.