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Chapter 4: Problem 80

A \(10.00-\mathrm{mL}\) . sample of vinegar, an aqueous solution of acetic acid \(\left(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right),\) is titrated with \(0.5062 \mathrm{M} \mathrm{NaOH},\) and 16.58 mL is required to reach the equivalence point. a. What is the molarity of the acetic acid? b. If the density of the vinegar is \(1.006 \mathrm{g} / \mathrm{cm}^{3},\) what is the mass percent of acetic acid in the vinegar?

Short Answer

Expert verified
a) The molarity of acetic acid in the vinegar is \(0.839 \: \text{mol/L}\). b) The mass percent of acetic acid in the vinegar is \(5.01\%\).

Step by step solution

01

Write the balanced chemical equation for the titration

The reaction between acetic acid and sodium hydroxide in the titration is as follows: HC₂H₃O₂(aq) + NaOH(aq) → NaC₂H₃O₂(aq) + H₂O(l) This equation is already balanced.
02

Calculate the moles of sodium hydroxide

Use the given volume and molarity of sodium hydroxide solution to find the moles of sodium hydroxide used in the titration: moles of NaOH = (volume of NaOH)(molarity of NaOH) moles of NaOH = (16.58 mL)(0.5062 mol/L) Make sure to convert the volume from mL to L: moles of NaOH = (0.01658 L)(0.5062 mol/L) = 0.00839 mol
03

Calculate moles of acetic acid

As per the balanced chemical equation in Step 1, the mole ratio between acetic acid and sodium hydroxide is 1:1. Therefore, the moles of acetic acid present in the 10.00-mL vinegar solution are equal to the moles of sodium hydroxide: moles of HC₂H₃O₂ = 0.00839 mol
04

Calculate the molarity of acetic acid

Now that we have the moles of acetic acid, we can find the molarity (moles of solute per liter of solution): molarity of HC₂H₃O₂ = (moles of HC₂H₃O₂) / (volume of vinegar in L) molarity of HC₂H₃O₂ = (0.00839 mol) / (0.01000 L) = 0.839 mol/L a) The molarity of acetic acid in the vinegar is 0.839 mol/L.
05

Calculate the mass of acetic acid in the vinegar sample

First, find the moles of acetic acid in the 10.00 mL sample: moles of HC₂H₃O₂ = (0.01000 L)(0.839 mol/L) = 0.00839 mol Next, convert moles of acetic acid to grams using the molar mass of acetic acid, which is 60.05 g/mol: mass of HC₂H₃O₂ = (0.00839 mol)(60.05 g/mol) = 0.5038 g
06

Calculate the mass percent of acetic acid

Use the density of the vinegar and the volume of the sample to find the mass of the vinegar: mass of vinegar = (volume of vinegar)(density of vinegar) mass of vinegar = (10.00 mL)(1.006 g/mL) = 10.06 g Next, calculate the mass percent of acetic acid in the vinegar: mass percent of HC₂H₃O₂ = [(mass of HC₂H₃O₂) / (mass of vinegar)] × 100 mass percent of HC₂H₃O₂ = [(0.5038 g) / (10.06 g)] × 100 = 5.01% b) The mass percent of acetic acid in the vinegar is 5.01%.

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Most popular questions from this chapter

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