Chapter 4: Problem 74

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 \(16.58 \mathrm{~mL}\) 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 the acetic acid solution is \(0.839556 \ \mathrm{M}\). b. The mass percent of acetic acid in the vinegar is \(5.007 \% \).

Step by step solution

The equivalence point is when the moles of the acid equal the moles of the base, so let's first calculate how many moles of NaOH we have: moles of NaOH = volume of NaOH solution * concentration of the NaOH solution moles of NaOH = 0.01658 L * 0.5062 M = 0.00839556 mol Here, 16.58 mL of NaOH solution is converted into L by dividing by 1000. #Step 2: Calculate moles of acetic acid solutions at the equivalence point#

Since we've reached the equivalence point, we know that the moles of acetic acid (HC2H3O2) are equal to the moles of the base NaOH: moles of acetic acid = moles of NaOH moles of acetic acid = 0.00839556 mol #Step 3: Calculate the molarity of the acetic acid solution#

Now we can use the moles of the acetic acid and the initial volume of the solution to calculate the molarity of the acetic acid: molarity of acetic acid = moles of acetic acid / volume of acetic acid solution molarity of acetic acid = 0.00839556 mol / 0.01 L = 0.839556 M a. The molarity of the acetic acid solution is 0.839556 M. #Step 4: Calculate the mass of acetic acid in the vinegar#

Knowing the molarity of acetic acid and the volume of the vinegar, we can find the mass of acetic acid: mass of acetic acid = moles of acetic acid * molar mass of acetic acid mass of acetic acid = 0.00839556 mol * 60 g/mol = 0.5037336 g Here, the molar mass of acetic acid (HC2H3O2) is 60 g/mol, calculated as (1 * 2 + 12 * 2 + 16 * 2 + 1 * 3). #Step 5: Calculate the mass of the vinegar#

Using the density and the volume of the vinegar, we can find the mass of the vinegar: mass of vinegar = density of vinegar * volume of vinegar * 1000 mass of vinegar = 1.006 g/cm³ * 10 cm³ = 10.06 g Here, 10 mL of vinegar is converted into cm³ as 1 mL = 1 cm³ #Step 6: Calculate the mass percent of acetic acid in the vinegar#

Finally, we can use the mass of acetic acid and the mass of vinegar to calculate the mass percent of acetic acid in the vinegar: mass percent of acetic acid = (mass of acetic acid / mass of vinegar) * 100 mass percent of acetic acid = (0.5037336 g / 10.06 g) * 100 = 5.007 % b. The mass percent of acetic acid in the vinegar is 5.007 %.