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Chapter 6: Problem 139

Citric acid, which can he ohtained from lemon juice, has the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\). A 0.250 -g sample of citric acid dissolved in \(25.0 \mathrm{mL}\) of water requires \(37.2 \mathrm{mL}\) of \(0.105 \mathrm{M}\) NaOH for complete neutralization. What number of acidic hydrogens per molecule does citric acid have?

Short Answer

Expert verified
Citric acid has 3 acidic hydrogens per molecule.

Step by step solution

01

Calculate moles of NaOH used in the neutralization

Given that 37.2 mL of 0.105 M NaOH were used in the neutralization reaction, we can calculate the moles of NaOH used by multiplying the volume by the molarity: Moles of NaOH = volume of NaOH (in L) × molarity of NaOH Moles of NaOH = \(37.2 \times 10^{-3}\, \mathrm{L} \times 0.105\, \mathrm{M}\) Moles of NaOH = \(3.906 \times 10^{-3}\, \mathrm{mol}\)
02

Determine the moles of citric acid in the sample

We are given that the mass of the citric acid sample is 0.250 g. To find the moles of citric acid, we will need the molar mass of citric acid (\(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\)): Molar mass of citric acid = \(6 \times 12.01\, \mathrm{g/mol} + 8 \times 1.01\,\mathrm{g/mol} + 7 \times 16.00\,\mathrm{g/mol}\) Molar mass of citric acid = \(192.12\, \mathrm{g/mol}\) Now we can calculate the moles of citric acid: Moles of citric acid = mass of citric acid / molar mass of citric acid Moles of citric acid = \(0.250\, \mathrm{g} / 192.12\, \mathrm{g/mol}\) Moles of citric acid = \(1.301 \times 10^{-3}\, \mathrm{mol}\)
03

Find the stoichiometric ratio between NaOH and citric acid in the neutralization reaction

In order to find the number of acidic hydrogens per molecule of citric acid, we first need to find the stoichiometric ratio between moles of NaOH and moles of citric acid. We can do this using the moles of NaOH and citric acid calculated in steps 1 and 2: Stoichiometric ratio = moles of NaOH / moles of citric acid Stoichiometric ratio = \(\frac{3.906 \times 10^{-3}\, \mathrm{mol}}{1.301 \times 10^{-3}\, \mathrm{mol}}\) Stoichiometric ratio ≈ 3.0
04

Determine the number of acidic hydrogens per molecule of citric acid

Since the stoichiometric ratio between NaOH and citric acid is approximately 3.0, this means that each molecule of citric acid reacts with 3 molecules of NaOH. The neutralization reaction involves the reaction of an acidic hydrogen (H\(^+\)) from citric acid with the hydroxide ion (OH\(^-\)) from NaOH. Therefore, the number of acidic hydrogens per molecule of citric acid is equal to the stoichiometric ratio, which is 3. Hence, citric acid has 3 acidic hydrogens per molecule.

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Most popular questions from this chapter

A solution is prepared by dissolving \(10.8 \mathrm{g}\) ammonium sulfate in enough water to make \(100.0 \mathrm{mL}\) of stock solution. A \(10.00-\) mL sample of this stock solution is added to \(50.00 \mathrm{mL}\) of water. Calculate the concentration of ammonium ions and sulfate ions in the final solution.

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