Question

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

Citric acid has 3 acidic hydrogens per molecule.

Step-by-step solution

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 = \(3.906 \times 10^{-3}\, \mathrm{mol}\)

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 = \(1.301 \times 10^{-3}\, \mathrm{mol}\)

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

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.

Key concepts

Molecular Formula

The molecular formula of a compound tells us the number and type of each atom present in one molecule of the compound. For citric acid, the molecular formula is \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7} \). This indicates that each molecule of citric acid contains six carbon atoms, eight hydrogen atoms, and seven oxygen atoms.
Understanding the molecular formula is crucial as it gives insights into the chemical structure and properties of the compound. For instance, the presence of multiple oxygen and hydrogen atoms suggests potential sites for chemical reactions, such as the acidic properties of citric acid.
Additionally, knowing the molecular formula allows us to calculate the molar mass of the compound, which is an essential step when converting grams to moles in chemical calculations.

Neutralization Reaction

A neutralization reaction occurs when an acid and a base react to form water and a salt. In the case of citric acid and sodium hydroxide (NaOH), this reaction is crucial for determining the number of acidic hydrogens in citric acid.
In this process, the acidic hydrogens (H\(^+\)) from citric acid react with the hydroxide ions (OH\(^-\)) from NaOH. This reaction essentially neutralizes the acid, forming water and resulting in a salt.
Neutralization reactions are important in various applications, from everyday products to industrial processes. Understanding these reactions is key to analyzing acid-base interactions and calculating the amount of reactants needed for complete neutralization.

Stoichiometric Ratio

The stoichiometric ratio reveals the relationship between the quantities of reactants involved in a chemical reaction. In the neutralization reaction between citric acid and NaOH, this ratio shows how many moles of NaOH react with one mole of citric acid.
From our previous calculations: the stoichiometric ratio is approximately 3.0. This tells us that three moles of NaOH are needed to completely react with one mole of citric acid.
Understanding the stoichiometric ratio is vital for solving chemical problems and ensuring that we have balanced chemical reactions. It helps in determining how much of each reactant must be used to avoid waste and achieve complete reaction.

Acidic Hydrogens

Acidic hydrogens are the hydrogen atoms in an acid that can be released as protons (H\(^+\)) during a reaction. In citric acid, these are the hydrogens participating in the neutralization reaction with NaOH.
From the analysis of the stoichiometric ratio, citric acid has 3 acidic hydrogens per molecule. This is evident from the fact that each molecule reacts with three molecules of NaOH.
The concept of acidic hydrogens is foundational in understanding how acids behave in reactions and how they donate protons. Recognizing the number of acidic hydrogens helps predict the strength of an acid and its reactivity in different chemical processes.