Question

Citric acid, which can be obtained from lemon juice, has the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7} .\) A \(0.250-\mathrm{g}\) sample of citric acid dissolved in \(25.0 \mathrm{~mL}\) of water requires \(37.2 \mathrm{~mL}\) of \(0.105 \mathrm{M} \mathrm{NaOH}\) 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 the moles of NaOH

Use the formula: moles = volume (in L) × concentration Moles of NaOH = \(0.0372 \,\text{L} \times 0.105 \,\mathrm{M}\) Moles of NaOH = \(0.003906 \,\text{mol}\)

Calculate the molar mass of citric acid

Use the molecular formula of citric acid: \(\mathrm{C}_{6}\mathrm{H}_{8}\mathrm{O}_{7}\) Molar mass of citric acid = \(6 \times \mathrm{M(C)} + 8 \times \mathrm{M(H)} + 7 \times \mathrm{M(O)}\) Molar mass of citric acid = \(6(12.01 \,\mathrm{g/mol}) + 8(1.01 \,\mathrm{g/mol}) + 7(16.00 \,\mathrm{g/mol})\) Molar mass of citric acid = \(192.12 \,\mathrm{g/mol}\)

Calculate the moles of citric acid

Use the formula: Moles = mass (in g) / molar mass (in g/mol) Moles of citric acid = \(0.250 \,\text{g} / 192.12 \,\mathrm{g/mol}\) Moles of citric acid = \(0.001302 \,\mathrm{mol}\)

Calculate the number of acidic hydrogens per molecule of citric acid

Divide the moles of NaOH by the moles of citric acid Number of acidic hydrogens per molecule =\(\frac{\text{moles of NaOH}}{\text{moles of citric acid}}\) Number of acidic hydrogens per molecule =\(\frac{0.003906}{0.001302} = 3\) There are 3 acidic hydrogens per molecule of citric acid.

Key concepts

Understanding the Molecular Formula

The molecular formula provides essential information about the composition of a compound. In our example, citric acid, with the molecular formula \(C_6H_8O_7\), contains six carbon atoms (C), eight hydrogen atoms (H), and seven oxygen atoms (O). A molecular formula is key to understanding many properties of a compound, including its reactivity and how it can interact with other substances.

When analyzing the molecular formula, it's crucial to identify the atomic composition, which helps in later calculations such as molar mass and the stoichiometry of chemical reactions. In the context of citric acid, the presence of multiple hydrogen atoms hints at its capability to donate protons (H+), a characteristic feature of acids. This information lays the groundwork for exploring reactions, such as neutralization, where these acidic hydrogen atoms play a central role.

Neutralization Reaction Explained

A neutralization reaction is a chemical process where an acid and a base react to form water and a salt. It is quintessential in understanding acid-base chemistry. In our exercise, citric acid acts as the acid, and sodium hydroxide (NaOH) serves as the base. This reaction is significant because it allows us to deduce important quantitative details about the reacting substances, such as the number of acidic hydrogens in the acid molecule that can participate in the reaction.

The volume and concentration of NaOH solution used to neutralize the citric acid tell us the amount of base required to completely react with the given mass of acid. By correlating the moles of NaOH with those of citric acid through calculations, we can infer the stoichiometry of the reaction and thus identify how many hydrogen ions are neutralized by NaOH, which ultimately unveils the number of acidic hydrogen atoms in a molecule of citric acid.

Molar Mass Calculation Step by Step

The molar mass of a substance is defined as the mass of one mole of its particles, usually expressed in grams per mole (g/mol). It is a pivotal concept in chemistry because it relates the mass of a substance to the amount of substance (moles). The calculation of molar mass involves multiplying the atomic mass of each element found in the molecular formula by the number of atoms of that element and adding these values together.

In citric acid, each carbon atom contributes 12.01 g/mol, each hydrogen 1.01 g/mol, and each oxygen 16.00 g/mol. Therefore, the molar mass of citric acid is calculated as \(6 \times 12.01 \,\text{g/mol} + 8 \times 1.01 \,\text{g/mol} + 7 \times 16.00 \,\text{g/mol} = 192.12 \,\text{g/mol}\). Knowing the molar mass allows us to transition from mass to moles, a necessary step in relating the amounts of reactants in a chemical reaction, such as determining the number of acidic hydrogens in our neutralization example.