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 -g sample of citric acid dissolved in 25.0 mL of water requires 37.2 mL of 0.105 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 the moles of NaOH used

To find the number of acidic hydrogens in citric acid, we first need to determine the moles of NaOH used in the neutralization reaction. The given information is the volume of NaOH, 37.2 mL, and its concentration, 0.105 M. We can use the formula \(moles = (volume \cdot concentration)\) to determine the moles of NaOH: \(moles_{NaOH} = volume_{NaOH} \cdot concentration_{NaOH}\)

Convert mL to L

Before calculating the moles of NaOH, we need to convert the volume from mL to L: \(volume_{NaOH} (L) = 37.2 \, \text{mL} \cdot \frac{1\, \text{L}}{1000\, \text{mL}} = 0.0372\, \text{L}\)

Calculate moles of NaOH

Now we can calculate the moles of NaOH used in the reaction: \(moles_{NaOH} = 0.0372\, \text{L} \cdot 0.105\, \text{M} = 0.003906\, \text{moles}\)

Find moles of citric acid

Since each molecule of citric acid will react with an integer number of NaOH molecules, we can start by assuming a 1:1 mole ratio between citric acid and the acidic hydrogens, and see if it is true. If not, we will continue with higher ratios. First, determine the moles of citric acid in the provided sample. Given sample mass is 0.250 g. Use the molar mass of citric acid, which can be calculated from the molecular formula: \(Molar \, mass_{citric \, acid} = 6 \cdot 12.01 + 8 \cdot 1.01 + 7 \cdot 16 = 192.12\, \text{g/mol}\) Determine the moles of citric acid by dividing the mass by the molar mass: \(moles_{citric \, acid} = \frac{0.250\, \text{g}}{192.12\, \text{g/mol}} = 0.001301\, \text{moles}\)

Determine the ratio between moles of NaOH and citric acid

Now we will compare the moles of NaOH with the moles of citric acid to determine the ratio between them: \(ratio = \frac{moles_{NaOH}}{moles_{citric \, acid}} = \frac{0.003906}{0.001301} \approx 3\)

Determine the number of acidic hydrogens per citric acid molecule

The ratio of approximately 3 indicates that each citric acid molecule has 3 acidic hydrogen atoms. Therefore, citric acid has 3 acidic hydrogens per molecule.

Key concepts

Neutralization Reaction

In acid-base chemistry, a neutralization reaction is a process where an acid and a base react to form water and a salt. During this type of reaction, the acidic and basic properties are neutralized, which often results in the formation of products that are neither acidic nor basic.

For example, when citric acid (\(\mathrm{C}_{6}\mathrm{H}_{8}\mathrm{O}_{7}\)) reacts with sodium hydroxide (NaOH), a commonly used strong base, the reaction results in the production of water and a sodium citrate solution.

• The sodium ions (\(\text{Na}^+\)) from NaOH replace the acidic hydrogen ions in citric acid, forming a salt.
• In our example, the overall chemical equation for the neutralization can be simplified to: \(\text{Citric Acid} + 3\text{NaOH} \rightarrow \text{Sodium Citrate} + 3\text{H}_2\text{O}\)
• The balanced equation shows the stoichiometric relationship between citric acid and NaOH as 1:3, meaning each molecule of citric acid reacts with three molecules of NaOH.

Understanding this treatment in stoichiometry helps in determining reaction quantities as well as in the practical application of titration methods and in deriving important properties such as the number of acidic hydrogens in an acid molecule.

Moles Calculation

Moles calculation is a fundamental aspect of chemistry and understanding chemical reactions. It helps in quantifying the substances involved in chemical reactions. Here's how you perform moles calculation, particularly useful in our neutralization context.

The mole concept allows us to calculate the number of particles, atoms, or molecules in a given amount of substance.

• The formula used is \(\text{moles} = \text{volume (L)} \times \text{concentration (M)}\), which allows us to find moles when you know the solution's concentration and quantity.
• In our neutralization example, we have 37.2 mL (or 0.0372 L after conversion) of NaOH with a concentration of 0.105 M. By applying the moles formula, we calculate the moles of NaOH used: \(moles_{\text{NaOH}} = 0.0372 \times 0.105 = 0.003906\).

Furthermore, understanding these calculations helps us comprehend how substances interact in reactions and what ratios of reactants are necessary for complete neutralization.

Citric Acid

Citric acid is a weak organic acid with the molecular formula\(\mathrm{C}_{6}\mathrm{H}_{8}\mathrm{O}_{7}\). It is commonly found in citrus fruits such as lemons and limes, which are its natural sources.

This acid is an important constituent in various biological and industrial processes due to its properties:

• Citric acid has three dissociable acidic protons (H+ ions), making it a triprotic acid. This is reflected in its chemical interaction with bases, such as sodium hydroxide in the neutralization process.
• Because each citric acid molecule needs three sodium hydroxide molecules for full neutralization, we derive that citric acid contains three acidic hydrogen atoms per molecule, as shown through our prior example and calculations.
• In everyday use, citric acid is added to food and drinks as a sour flavoring and preservative. It is also used in cleaning products due to its ability to chelate metals and enhance cleaning efficiency.

Understanding the chemical nature and applications of citric acid further fosters fundamental insight into concepts of acid-base chemistry and their applications in real-world scenarios.