Question

Citric acid, which can be obtained from lemon juice, has the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{O}_{7} .\) 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, as determined through stoichiometry and mole calculations using the given mass, volume, and concentration values.

Step-by-step solution

Calculate the moles of NaOH used in the reaction

We know that the concentration of NaOH, c(NaOH), is 0.105 M, and the volume used to neutralize the citric acid is 37.2 mL. To determine the moles of NaOH used, we can use the following formula: n(NaOH) = c(NaOH) × V(NaOH) where n(NaOH) is the moles of NaOH, c(NaOH) is the concentration of NaOH, and V(NaOH) is the volume of NaOH in L. Remember to convert the given volume of NaOH from mL to L. n(NaOH) = 0.105 mol/L × (37.2 mL × 0.001 L/mL) n(NaOH) = 0.105 mol/L × 0.0372 L n(NaOH) = 0.003906 mol

Determine the moles of citric acid, H₃A

We know that the mass of the citric acid sample is 0.250 g. To find the moles of citric acid, we can use the molar mass of citric acid which is 192.124 g/mol (from the molecular formula C₆H₈O₇). Use the formula: n(H₃A) = mass(H₃A) / M(H₃A) where n(H₃A) is the moles of citric acid, mass(H₃A) is the mass of the citric acid sample, and M(H₃A) is the molar mass of citric acid. n(H₃A) = 0.250 g / 192.124 g/mol n(H₃A) = 0.00130 mol

Calculate the stoichiometric coefficient of hydrogens in the balanced equation

In the balanced equation, we have: H₃A + x NaOH -> NaₓA + 3x H₂O Let's find the stoichiometric coefficient (x) by dividing the number of moles of NaOH (0.003906 mol) by the number of moles of citric acid (0.00130 mol). x = n(NaOH) / n(H₃A) x = 0.003906 mol / 0.00130 mol x = 3 So, the balanced equation becomes: H₃A + 3 NaOH -> Na₃A + 3 H₂O

Determine the number of acidic hydrogens per molecule

The stoichiometric coefficient x we have calculated tells us that there are 3 moles of acidic hydrogens in each mole of citric acid. In other words, there are 3 acidic hydrogens per molecule of citric acid. Therefore, citric acid has 3 acidic hydrogens per molecule.

Key concepts

Molecular Formula of Citric Acid

Citric acid is a natural compound that can be extracted from citrus fruits like lemons. Its molecular formula is \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7} \), indicating it contains 6 carbon atoms, 8 hydrogen atoms, and 7 oxygen atoms in each molecule. The molecular formula gives us a direct insight into the composition of the substance, detailing the exact number and type of each atom bonded together in a single molecule. This is important for chemical reactions as it tells us what molecules will look like and how they can interact with others.

Understanding the molecular formula is crucial for determining properties like the molar mass, which is essential for converting between mass and moles, a common step in quantitative chemistry.

Neutralization Process

In the neutralization process, an acid reacts with a base to produce salt and water, effectively cancelling out each other's chemical properties. During the experiment with citric acid and sodium hydroxide \( (\mathrm{NaOH}) \), each acidic hydrogen in the citric acid molecule reacts with one sodium hydroxide molecule.

For citric acid, which is a triprotic acid because it has three acidic hydrogen atoms, the balanced chemical equation would be:
\( \mathrm{H}_{3}\mathrm{A} + 3\mathrm{NaOH} \rightarrow \mathrm{Na}_3\mathrm{A} + 3\mathrm{H}_2\mathrm{O} \)
Here, H₃A represents citric acid and \( \mathrm{Na}_3\mathrm{A} \) is our resulting salt. This process shows how acids and bases interact at a molecular level and lays the foundation for understanding titrations in chemistry.

Moles Calculation

Calculating moles is essential in chemistry as it helps us understand the quantity of substances involved in reactions. The moles of a substance can be calculated using the formula:

• \( n = \text{mass} / \text{molar mass} \)

This formula lets us convert mass to moles using the known molar mass from the molecular formula. For instance, with citric acid \((\mathrm{C}_6\mathrm{H}_8\mathrm{O}_7)\) having a molar mass of 192.124 g/mol, and given a sample mass of 0.250 g, the moles are calculated as follows: \( n(\mathrm{H}_3\mathrm{A}) = 0.250 \text{ g} / 192.124 \text{ g/mol} \), which equals approximately 0.00130 mol.

In reactions, understanding the moles of both reactants and products is crucial to determine how much of each substance will be needed or produced.

Stoichiometry in Reactions

Stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It allows chemists to predict the outcomes of reactions based on the proportions of each element or compound involved.

In our citric acid problem, we used stoichiometry to find how many moles of \( \mathrm{NaOH} \) were needed to neutralize a specific amount of citric acid. The calculation involves dividing the moles of \( \mathrm{NaOH} \) by the moles of citric acid: \( x = \frac{0.003906 \text{ mol}}{0.00130 \text{ mol}} = 3 \). This shows that three moles of \( \mathrm{NaOH} \) are required per mole of citric acid, confirming the presence of three acidic hydrogens in each citric acid molecule.

Stoichiometry connects theoretical chemistry with practical chemical reactions, making it a cornerstone of practicing and understanding chemistry fully.