Assume that you have 1.00 g of a mixture of benzoic acid (Mol. wt. = 122) and gallic acid (Mol. wt. = 170)), both of which contain one acidic hydrogen that reacts with NaOH. On titrating the mixture with 0.500 M NaOH, 14.7 mL of base is needed to completely react with both acids. What mass in grams of each acid is present in the original mixture?

Verified step by step guidance

1. Identify the chemical reaction: Both benzoic acid and gallic acid react with NaOH in a 1:1 molar ratio, meaning one mole of each acid reacts with one mole of NaOH.
2. Calculate the moles of NaOH used: Use the concentration and volume of NaOH to find the total moles of NaOH that reacted. Use the formula: \( \text{moles of NaOH} = M \times V \), where \( M \) is the molarity and \( V \) is the volume in liters.
3. Set up equations for the moles of each acid: Let \( x \) be the moles of benzoic acid and \( y \) be the moles of gallic acid. From the stoichiometry, \( x + y = \text{moles of NaOH} \).
4. Relate moles to mass: Use the molecular weights to express the mass of each acid in terms of \( x \) and \( y \). For benzoic acid, \( \text{mass} = 122x \), and for gallic acid, \( \text{mass} = 170y \). The total mass of the mixture is 1.00 g, so \( 122x + 170y = 1.00 \).
5. Solve the system of equations: Use the two equations \( x + y = \text{moles of NaOH} \) and \( 122x + 170y = 1.00 \) to solve for \( x \) and \( y \), which will give you the moles of each acid. Convert these moles to grams using their respective molecular weights.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using the balanced chemical equation to determine the relationships between the amounts of substances consumed and produced. In this case, stoichiometry will help relate the volume of NaOH used in the titration to the moles of benzoic and gallic acids present in the mixture.

Molarity and Volume Relationships

Molarity is a measure of concentration defined as moles of solute per liter of solution. In titration problems, the volume of titrant (NaOH) used can be converted to moles using its molarity. This relationship is crucial for determining how many moles of each acid reacted, which can then be used to find their respective masses in the mixture.

Acid-Base Neutralization

Acid-base neutralization is a chemical reaction where an acid reacts with a base to produce water and a salt. In this scenario, both benzoic acid and gallic acid react with NaOH, consuming one mole of NaOH per mole of acid. Understanding this concept is essential for calculating the amount of each acid in the mixture based on the total moles of NaOH used in the titration.