Question

When \(0.2081 \mathrm{~g}\) of an organic acid was dissolved in \(50.00 \mathrm{~mL}\) of \(0.1016 \mathrm{M} \mathrm{NaOH}\), it took \(23.78 \mathrm{~mL}\) of \(0.1182 \mathrm{M} \mathrm{HCl}\) to neutralize the \(\mathrm{NaOH}\) that was not used up by the sample of the organic acid. Calculate the formula mass from the data given. Is the answer necessarily the molecular mass of the organic acid? Explain.

Short answer

The formula mass calculated is not necessarily the molecular mass of the organic acid; if the acid releases more than one proton when reacting with NaOH, the molecular mass would be an integer multiple of the formula mass.

Step-by-step solution

Calculate the moles of NaOH used

Determine the initial moles of NaOH in solution using the concentration and volume. The formula for moles is \(\text{moles} = \text{concentration} \times \text{volume}\). Use the volume in liters.

Calculate the moles of HCl used

Using the volume and concentration of HCl, calculate the moles of HCl used to neutralize the remaining NaOH. Convert the volume from milliliters to liters and use the formula \(\text{moles} = \text{concentration} \times \text{volume}\).

Calculate the moles of NaOH that reacted with the organic acid

Subtract the moles of HCl (which is equivalent to the moles of unreacted NaOH) from the initial moles of NaOH to find the moles of NaOH that reacted with the organic acid.

Calculate the formula mass of the organic acid

Divide the mass of the organic acid by the moles of NaOH that reacted with it to find the formula mass of the organic acid (as one mole of the acid reacts with one mole of NaOH). Formula mass is given by \(\text{Formula Mass} = \frac{\text{Mass of the organic acid}}{\text{Moles of NaOH reacted}}\).

Reflect on the nature of the formula mass

Consider whether the formula mass obtained is necessarily the molecular mass. The formula mass represents the mass of the acid that reacted with one mole of NaOH. If the organic acid ionizes only once in the reaction, then the formula mass is the molecular mass. However, if the acid has multiple ionizable protons and ionizes more than once, the molecular mass would be higher.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships, or ratios, of reactants and products in chemical reactions. It is foundational for carrying out titration calculations, as it allows us to understand the amounts of substances involved in reactions.

To successfully engage in stoichiometry, one must understand the mole concept, which is a standard unit of measurement in chemistry used to express amounts of a substance. It’s connected to Avogadro's number, which is approximately \(6.022 \times 10^{23}\), representing the number of atoms, ions, or molecules in one mole of substance.

Stoichiometric Coefficients

These coefficients reflect how many moles of each substance are needed or produced in a reaction. They are derived from the balanced chemical equation for the reaction and are vital to titration calculations, ensuring the mole ratio of reactants to products is maintained.

Moles to Mass

Stoichiometry also involves converting moles to mass or volume, depending on the substance's state and conditions. Here, we use molar mass (the mass of one mole of a substance) to convert between moles and grams.

Improvement Advice: In our example, it’s critical to conceptualize that each unit—grams, moles, liters—is a way to count particles, be that atoms, molecules, or ions, so understanding stoichiometry is understanding the counting of particles within a chemical process.

Neutralization Reaction

A neutralization reaction occurs when an acid and a base react to form water and a salt. This reaction is particularly important in titration calculations, where we determine the concentration of an unknown solution using a solution of known concentration based on the premise of neutralization.

In most neutralization reactions involving strong acids and strong bases, the net ionic equation simplifies to \( \text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O} \), indicating that acid-base reactions essentially involve the transfer of a proton from an acid to a base.

Equivalence Point

The point in a titration at which the amount of acid equals the amount of base is known as the equivalence point. This is the goal of a titration, and precise calculations are necessary to determine when this point has been reached.

Improvement Advice: Each titration curve should be examined not just as a graph but as a story of how the acidic and basic molecules interact, gradually changing the pH. Visualizing this makes the concept of neutralization more tangible.

Molecular Mass Determination

The determination of molecular mass is a fundamental step in chemical analysis and in our example, it's found through titration. The process is based on the concept that the molecular mass is the mass of a given molecule - it is the sum of the atomic masses of all atoms present in the molecule.

Empirical vs Molecular Formulas

'Empirical formula' gives the simplest whole number ratio of atoms in a compound whereas 'molecular formula' provides the actual number of each type of atom in a molecule. In some cases, such as in our organic acid example, the molecular mass can be deduced directly from the stoichiometry of the neutralization reaction.

Molecular mass determination is not always straightforward, because the mass obtained from these studies may represent a multiple of the empirical formula unit, rather than the actual molecular formula. For instance, dicarboxylic acids may appear to have half the mass if each molecule reacts with two moles of a base, rather than one.

Improvement Advice: It’s essential to consider the nature of the substance in question when deducing molecular mass. For substances that can ionize more than once, special consideration must be taken to understand the stoichiometry of the reactants, such as in the case of polyprotic acids.