Problem 128 - Introductory Chemistry Atoms First

Question

Propionic acid has one acidic proton per molecule. A solution is prepared by dissolving \(0.273 \mathrm{~g}\) of propionic acid in enough water to yield \(100.0 \mathrm{~mL}\) of solution. This solution is neutralized by \(36.82 \mathrm{~mL}\) of \(0.1001 \mathrm{M} \mathrm{NaOH}(a q)\). (a) What is the molar concentration of the propionic acid? (b) What is the molar mass of propionic acid?

Step-by-Step Solution

Answer

(a) The molar concentration of propionic acid is \(0.03687 \mathrm{~mol/L}\). (b) The molar mass of propionic acid is \(74.03 \mathrm{~g/mol}\).

Step 1: Find the moles of NaOH used in the reaction

We are given that 36.82 mL of 0.1001 M NaOH solution is used to neutralize the propionic acid. To find the moles of NaOH used in the reaction, we will use the formula: Moles of NaOH = Volume of NaOH (L) × Molarity of NaOH (mol/L) The volume of NaOH must be converted from mL to L first: Volume of NaOH (L) = Volume of NaOH (mL) / 1000 = 36.82 mL / 1000 = 0.03682 L Now, we can find the moles of NaOH: Moles of NaOH = 0.03682 L × 0.1001 mol/L = 0.003687 moles

Step 2: Find the moles of propionic acid

Since propionic acid has one acidic proton per molecule, it reacts with NaOH in a 1:1 ratio. Therefore, the moles of propionic acid will be equal to the moles of NaOH used in the reaction. Moles of propionic acid = Moles of NaOH = 0.003687 moles

Step 3: Calculate the molar concentration of propionic acid

Molar concentration is defined as the moles of solute per liter of solution. We are given that 0.273 g of propionic acid is dissolved in 100 mL of solution. To find the molar concentration, we first need to convert the volume of the solution from mL to L: Volume of solution (L) = Volume of solution (mL) / 1000 = 100 mL / 1000 = 0.1 L Now, we can find the molar concentration of propionic acid: Molar concentration of propionic acid = Moles of propionic acid / Volume of solution (L) = 0.003687 moles / 0.1 L = 0.03687 mol/L So, the molar concentration of propionic acid is 0.03687 mol/L. (a) The molar concentration of propionic acid is 0.03687 mol/L.

Step 4: Calculate the molar mass of propionic acid

To find the molar mass of propionic acid, we can use the formula: Molar mass = Mass of propionic acid (g) / Moles of propionic acid We are given that 0.273 g of propionic acid is dissolved in the solution: Molar mass = 0.273 g / 0.003687 moles = 74.03 g/mol (b) The molar mass of propionic acid is 74.03 g/mol.

Key Concepts

Molar Concentration Calculation

Understanding molar concentration—also referred to as molarity—is essential for analyzing solutions in chemistry. It's defined as the number of moles of solute (here, propionic acid) per liter of solution. To calculate it, you need two pieces of information: the moles of the solute and the total volume of the solution in liters.

To put it into an equation, the general formula is:
\[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]
In the context of titrating propionic acid with NaOH, you start by finding the number of moles of NaOH used, which equals the moles of propionic acid because of the 1:1 stoichiometry in their reaction. After that, you simply divide this value by the volume of the propionic acid solution (in liters) to get its molarity.

Acid-Base Titration

The process of acid-base titration is a quantitative chemical analysis used to determine the concentration of an acid or base in a solution. It involves the controlled addition of a solution of known concentration (the titrant) to a solution of unknown concentration (the analyte) until the reaction between the acid and base is complete—normally indicated by a color change from an indicator used or by reaching a pH that corresponds to the equivalence point.

In the example of propionic acid and NaOH, NaOH is the titrant of known molarity, and the moment it completely neutralizes the acid defines the end point of the titration. This equivalence point allows us to infer the exact amount of acid that reacted based on the volume and concentration of the base used, using the stoichiometry of the reaction.

Molar Mass Determination

To determine the molar mass of a substance, one can use the data obtained from a titration experiment. The molar mass is calculated by taking the mass of the solute (in our case, propionic acid) and dividing it by the moles of the solute.

The formula for determining molar mass is:
\[ \text{Molar Mass} = \frac{\text{Mass of the solute (g)}}{\text{Moles of the solute}} \]
This calculation lets you find out how much one mole of the substance weighs in grams, which is fundamental for converting between mass and moles in chemical reactions. In the given exercise, the titration data gives you the moles of propionic acid, which, when divided into the mass of the propionic acid used, yields its molar mass.

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the quantification of reactants and products in a chemical reaction. It involves understanding and applying the balanced chemical equation to calculate relative amounts of substances consumed and produced in a reaction.

For the propionic acid titration, knowing that propionic acid and NaOH react in a 1:1 molar ratio (from their balanced equation) is critical. This stoichiometric relationship means that for every mole of NaOH used, one mole of propionic acid is neutralized. With the moles of NaOH known, you can directly determine the moles of propionic acid. Stoichiometry forms the backbone of solutions chemistry, allowing scientists and students alike to predict and measure outcomes of chemical reactions.