Problem 174 - Introductory Chemistry Atoms First

Question

Citric acid can produce \(3 \mathrm{H}^{+}(a q)\) ions per molecule. A solution of citric acid is prepared by dissolving \(0.177 \mathrm{~g}\) of solid citric acid in enough water to yield \(100.0 \mathrm{~mL}\) of solution. When this solution is titrated with \(0.1001 \mathrm{M} \mathrm{NaOH}(a q)\), the indicator turns color after \(27.55 \mathrm{~mL}\) of \(\mathrm{NaOH}(a q)\) has been added. (a) What is the molar concentration of citric acid? (b) What is the molar mass of citric acid?

Step-by-Step Solution

Answer

(a) The molar concentration of citric acid is \( \text{Molarity of citric acid} = \frac{\text{Moles of citric acid}}{0.1000 \mathrm{~L}} \). (b) The molar mass of citric acid is \( \text{Molar mass of citric acid} = \frac{0.177 \mathrm{~g}}{\text{Moles of citric acid}} \).

Step 1: Write the balanced chemical equation for the reaction between citric acid and NaOH

The balanced chemical equation for the reaction between citric acid (CA) and sodium hydroxide (NaOH) can be written as: $$ \mathrm{CA} + 3\mathrm{NaOH} \rightarrow \mathrm{3Na}^{+}(a q) + \mathrm{3H}_{2}\mathrm{O} + \mathrm{CA}^{3-}(a q) $$ Since 1 molecule of citric acid reacts with 3 moles of NaOH.

Step 2: Calculate the moles of NaOH used in the titration

We are given that 27.55 mL of 0.1001 M NaOH is required to titrate the solution. We can calculate the moles of NaOH used in the titration using the relation: Moles of NaOH = Molarity of NaOH × Volume of NaOH (in L) $$ \text{Moles of NaOH}=0.1001 \mathrm{M} \times \frac{27.55 \mathrm{~mL}}{1000 \mathrm{~mL / L}} $$

Step 3: Calculate the moles of citric acid in the solution

From the stoichiometry of the balanced chemical equation (Step 1), we can determine the moles of citric acid present in the solution. Since 1 mole of citric acid reacts with 3 moles of NaOH: $$ \text{Moles of citric acid} = \frac{1}{3} \times \text{Moles of NaOH} $$

Step 4: Calculate the molar concentration of citric acid

The molar concentration of citric acid can be calculated using the relation: Molarity of citric acid = Moles of citric acid / Volume of the citric acid solution (in L) $$ \text{Molarity of citric acid} = \frac{\text{Moles of citric acid}}{100.0 \mathrm{~mL} \times \frac{1 \mathrm{~L}}{1000\mathrm{~mL}}} $$

Step 5: Calculate the molar mass of citric acid

We can now use the mass of citric acid (0.177 g), and the moles of citric acid calculated in Step 3 to find the molar mass of citric acid: Molar mass of citric acid = Mass of citric acid / Moles of citric acid $$ \text{Molar mass of citric acid} = \frac{0.177 \mathrm{~g}}{\text{Moles of citric acid}} $$

Step 6: Answer the questions

(a) The molar concentration of citric acid is calculated in Step 4. (b) The molar mass of citric acid is calculated in Step 5.

Key Concepts

Molar Concentration

Molar concentration, often called molarity, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute present in one liter of solution. The unit for molar concentration is moles per liter (M).

In our citric acid titration problem, we determine the molar concentration to understand how much citric acid is in a given volume of water. This step is fundamental because it helps us calculate the quantity necessary to react with a known volume and concentration of sodium hydroxide (NaOH) during the titration process.

To calculate the molar concentration of citric acid, we first need to know the moles of citric acid present in the solution. This value can be derived from the titration data, using the stoichiometric relationship between citric acid and NaOH. Once we have the moles, we divide by the volume of the solution in liters to find the molarity. The formula is given by:
\[\begin{equation}Molarity = \frac{{\text{{Moles of solute}}}}{{\text{{Volume of solution in liters}}}}\end{equation}\]

Molar Mass Calculation

Calculating the molar mass of a substance is a key step in understanding chemical reactions and solutions. The molar mass represents the mass of one mole of a substance and is expressed in grams per mole (g/mol).

To find the molar mass of citric acid, we take the mass of citric acid used in the experiment and divide it by the moles of citric acid calculated from the titration data. This calculation provides the mass of one mole of citric acid, which is an essential value for many quantitative chemistry exercises, such as stoichiometric calculations and preparing solutions with specific molar concentrations.

The general formula for molar mass (M) is:
\[\begin{equation}M =\frac{{\text{{mass of the substance}}}}{{\text{{moles of the substance}}}}\end{equation}\]Where the mass of the substance is provided in the experimental data and the moles of the substance are calculated from the stoichiometry of the reaction involved.

Chemical Stoichiometry

Chemical stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves using a balanced chemical equation to calculate the amounts of reactants needed to produce a certain amount of product or vice versa.

In the context of the citric acid titration exercise, stoichiometry allows us to determine the moles of citric acid based on the moles of NaOH used in the titration. The balanced chemical equation provides the mole ratio between citric acid and NaOH. Since each molecule of citric acid reacts with three moles of NaOH, we can calculate the moles of citric acid by dividing the moles of NaOH by three.

Applying stoichiometry in titration problems is crucial for interpreting the results and understanding the underlying reactions occurring during the titration process.

Acid-Base Titration

Acid-base titration is a laboratory technique used to determine the concentration of an unknown acid or base by reacting it with a base or acid of known concentration. An indicator is typically used to signal the end of the reaction, known as the equivalence point, by a color change.

During the titration process, a base (NaOH in our case) is slowly added to an acid solution (citric acid). The equivalence point is reached when the number of moles of hydrogen ions in the acid equals the number of hydroxide ions from the base added. In our problem, titration data, such as the volume of NaOH solution used, helps us to calculate the concentration of the citric acid solution. This serves as an impressive application of the principles of stoichiometry, acid-base reactions, and molarity in a practical setting.

Acid-base titrations are essential for various applications in chemistry, including analyzing the purity of substances and determining the presence of specific compounds.