Question

One method for determining the purity of aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) is to hydrolyze it with NaOH solution and then to titrate the remaining NaOH. The reaction of aspirin with NaOH is as follows: $$\begin{aligned} &\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}(s)+2 \mathrm{OH}^{-}(a q)\\\&\text { Aspirin } \quad \frac{\text { Boil }}{10 \min } \underset{\text { Salicylate ion }}{\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{O}_{3}^{-}(a q)}+\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \end{aligned}$$ A sample of aspirin with a mass of 1.427 g was boiled in \(50.00 \mathrm{mL}\) of \(0.500 \mathrm{M} \mathrm{NaOH} .\) After the solution was cooled, it took \(31.92 \mathrm{mL}\) of \(0.289 \mathrm{M}\) HCl to titrate the excess NaOH. Calculate the purity of the aspirin. What indicator should be used for this titration? Why?

Short answer

The purity of the aspirin sample is calculated as follows: \(n_\text{HCl} = 0.03192 \times 0.289 = 0.00921728 \ \text{mol}\), \(n_\text{NaOH(total)} = 0.050 \times 0.500 = 0.025 \ \text{mol}\), \(n_\text{NaOH(excess)} = 0.00921728 \ \text{mol}\), \(n_\text{NaOH(reacted)} = 0.025 - 0.00921728 = 0.01578272 \ \text{mol}\), \(n_\text{aspirin} =0.00789136 \ \text{mol}\),\(\text{Mass}_\text{pure aspirin} = 0.00789136 \times 180.16 = 1.42160 \ \text{g}\), and \(\text{Purity} = \frac{1.42160}{1.427} \times 100\% \approx 99.62\%\). Phenolphthalein should be used as an indicator for this titration.

Step-by-step solution

Determine the moles of HCl used in the titration

First, we need to find the moles of HCl used in the titration. We can do this by using the volume of HCl and its molarity: \(n_\text{HCl} = V_\text{HCl} \times M_\text{HCl}\) Where: \(n_\text{HCl}\) = moles of HCl \(V_\text{HCl}\) = volume of HCl in liters (0.03192 L) \(M_\text{HCl}\) = molarity of HCl (0.289 mol/L)

Determine the excess moles of NaOH

Since the volume and molarity of NaOH are given, we can calculate the total moles of NaOH used in the reaction: \(n_\text{NaOH(total)} = V_\text{NaOH} \times M_\text{NaOH}\) Where: \(n_\text{NaOH(total)}\) = total moles of NaOH used in the reaction \(V_\text{NaOH}\) = volume of NaOH in liters (0.050 L) \(M_\text{NaOH}\) = molarity of NaOH (0.500 mol/L) The moles of excess NaOH can be found by equating the moles of NaOH with the moles of HCl, since they react in a 1:1 ratio: \(n_\text{NaOH(excess)} = n_\text{HCl}\)

Calculate the moles of NaOH reacted with aspirin

Now we can find the moles of NaOH that reacted with aspirin by subtracting the excess moles of NaOH from the total moles of NaOH: \(n_\text{NaOH(reacted)} = n_\text{NaOH(total)} - n_\text{NaOH(excess)}\)

Calculate the moles of aspirin

From the balanced chemical equation, 1 molecule of aspirin reacts with 2 moles of NaOH. So, we can now find the moles of aspirin reacted: \(n_\text{aspirin} = \frac{1}{2}n_\text{NaOH(reacted)}\)

Calculating the purity of aspirin

Once we have the number of moles of aspirin in the sample, we can calculate the mass of pure aspirin. The molar mass of aspirin (C9H8O4) is 180.16 g/mol. So, the mass of pure aspirin in the sample can be calculated as: \(\text{Mass}_\text{pure aspirin} = n_\text{aspirin} \times \text{Molar mass of aspirin}\) Then, we can find the purity of the aspirin sample by dividing the mass of pure aspirin by the total mass of the sample and multiplying by 100 to obtain a percentage: \(\text{Purity} = \frac{\text{Mass}_\text{pure aspirin}}{\text{Mass}_\text{sample}} \times 100\%\)

Choose an appropriate indicator for the titration

Phenolphthalein is a common indicator for titrations involving strong acids (like HCl) and strong bases (like NaOH). It changes color from colorless to pink as the solution turns from acidic to slightly basic. Therefore, phenolphthalein would be a suitable indicator for this titration.

Key concepts

Titration

Titration is an analytical technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration, referred to as the titrant. This process involves adding the titrant to the unknown solution gradually until the reaction between the two is complete, which is indicated by a color change (end point). In the given exercise, titration is performed to find the excess amount of NaOH by reacting it with a known concentration of HCl.
For the accuracy of results, the titration must be performed carefully, with the use of proper equipment such as a calibrated burette, and under conditions that allow precise measurement of the volume of the titrant used. This is critical for our calculation of the purity of aspirin since it depends on the amount of unreacted NaOH that can be quantified by titration with HCl.

Acid-Base Neutralization

Acid-base neutralization is a type of chemical reaction in which an acid reacts with a base to produce water and a salt. This reaction is pivotal in chemistry, especially in the process of titration to determine the purity or concentration of substances. In the context of our aspirin purity analysis, the NaOH (base) initially reacts with aspirin, and the excess NaOH is neutralized by HCl (acid).
Understanding the neutralization reaction is key for students as it helps in identifying the equivalent point during a titration. For example, with the aspirin exercise, the neutralization of excess NaOH with HCl allows us to deduce the amount of NaOH that actually reacted with aspirin, hence guiding us to estimate the purity of aspirin.

Stoichiometry

Stoichiometry is the part of chemistry that focuses on the quantitative relationships between the substances involved in a chemical reaction. It allows us to predict the amounts of products and reactants in a chemical reaction using the balanced chemical equation. In our aspirin analysis, stoichiometry helps us relate the moles of NaOH used in the reaction to the moles of aspirin, thanks to the molar ratios provided by the balanced chemical equation.
To calculate the purity of aspirin, we utilize stoichiometry to figure out the relationship between the moles of NaOH and aspirin, considering that one mole of aspirin reacts with two moles of NaOH. This relationship is the backbone of the entire calculation process and reinforces the importance of a balanced chemical equation in quantitative analysis.

Molar Mass

The molar mass is a fundamental concept in chemistry and represents the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol). Understanding the molar mass is essential for converting between the mass of a substance and the number of moles. In the process of determining the purity of aspirin, we used the molar mass of aspirin (\(180.16 \text{ g/mol}\)) to convert the moles of reacted aspirin into grams.
Knowing the molar mass allows students to transition from the microscopic scale of atoms and molecules to the macroscopic scale that can be measured practically. This conversion is essential to complete our calculation and find the purity percentage of the aspirin sample by relating the pure aspirin's mass to the total mass of the sample.

Chemical Indicators

A chemical indicator is a substance that undergoes a distinct observable change, typically a color change, under specific conditions. In titrations, indicators are used to signal the end point, which occurs when the amount of titrant added is stoichiometrically equivalent to the concentration of the unknown solution. For the aspirin purity analysis, phenolphthalein is suggested as an appropriate indicator.
Phenolphthalein indicates the endpoint by changing color from colorless to pink as the solution changes from acidic to neutral or slightly basic. This choice is crucial since an incorrect indicator can lead to an inaccurate determination of the endpoint, affecting the accuracy of the titration and the purity calculation. Students should understand the importance of selecting the right indicator based on the strength of the acids and bases involved in their titration.