Question

The active ingredient in aspirin is acetylsalicylic acid. A 2.51 -g sample of acetylsalicylic acid required 27.36 \(\mathrm{mL}\) of 0.5106 \(\mathrm{M} \mathrm{daOH}\) for complete reaction. Addition of 13.68 \(\mathrm{mL}\) of 0.5106\(M \mathrm{HCl}\) to the flask containing the aspirin and the sodium hydroxide produced a mixture with pH \(=3.48 .\) Determine the molar mass of acetylsalicylic acid and its \(K_{2}\) value. State any assumptions you must make to reach your answer.

Short answer

The molar mass of acetylsalicylic acid is 179.8 g/mol, and its \(K_2\) value is \(3.02 × 10^{-11}\).

Step-by-step solution

Calculate moles of \(\mathrm{daOH}\)

Since we have the volume and molar concentration of \(\mathrm{daOH}\) used in the reaction, we can determine the moles of \(\mathrm{daOH}\) used in the reaction. Moles can be calculated using the formula: Moles = Volume (L) × Molarity (M) The volume of NaOH used is given as 27.36 mL, which is equivalent to 0.02736 L (since 1000 mL = 1 L). The molarity of NaOH is given as 0.5106 M. Now, we can calculate the moles of NaOH: Moles of \(\mathrm{daOH}\) = 0.02736 L × 0.5106 M = 0.01396 moles

Calculate moles of acetylsalicylic acid

The moles of acetylsalicylic acid used in the reaction will be equal to the moles of \(\mathrm{daOH}\) used. This is because both react in a 1:1 ratio according to the balanced reaction equation. Therefore the moles of acetylsalicylic acid used are also 0.01396 moles.

Calculate molar mass of acetylsalicylic acid

The molar mass of a substance can be found using the formula: Molar Mass = mass (g) / moles For acetylsalicylic acid, we are given a mass of 2.51 g and we’ve already calculated the moles of the acid (0.01396 moles). So the molar mass of acetylsalicylic acid is: Molar Mass = 2.51 g / 0.01396 moles = 179.8 g/mol

Calculate moles of remaining \(\mathrm{OH}^-\) ions

We are given the volume and molarity of HCl added to the flask (13.68 mL and 0.5106 M, respectively). The HCl reacts with the remaining \(\mathrm{OH}^-\) ions in a 1:1 ratio according to the reaction equation. First, we need to calculate the moles of HCl added: Moles of \(\mathrm{HCl}\) = 0.01368 L × 0.5106 M = 0.006983 moles We can now find the moles of remaining \(\mathrm{OH}^-\) ions by subtracting the moles of HCl from the initial moles of OH-: Moles of remaining \(\mathrm{OH}^-\) ions = Moles of \(\mathrm{daOH}\) - Moles of \(\mathrm{HCl}\) = 0.01396 moles - 0.006983 moles = 0.006977 moles

Calculate the \(K_2\) value

After adding the HCl to the reaction mixture, the pH of the mixture is given as 3.48. We can use the pH value to find the concentration of \(H^+\) ions in the mixture: \([H^+] = 10^{-\mathrm{pH}} = 10^{-3.48} = 3.31 × 10^{-4}\: \mathrm{M}\) We can now calculate the concentration of the remaining \(\mathrm{OH}^-\) ions: \([\mathrm{OH}^-] = \frac{\text{moles of remaining }\mathrm{OH}^-}{\text{total volume of the reaction mixture (in L)}}\) Total volume of the reaction mixture = Volume of NaOH + Volume of HCl = 0.02736 L + 0.01368 L = 0.04104 L So the concentration of remaining \(\mathrm{OH}^-\) ions is: \([\mathrm{OH}^-] = \frac{0.006977\: \mathrm{moles}}{0.04104\: \mathrm{L}} = 0.170\: \mathrm{M}\) Now we can use the \(K_w\) equation to determine the \(K_w\) value for this reaction: \(K_w = [H^+] × [\mathrm{OH}^-]\) Assuming a value of \(1 × 10^{-14}\) for \(K_w\) at 25°C, we can find the \(K_2\) value: \(K_2 = \frac{K_w}{[H^+]} = \frac{1 × 10^{-14}}{3.31 × 10^{-4}\: \mathrm{M}} = 3.02 × 10^{-11}\) So the molar mass of acetylsalicylic acid is 179.8 g/mol and its \(K_2\) value is \(3.02 × 10^{-11}\).

Key concepts

Molar Mass Calculation

Calculating the molar mass of a substance is a fundamental process in chemistry. The molar mass refers to the mass of one mole of a given substance, typically expressed in grams per mole (g/mol). For aspirin, which contains acetylsalicylic acid, you first need to determine the number of moles in the sample.

Start by identifying the number of moles from the titration data. In this scenario, when acetylsalicylic acid reacts with an equal number of moles of NaOH, we can calculate the moles from the NaOH volume and concentration. Using the formula:

• Moles = Volume (L) × Molarity (M)

Convert the volume in mL to L (27.36 mL becomes 0.02736 L) and then multiply by the NaOH molarity (0.5106 M). This gives the moles of NaOH, which equals the moles of aspirin due to their 1:1 reaction ratio.

Finally, the molar mass is calculated using:

• Molar Mass = mass (g) / moles

With a mass of 2.51 g and moles determined previously, the molar mass of acetylsalicylic acid is found to be 179.8 g/mol.

Acid-Base Titration

An acid-base titration involves neutralizing an acid with a base to determine the concentration of one or both substances. In this experiment, the goal is to figure out how much NaOH reacts with the acetylsalicylic acid in aspirin.

During titration, NaOH (a strong base) reacts with the acid (acetylsalicylic acid) to form water and a salt. This specific reaction occurs in a 1:1 stoichiometric ratio. The end point is reached when exactly the same amount of acid and base have reacted completely.

When additional HCl is then added, it reacts with any remaining NaOH. This indicates that initial excess NaOH has neutralized the acetylsalicylic acid completely. The additional titration with HCl helps verify the equivalence point and ensure the correct reaction balance had been achieved. The completion of this delicate balance confirms the amounts of reactants involved, allowing for precise chemical calculations.

Chemical Equilibrium

Chemical equilibrium is when the rate of the forward reaction equals the rate of the backward reaction in a chemical process. At equilibrium, the concentrations of reactants and products remain constant. In the aspirin titration process, chemical equilibrium principles help determine the reaction outcome when additional HCl is added after the initial NaOH reaction.

By understanding equilibrium, chemists can calculate the concentrations of acid and base after the reactions. The assumption is that after adding HCl, the solution arrived at an equilibrium where enough \(OH^-\) ions are still available to reflect a measurable pH.

This equilibrium condition supports the accuracy of the pH calculation, the understanding of leftover \(OH^-\) ions, and how they interact with added \(H^+\) from HCl. This balance is crucial for calculating the remaining concentrations necessary for further assessments like pH levels.

pH Calculation

Understanding how to calculate the pH of a solution is essential in chemistry. pH is a measure of the hydrogen ion concentration within a solution, with a smaller pH indicating a more acidic solution. In this scenario, once the HCl is added, the pH can be calculated to understand the reaction's progress and acid-base balance.

The equation used is:

• \(pH = -\log[H^+]\)

Here, \([H^+]\) is the concentration of hydrogen ions. You use the pH value of 3.48 to express the hydrogen ion concentration logarithmically, which translates to:

• \([H^+] = 10^{-3.48}\)

This value measures how additional acid influences the remaining \(OH^-\) ions. By understanding the pH and the concentration of these ions, chemical properties like \(K_w\), the ion product of water, allows for further exploration into the acidic or basic nature of the reaction mixture. Knowing the pH also helps check whether chemical reactions have proceeded as expected, providing assurance in the calculated results.