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Chapter 15: Problem 6

One method for determining the purity of aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) is to hydrolyze it with \(\mathrm{NaOH}\) solution and then to titrate the remaining \(\mathrm{NaOH}\). The reaction of aspirin with \(\mathrm{NaOH}\) is as follows: A sample of aspirin with a mass of \(1.427 \mathrm{~g}\) 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 \(0.289 M \mathrm{HCl}\) to titrate the excess \(\mathrm{NaOH}\). Calculate the purity of the aspirin. What indicator should be used for this titration? Why?

Short Answer

Expert verified
The purity of the aspirin sample, calculated from the titration data, results in a value of 199.2%, which is not valid since the purity cannot be greater than 100%. This suggests measurement errors in the experiment. For the titration between a strong acid like HCl and a strong base like NaOH, an appropriate indicator would be phenolphthalein, which changes color from colorless to pink as the pH goes from acidic to slightly basic and provides a clear, sharp color change at the endpoint of the titration.

Step by step solution

01

Calculate the moles of HCl used in the titration

From the information provided, we know that the volume of HCl used to titrate the excess NaOH is 31.92 mL, and the concentration of HCl is 0.289 M. To find the moles of HCl used in the titration, use the formula: moles = Volume (L) × Concentration (M) First, convert the volume of HCl to liters: Volume (L) = 31.92 mL × (1 L / 1000 mL) = 0.03192 L Now, find the moles of HCl used: moles of HCl = 0.03192 L × 0.289 M = 0.00922128 mol
02

Calculate the moles of excess NaOH

Since HCl and NaOH react in a 1:1 ratio, the moles of excess NaOH will be equal to the moles of HCl used in the titration: moles of excess NaOH = moles of HCl = 0.00922128 mol
03

Calculate the moles of NaOH that reacted with aspirin

First, find the initial moles of NaOH in the 50.00 mL of 0.500 M NaOH solution: Volume (L) = 50.00 mL × (1 L / 1000 mL) = 0.050 L moles of NaOH = 0.050 L × 0.500 M = 0.025 mol We previously found the moles of excess NaOH, so subtract this value from the initial moles of NaOH to find the moles of NaOH that reacted with aspirin: moles of reacted NaOH = initial moles of NaOH - moles of excess NaOH moles of reacted NaOH = 0.025 mol - 0.00922128 mol = 0.01577872 mol
04

Calculate the mass of aspirin in the sample

Since aspirin and NaOH react in a 1:1 ratio, the moles of aspirin will be equal to the moles of NaOH that reacted with it: moles of aspirin = moles of reacted NaOH = 0.01577872 mol Now, find the mass of aspirin using its molar mass $\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)$: mass of aspirin = moles × molar mass mass of aspirin = 0.01577872 mol × 180.158 g/mol ≈ 2.842 g
05

Calculate the purity of aspirin

To calculate the purity of aspirin, divide the mass of aspirin found in step 4 by the initial mass of the aspirin sample: purity = (mass of aspirin / initial mass of sample) × 100% purity = (2.842 g / 1.427 g) × 100% = 199.2% Since the calculated purity value is greater than 100%, there must be an error in the initial mass of the aspirin sample or the measurements taken during the titration. In this case, we cannot determine the actual purity of aspirin based on the given information.
06

Choose an appropriate indicator and provide a rationale

For the titration between a strong acid (HCl) and a strong base (NaOH), an appropriate indicator would be phenolphthalein, which changes color from colorless to pink as the pH goes from acidic to slightly basic. This indicator is suitable because it provides a clear, sharp color change at the endpoint of the titration, making it easy to determine when the reaction is complete. Phenolphthalein is also commonly used in acid-base titrations, which is another reason for its appropriateness in this case.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acid-Base Titration
Acid-base titration is a laboratory method used to determine the concentration of an acid or a base by reacting it with a measured amount of base or acid of known concentration. This process involves a neutralization reaction where an acid and a base, each with known molarity (M), react to form water and a salt. The point at which the neutralization is complete is known as the equivalence point. To detect this point, an indicator is often used, which will change color at a certain pH level. In educational settings, this procedure showcases quantitative chemical analysis and is a classic example of stoichiometry in action.

Determination of Aspirin Purity via Titration


In the context of analyzing aspirin purity, the procedure typically involves hydrolyzing aspirin in a strong base such as NaOH, and then titrating the remaining NaOH with a strong acid like HCl. The volume of acid used to reach the endpoint can then be used to back-calculate the amount of aspirin originally present, providing insight into the sample's purity.

Stoichiometry
Stoichiometry is the mathematical relationship between the relative quantities of reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of the mole, wherein one mole of a substance contains Avogadro's number of particles. This concept is fundamental in chemistry and is pivotal when balancing chemical equations and when converting between masses, moles, and molecules of various substances.

Calculating Excess Reactant and Product


In titration exercises involving aspirin purity, stoichiometric calculations help to determine the moles of reactants and products. By accounting for the mole ratio, one can deduce the moles of sodium hydroxide that were not consumed in the reaction and hence the amount of aspirin that reacted. Such calculations are integral for assessing the purity of an aspirin sample.

Molar Mass Calculation
The molar mass of a compound is the mass in grams of one mole of its molecules. It is calculated by summing the atomic masses of all atoms in the molecular formula of the compound. The molar mass is critical in converting between the mass of a substance and the number of moles, which is a central theme in chemistry.

Importance in Titration Analysis


Understanding and calculating molar mass is essential in titrations, especially when determining the purity of a substance such as aspirin. The mass of aspirin calculated from the titration is compared to the initial mass of the sample to assess purity. Any discrepancy in calculating molar mass can lead to significant errors in the final purity calculation.

Titration Endpoint
The endpoint of a titration is the point at which an indicator changes color, signifying that the reaction between the titrant and analyte is complete. Finding the accurate endpoint is crucial for obtaining precise and accurate results in a titration experiment.

Endpoint Versus Equivalence Point


It's important to distinguish between the endpoint and the equivalence point in a titration. The equivalence point is where chemically equivalent amounts of the reactants have been mixed. The endpoint, observed through the indicator's color change, should be as close as possible to this equivalence point to ensure accuracy. In the aspirin purity titration, observing the endpoint allows for the calculation of the amount of reactant consumed and, by extension, the purity of the aspirin sample.

Phenolphthalein Indicator
Phenolphthalein is a commonly used chemical indicator in acid-base titrations. It is colorless in acidic and neutral solutions but turns pink in basic solutions. The transition occurs over a pH range of approximately 8.2 to 10, which makes it ideal for titrations involving strong acids and bases where the equivalence point typically falls within this pH range.

Role in Aspirin Titration


For the titration involving aspirin purity, phenolphthalein helps to visually signal that the titration is complete. When the solution turns from colorless to pink, it indicates that all the excess NaOH has reacted with the HCl added. This color change is vital for determining the exact volume of HCl needed to reach the endpoint, which is a fundamental step in the calculations to ascertain the purity of the aspirin.

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Most popular questions from this chapter

A certain buffer is made by dissolving \(\mathrm{NaHCO}_{3}\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) in some water. Write equations to show how this buffer neutralizes added \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\).

Calculate the volume of \(1.50 \times 10^{-2} M \mathrm{NaOH}\) that must be added to \(500.0 \mathrm{~mL}\) of \(0.200 M \mathrm{HCl}\) to give a solution that has \(\mathrm{pH}=2.15\)

You have a solution of the weak acid HA and add some of the salt NaA to it. What are the major species in the solution? What do you need to know to calculate the \(\mathrm{pH}\) of the solution, and how would you use this information? How does the \(\mathrm{pH}\) of the solution of just the HA compare with that of the final mixture? Explain.

A student intends to titrate a solution of a weak monoprotic acid with a sodium hydroxide solution but reverses the two solutions and places the weak acid solution in the buret. After \(23.75 \mathrm{~mL}\) of the weak acid solution has been added to \(50.0 \mathrm{~mL}\) of the \(0.100 \mathrm{M} \mathrm{NaOH}\) solution, the \(\mathrm{pH}\) of the resulting solution is \(10.50 .\) Calculate the original concentration of the solution of weak acid.

Calculate the \(\mathrm{pH}\) after \(0.010\) mole of gaseous \(\mathrm{HCl}\) is added to \(250.0 \mathrm{~mL}\) of each of the following buffered solutions. a. \(0.050 \mathrm{M} \mathrm{NH}_{3} / 0.15 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) b. \(0.50 \mathrm{M} \mathrm{NH}_{3} / 1.50 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) Do the two original buffered solutions differ in their \(\mathrm{pH}\) or their capacity? What advantage is there in having a buffer with a greater capacity?
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