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Chapter 16: Problem 95

Salicylic acid, \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{OHCOOH}\), is used in the manufacture of acetylsalicylic acid (aspirin) and methyl salicylate (wintergreen flavor). A saturated solution of salicylic acid contains \(2.2 \mathrm{~g}\) of the acid per liter of solution and has a pH of \(2.43 .\) What is the value of \(K_{a} ?\)

Short Answer

Expert verified
The value of \(K_a\) for salicylic acid is approximately \(8.5 \times 10^{-3}\).

Step by step solution

01

Understanding the Problem

We need to find the acid dissociation constant \(K_a\) for salicylic acid using the given concentration and pH of its saturated solution.
02

Calculating Molarity

First, convert the grams of salicylic acid to moles. The molar mass of salicylic acid (\(C_6H_4OHCOOH\)) is approximately 138.12 g/mol. The molarity \(M\) of the solution is \(\frac{2.2 \text{ g/L}}{138.12 \text{ g/mol}} \approx 0.0159 \text{ mol/L}\).
03

Determining Hydrogen Ion Concentration

Use the pH to find the concentration of \(\text{H}^+\) ions: \([\text{H}^+] = 10^{-2.43} \approx 3.71 \times 10^{-3} \text{ M}\).
04

Setting up the Expression for Ka

We know from the dissociation of salicylic acid \((HA)\): \(HA \leftrightarrow H^+ + A^-\). Since the initial concentration of \(HA\) is its molarity (0.0159 M), the concentration of \(HA\) at equilibrium is \(0.0159 - x\) where \(x\) is \([H^+]\). Using this, \([A^-] = [H^+] = 3.71 \times 10^{-3} \text{ M}\).
05

Solve for Ka Using the Expression

\[K_a = \frac{[H^+][A^-]}{[HA]} = \frac{(3.71 \times 10^{-3})(3.71 \times 10^{-3})}{0.0159 - 3.71 \times 10^{-3}}\]Calculate \(K_a\) to find \[K_a \approx 8.5 \times 10^{-3}\].

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Key Concepts

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

Salicylic Acid
Salicylic acid is an organic acid with the chemical formula \(C_6H_4OHCOOH\). It is commonly found in plants and is known for its use in producing aspirin and flaxment wintergreen flavor. This compound comprises both phenol and carboxylic acid functional groups. It is known to be slightly soluble in water, hence the need to calculate its concentration in a saturated solution. Understanding its solubility helps in applications like formulating pharmaceuticals. When dissolved, the acid can release protons, making the solution acidic, which we measure using pH.
Molarity Calculation
Molarity is a way of expressing concentration as the number of moles of solute per liter of solution. In the problem involving salicylic acid, the weight given is \(2.2\) grams per liter. For substances like salicylic acid, which have known molar masses, converting grams to moles is straightforward.
  • Molar mass of salicylic acid: approximately \(138.12 \, g/mol\).
  • Moles of solute = \( \frac{2.2 \, g}{138.12 \, g/mol} \approx 0.0159 \, mol\).
  • Molarity of the solution = \(0.0159 \, mol/L\).
The importance of molarity lies in its role in chemical reactions, whereby it helps determine the number of solute particles in a given volume, critical during titrations and reactions involving precise concentrations.
pH and Hydrogen Ion Concentration
Understanding pH is crucial when dealing with acids like salicylic acid. pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. A pH of \(2.43\) implies that the solution is quite acidic, meaning it has a high concentration of hydrogen ions.
  • To determine the concentration of \([H^+]\), use the formula: \([H^+] = 10^{-pH}\).
  • For a pH of \(2.43\), \([H^+] \approx 3.71 \times 10^{-3}\) M.
Understanding the hydrogen ion concentration helps in many calculations, one of which is determining the acid dissociation constant \(K_a\). This constant measures an acid's strength and its ability to donate protons to the solution. It's calculated using the equilibrium concentrations of the reactants and products in the dissociation reaction.

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Most popular questions from this chapter

a. For each of the following salts, write the reaction that occurs when it dissociates in water: \(\mathrm{NaCl}(s), \mathrm{NaCN}(s)\) \(\mathrm{KClO}_{2}(s), \mathrm{NH}_{4} \mathrm{NO}_{3}(s), \mathrm{K} \operatorname{Br}(a q),\) and \(\mathrm{NaF}(s)\) b. Consider each of the reactions that you wrote above, and identify the aqueous ions that could be proton donors (acids) or proton acceptors (bases). Briefly explain how you decided which ions to choose. c. For each of the acids and bases that you identified in part \(\mathrm{b}\), write the chemical reaction it can undergo in aqueous solution (its reaction with water). d. Are there any reactions that you have written above that you anticipate will occur to such an extent that the \(\mathrm{pH}\) of the solution will be affected? As part of your answer, be sure to explain how you decided. e. Assume that in each case above, \(0.01 \mathrm{~mol}\) of the salt was dissolved in enough water at \(25^{\circ} \mathrm{C}\) to make \(1.0 \mathrm{~L}\) of solution. In each case, what additional information would you need in order to calculate the pH? If there are cases where no additional information is required, be sure to state that as well. f. Say you take \(0.01 \mathrm{~mol}\) of \(\mathrm{NH}_{4} \mathrm{CN}\) and dissolve it in enough water at \(25^{\circ} \mathrm{C}\) to make \(1.0 \mathrm{~L}\) of solution. Using chemical reactions and words, explain how you would go about determining what effect this salt will have on the \(\mathrm{pH}\) of the solution. Be sure to list any additional information you would need to arrive at an answer.

What is the hydronium-ion concentration of a \(2.00 M\) solution of 2,6 -dinitrobenzoic acid, \(\left(\mathrm{NO}_{2}\right)_{2} \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{COOH},\) for which \(K_{a}=7.94 \times 10^{-2} ?\)

Calculate the \(\mathrm{pH}\) of a solution obtained by mixing \(456 \mathrm{~mL}\) of \(0.10 \mathrm{M}\) hydrochloric acid with \(285 \mathrm{~mL}\) of \(0.15 M\) sodium hydroxide. Assume the combined volume is the sum of the two original volumes.

A buffer is prepared by mixing \(525 \mathrm{~mL}\) of \(0.50 \mathrm{M}\) formic acid, \(\mathrm{HCHO}_{2}\), and \(475 \mathrm{~mL}\) of \(0.50 \mathrm{M}\) sodium formate, \(\mathrm{NaCHO}_{2}\). Calculate the pH. What would be the pH of \(85 \mathrm{~mL}\) of the buffer to which \(8.6 \mathrm{~mL}\) of \(0.15 \mathrm{M}\) hydrochloric acid had been added?

Cyanoacetic acid, \(\mathrm{CH}_{2} \mathrm{CNCOOH},\) is used in the manufacture of barbiturate drugs. An aqueous solution containing \(5.0 \mathrm{~g}\) in a liter of solution has a pH of 1.89 . What is the value of \(K_{a} ?\)
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