The pH of a solution of acetylsalicylic acid (commonly known as aspirin, \"HA\"

Question

The pH of a solution of acetylsalicylic acid (commonly known as aspirin, "HA" = HC_9 H_7 O_4) was determined to be 1.74. If the K_a value for this weak acid is 3.3 times 10^-4, answer the following questions: What is the concentration of H_3 O^+ ions in this solution? What is the concentration of C_9 H_7 O_4^-(A^-) in this solution? Assume the auto-ionization of water is negligible. What is the concentration of un-ionized acetylsalicy acid (HA) still present in the solution? How many moles of acetylsalicylic acid (HC_9 H_7 O_4) must have been dissolved in 1.00 L of water to prepare this solution? A second solution is prepared by dissolving 2.00 moles of acetylsalicylic acid in 1.00 L of water. What would be the pH of this second solution? Comment on the effect of concentration on the pH of the solution. Are these two quantities proportional?

Explanation / Answer

3. For the given acetylsalicylic acid

a. pH = -log[H3O+] = 1.74

concentration of [H3O+] = 0.0182 M

b. concentration of [C9H7O4-] = 0.0182 M

c. concentration of unionized [HA] = (0.0182)^2/3.3 x 10^-4 = 1.004 M

d. moles of acetyl salicylic acid dissolved in 1 L = (1.004 + 0.0182) M x 1 L = 1.022 moles

e. molarity of acetyl salicylic acid solution = 2 moles/1 L = 2 M

let x amount of HA has dissociated,

Ka = 3.3 x 10^-4 = x^2/(2 - x)

x^2 + 3.3 x 10^-4x - 6.6 x 10^-4 = 0

x = [H3O+] = 0.0255 M

pH = -log[H3O+] = 1.593

f. Comparing the two values, as the concentration of solution increases, the pH of the solution goes down.

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