Acetylsalicylic acid (C_9H_8O_4), commonly known as aspirin, has been used for o

Question

Acetylsalicylic acid (C_9H_8O_4), commonly known as aspirin, has been used for over a hundred years as an effective pain reliever. When aspirin reaches the blood stream, it dissociates into H^+ and its conjugate base, effectively decreasing the pH of blood: HA H^+ + A^- A person may go into shock or die if blood pH drops below 6.8. However, buffers in the blood help dampen changes in blood pH. The main buffer is the bicarbonate system: H_2CO_3 H^+ + HCO_3^- When aspirin dissociates, the bicarbonate equilibrium shifts towards carbonic acid (H_2CO_3), thus reducing the concentration of H^+ in the blood stream. The initial concentration of H_2CO_3 and HCO_3^- in the blood stream is 0.0014 mol/L and 0.0266 mol/L, respectively. The aspirin equilibrium has pK_a = 3.6, whereas the bicarbonate equilibrium has pK_a = 6.36. Assume that the blood volume in the body is 5 L and the molecular weight of the acetylsalicylic acid is 180.2 g/mol. a. Calculate the equilibrium constants (K_a) for the two dissociation reactions. b. Write molar balances for the species involved in the bicarbonate equilibrium. c. Calculate the moles of carbonic acid at equilibrium when the patient goes into shock (pH = 6.8). d. Write molar balances for the species involved in the acetylsalicylic acid equilibrium. e. Calculate the mass of aspirin to be consumed for the patient to go into shock (pH = 6.8).

Explanation / Answer

aspirin HA

HA <==> H+ + A-

the H+ formed then,

H+ + HCO3- <==> H2CO3

initial pH of buffer

pH = pKa + log(HCO3-/H2CO3)

      = 6.36 + log(0.0266/0.0014)

      = 7.64

3a. Ka for aspirin = 3.6

pKa = -logKa

Ka = 2.51 x 10^-4

Ka of H2CO3/HCO3

pKa = 6.36

Ka = = 4.36 x 10^-7

3b. molar balances for H2CO3/HCO3-

[H+] = 0.0014[H2CO3] + 0.0266[HCO3-]

3c. moles H2CO3 = 0.0014 M x 5 L = 0.007 mol

moles HCO3- = 0.0266 M x 5 L = 0.133 mol

3d. molar balance for acetylsalicylic acid (aspirin)

[HA] = [A-] + [H+]

3e. pH = -log[H+] = 6.8

[H+] = 1.585 x 10^-7 M

[H+] = [A-]

[HA] = [[(1.585 x 10^-7)/Ka = 2.51 x 10^-4] + 1.585 x 10^-7]

        = 1.59 x 10^-7 M

mass aspiring needed = 1.59 x 10-7 M x 5 L x 180.2 h/mol = 1.433 x 10^-4 g

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