(a) Calculate the percent ionization of a 0.20 M solution of the monoprotic acetylsalicylic acid

(a) Calculate the percent ionization of a 0.20 M solution of...

(a) Calculate the percent ionization of a $0.20 \mathrm{M}$ solution of the monoprotic acetylsalicylic acid (aspirin) for which $K_{\mathrm{a}}=3.0 \times 10^{-4}$. (b) The pH of gastric juice in the stomach of a certain individual is 1.00 . After a few aspirin tablets have been swallowed, the concentration of acetylsalicylic acid in the stomach is $0.20 M .$ Calculate the percent ionization of the acid under these conditions. What effect does the nonionized acid have on the membranes lining the stomach? (Hint: See the Chemistry in Action essay "Antacids and the pH Balance in Your Stomach" in Section $15.12 .)$

Key Concepts

Effect of pH on Acid-Base Equilibrium

The pH of a solution profoundly affects the position of an acid-base equilibrium. In high proton (low pH) environments, weak acids tend to remain largely undissociated, while in higher pH conditions, they ionize more. This relationship is essential for understanding how the extent of ionization changes under different conditions, which in turn affects the potency of the acid in biochemical systems.

Acid Dissociation Constant (Ka)

Ka is a quantitative measure of the strength of a weak acid in solution. It represents the equilibrium constant for the dissociation of an acid into its conjugate base and a proton. Understanding Ka is essential in calculating the extent of ionization of an acid in solution, which influences many properties, including pH and the acid’s chemical behavior under different conditions.

Percent Ionization

Percent ionization is the fraction of a total amount of acid or base that ionizes in solution, expressed as a percentage. It indicates how much of the acid converts to its ionic form in equilibrium. This concept is particularly important for weak acids like acetylsalicylic acid, where only a portion of the molecules dissociates, and it is used to predict the acid’s reactivity and its interactions in varied pH environments.

Membrane Permeability and Lipid Solubility

The degree of ionization of a substance influences its lipid solubility and, consequently, its ability to cross biological membranes. Nonionized forms of weak acids are more lipid-soluble and can more readily penetrate cell membranes, potentially causing direct damage. In the context of the stomach, the nonionized acetylsalicylic acid can diffuse into the cells lining the stomach, contributing to irritation and other adverse effects on the gastric mucosa.

Transcript

00:01 Ionization of a 0 .2 molar solution of monoprotic acetylacetic acid.

00:05 And we're given the acid dissociation constant of 3 .0 times 10 to the minus 4th.

00:11 What am i asked to do? okay, percentionization.

00:14 So let's go ahead and write down our dissociation.

00:25 That'll be h plus and c9h704 minus.

00:34 We're going to do an ice table for this.

00:37 And that will be, i believe, it was 0 .20 minus x plus x and plus x 0 .20 minus x, x, x and x.

00:52 So our ka will be equal to our hydrogen ion or hydronium, if you prefer to write it that way, concentration times our anion, and i think it's called acetylacillate, acetylacillate, and then my acid, i hope i can, yes, i'm going to assume that my 5 % rule applies here.

01:29 So my ka is 3 .0 times 10 to the minus 4th equals x squared, and then i'm just going to do 0 .20, and x will equal 7 .746 times 10 to the minus 3rd more.

01:46 So my percent ionization will be equal to 7 .746 times 10 to the minus third divided by 0 .20.

02:04 Both these are molar times 100.

02:08 And this will equal 3 .87%.

02:14 And it looks like, let me get down to my actual problem again.

02:19 I bet i have to go to two sake bakes.

02:21 Yes.

02:22 So i'm going to go to 3 .9.

02:27 So i satisfy my significant figures rules.

02:31 And this is my percent ionization.

02:39 That's my answer for a...