Question

(a) Calculate the percent ionization of a \(0.20 \mathrm{M}\) solution of the monoprotic acetylsalicylic acid (aspirin). \(\left(K_{\mathrm{a}}=3.0 \times 10^{-4} .\right)(\mathrm{b})\) The \(\mathrm{pH}\) 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 \(0.20 \mathrm{M}\) Calculate the percent ionization of the acid under these conditions.

Short answer

The percent ionization of a 0.20 M solution of acetylsalicylic acid is 1.225%, while in the stomach it ionizes up to 50%.

Step-by-step solution

Setup the Equation

We can use the formula for the ionization of a weak acid : \(HA \leftrightarrow H^{+}+A^{-}\), Where, \(HA\) is the weak acid. We also know that the ionization constant \(Ka = \frac{[H^{+}][A^{-}]}{[HA]}\), where \([H^{+}]\) is the concentration of the H+ ion, \([A^-]\) is the concentration of the A- ion, and \([HA]\) is the initial concentration of the aciditylsalicyclic acid.

Calculation Percent ionization for a 0.20 M solution

Given that `Ka = 3.0 x 10^-4` and `HA = 0.20 M`. Setting up the ionization equation, `Ka = x^2/(0.20-x)`. Solving this results in x = 0.00245 M. Then, calculate the percent ionization using the formula \((\frac{x}{HA})\times 100%\), which results in \(1.225\%\).

Calculation for Gastric Juice

Knowing that pH = -log[H+] and the provided pH is 1.00, we can find that \([H+] = 10^{(-pH)}\), giving us \([H+] = 10^{-1}\) = 0.10. We can then calculate the percent ionization in the same way as in step 2, using \([H+]\) instead of x (as it is the same), and getting a percentage of \(50\%\).

Key concepts

Understanding Weak Acids

Weak acids are a fascinating topic in chemistry and are characterized by their ability to only partially ionize in an aqueous solution. This partial ionization means they don’t release all their hydrogen ions into the solution, unlike strong acids that completely dissociate. A common example of a weak acid is acetylsalicylic acid, or aspirin, which is only slightly ionized in water. It’s important to understand how this property affects the behavior and reactivity of weak acids.
Key characteristics of weak acids include:

• They have a reversible reaction with water, represented by the equilibrium equation:
  HA ⇌ H⁺ + A^-, where HA is the weak acid.
• Since weak acids do not fully dissociate, the concentrations of the hydrogen ions and the remaining acid are both considered in equilibrium calculations.
• Weak acids have a lower tendency to donate their protons compared to strong acids. This is quantified by their ionization constant, or Ka, which is unique to each acid.

Understanding Ionization Constant (Ka)

The ionization constant, Ka, is a crucial concept when discussing weak acids. It serves as a measure of the strength of an acid in a solution, indicating how well the acid can donate protons to the solvent.
For any weak acid HA, the equilibrium expression used to quantify the ionization process is given by:
\[ K_{a} = \frac{[H^+][A^-]}{[HA]} \]
Here are some important points about Ka:

• A larger Ka value indicates a stronger weak acid as it ionizes more fully in solution. Conversely, a smaller Ka signifies a weaker acid.
• The Ka value can be used to calculate the degree of ionization of the acid and is crucial in determining the pH of a solution containing a weak acid.
• In practical applications, knowing Ka allows scientists to predict the behavior of weak acids under different conditions, like varying concentration or pH levels.

For example, in the case of acetylsalicylic acid with a Ka of \(3.0 \times 10^{-4}\), it provides insight into its partial ionization level in solutions.

Exploring Gastric pH

The gastric pH is an important factor in chemistry and medicine, as it plays a crucial role in digestion and drug absorption. Typically, the pH of stomach acid is very low, around 1.0 to 3.0, due to the presence of hydrochloric acid (HCl). This low pH creates an acidic environment needed for activating digestive enzymes and for pathogen defense.
Understanding gastric pH can be important for different reasons:

• Drug Stability and Absorption: Many drugs, including weak acids like aspirin, can be affected by the gastric pH, as their ionization state can change. This affects how they are absorbed in the body.
• Proteins Digestion: The acidic environment helps denature proteins, making them easier for enzymes to break down during digestion.
• Pain and Irritation: The acidic condition can sometimes cause discomfort or conditions such as acid reflux if it becomes too aggressive.

In the context of aspirin, when it is consumed, the low pH increases the percent ionization, altering its absorption dynamics, as observed in the given exercise calculations where the gastric pH leads to a 50% ionization of the aspirin in the stomach.