The AIDS drug stavudine (also known as d4T) is a weak base and a pKb of 9.8. What percentage of the base is protonated in an aqueous zalcitabine solution containing 565 mg L^-1?
What are the steps to solving this problem?
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To solve this problem, you need to use the concept of the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of a weak acid or the pKb of a weak base. In this case, we have the pKb of stavudine (d4T) which is 9.8, so we can use the Henderson-Hasselbalch equation.
Here are the steps to solve this problem:
Step 1: Calculate the concentration of the base (d4T) in the solution.
Given that the solution contains 565 mg L^-1 of d4T, we need to convert this to moles L^-1 by dividing by the molar mass.
Step 2: Calculate the concentration of the conjugate acid (d4TH^+).
Since stavudine (d4T) is a weak base, we can assume that it reacts with water to form its conjugate acid (d4TH^+) and hydroxide ions (OH^-). At equilibrium, the concentrations of d4TH^+ and OH^- are the same. So, the concentration of d4TH^+ is equal to the concentration of OH^-.
Step 3: Calculate the concentration of hydroxide ions (OH^-).
Since the concentration of d4TH^+ is equal to the concentration of OH^-, we can calculate the concentration of OH^- using the concentration of d4T and the concentration of d4TH^+.
Step 4: Calculate the concentration of hydroxonium ions (H3O^+).
Since the concentration of hydroxide ions is known, we can use the fact that Kw = [H3O^+][OH^-] to calculate the concentration of H3O^+.
Step 5: Calculate the pH of the solution.
Now that we have the concentration of H3O^+, we can take the negative logarithm (base 10) of the concentration to calculate the pH.
Step 6: Calculate the percentage of the base (d4T) that is protonated.
To calculate the percentage of the base that is protonated, we need to know the ratio of the concentration of the protonated form (d4TH^+) to the total concentration of the base (d4T). We can calculate this ratio and then multiply it by 100 to get the percentage.
These steps will help you solve the problem of determining what percentage of the base is protonated in the given aqueous zalcitabine solution.