How much 5 M KOH must be added to 1.0 L of 0.1 M glycine at pH 9.0 to bring its pH to exactly 10.0? The amino group of glycine has a pKa of 9.6.
To solve this problem, we need to consider the Henderson-Hasselbalch equation, which relates the pH of a solution to the concentration of its acidic and basic species. The equation is given as:
pH = pKa + log([A-]/[HA])
In this case, we want to increase the pH of the solution by adding a strong base, which will convert some of the glycine (HA) to its conjugate base (A-). We need to determine the amount of KOH required to achieve a pH of 10.0.
Given:
- Volume of glycine solution (V) = 1.0 L
- Concentration of glycine (HA) = 0.1 M
- pH of glycine solution = 9.0
- pKa of amino group of glycine = 9.6
Step 1: Calculate the concentration of A- in the glycine solution.
Using the Henderson-Hasselbalch equation, we can rearrange it to solve for [A-]:
pH = pKa + log([A-]/[HA])
10.0 = 9.6 + log([A-]/0.1)
Solving for [A-], we get:
log([A-]/0.1) = 10.0 - 9.6
log([A-]/0.1) = 0.4
[A-]/0.1 = 10^0.4
[A-] = 0.1 * 10^0.4
[A-] ≈ 0.251 M
Step 2: Determine the amount of KOH needed to convert all the remaining glycine (HA) to A-.
To completely convert all the remaining glycine (HA) to A-, we need to add the same amount of moles of KOH as there are moles of glycine (HA).
Moles of glycine (HA) = Concentration of glycine (HA) * Volume of glycine solution (V)
Moles of glycine (HA) = 0.1 M * 1.0 L
Moles of glycine (HA) = 0.1 mol
Therefore, we need to add 0.1 mol of KOH to convert all the glycine (HA) to A-.
Step 3: Convert moles of KOH to grams.
The molar mass of KOH is 56.11 g/mol. To calculate the mass of KOH needed:
Mass of KOH = Moles of KOH * Molar mass of KOH
Mass of KOH = 0.1 mol * 56.11 g/mol
Mass of KOH = 5.611 g
Therefore, 5.611 grams of 5 M KOH must be added to 1.0 L of the glycine solution to bring its pH to exactly 10.0.