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 understand the concept of pH, pKa, and the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is commonly used to calculate the pH of a solution containing a weak acid and its conjugate base, or a weak base and its conjugate acid. It is given by the equation:
pH = pKa + log([A-]/[HA])
Where:
- pH is the measure of acidity or alkalinity of a solution.
- pKa is the negative logarithm (base 10) of the acid dissociation constant, which indicates the strength of an acid.
- [A-] is the concentration of the conjugate base.
- [HA] is the concentration of the weak acid.
In this case, we want to calculate how much 5 M KOH must be added to 1.0 L of 0.1 M glycine to bring its pH to exactly 10.0. To do this, we need to manipulate the Henderson-Hasselbalch equation to solve for the concentration of the conjugate base, [A-], when the pH is 10.0.
First, we need to calculate the concentration of the weak acid, [HA], which is glycine. Since the concentration is given as 0.1 M, [HA] = 0.1 M.
Next, we can rearrange the Henderson-Hasselbalch equation to solve for [A-]:
[A-] = 10^(pH - pKa) * [HA]
Substituting the given values: pH = 10.0, pKa = 9.6, and [HA] = 0.1 M, we can calculate [A-]:
[A-] = 10^(10.0 - 9.6) * 0.1
Simplifying the calculation, [A-] = 0.25 M.
Now, we know the concentration of the conjugate base, [A-], that we want to achieve. The concentration of [A-] can be increased by adding KOH. By adding KOH, it will react with glycine to form the conjugate base (glycine minus a proton).
To determine the amount of KOH required, we can use the equation:
[A-] = moles of KOH / volume of solution in liters
Rearranging the equation, we get:
moles of KOH = [A-] * volume of solution in liters
Substituting the values: [A-] = 0.25 M and volume of solution = 1.0 L, we can calculate the moles of KOH required:
moles of KOH = 0.25 M * 1.0 L = 0.25 mol
Finally, to calculate the amount of 5 M KOH required, we use the relationship between moles, concentration, and volume:
moles = concentration * volume
Rearranging the equation, we can solve for the volume:
volume = moles / concentration
Substituting the values: moles = 0.25 mol and concentration = 5 M, we can calculate the volume of 5 M KOH required:
volume = 0.25 mol / 5 M = 0.05 L = 50 mL
Therefore, 50 mL of 5 M KOH must be added to 1.0 L of 0.1 M glycine to bring its pH to exactly 10.0.