A buffer solution is made by dissolving 0.45
moles of a weak acid (HA) and 0.23 moles of
KOH into 720 mL of solution. What is the
pH of this buffer? Ka = 6.2 × 10−6
for HA.
Answer in units of pH.
i need the answer
To determine the pH of the buffer solution, we need to calculate the concentration of the acid (HA) and its conjugate base. Let's break down the process step by step:
1. Calculate the concentration of the acid (HA):
The number of moles of HA dissolved = 0.45 moles
Volume of the solution = 720 mL = 0.72 L
Concentration of HA = moles/volume = 0.45 moles / 0.72 L = 0.625 M
2. Calculate the concentration of the conjugate base (A-):
Since the weak acid (HA) reacts with KOH to form a buffer solution, the moles of KOH will determine the moles of the conjugate base (A-). Here, we have 0.23 moles of KOH, so we also have 0.23 moles of A-.
3. Calculate the ratio of conjugate base (A-) to acid (HA):
The ratio of moles of A- to HA is given by:
Ratio = moles of A- / moles of HA
= 0.23 moles / 0.45 moles
≈ 0.511
4. Calculate the pKa of the weak acid (HA):
The pKa is the negative logarithm (base 10) of the acid dissociation constant (Ka) for the weak acid (HA).
pKa = -log(Ka)
= -log(6.2 × 10^(-6))
≈ 5.21
5. Calculate the pH of the buffer solution:
When a weak acid is in equilibrium with its conjugate base, the pH can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Substituting the known values:
pH = 5.21 + log(0.23/0.45)
≈ 5.21 + log(0.511)
≈ 5.21 + (-0.290)
≈ 4.92
Therefore, the pH of the buffer solution is approximately 4.92.
To find the pH of the buffer solution, we need to consider the equilibrium between the weak acid (HA) and its conjugate base (A-).
Step 1: Calculate the concentration of the weak acid (HA) and its conjugate base (A-).
Given:
moles of HA = 0.45 moles
moles of KOH = 0.23 moles
volume of solution = 720 mL = 0.72 L
The concentration of HA can be calculated using the formula:
[HA] = moles of HA / volume of solution
[HA] = 0.45 moles / 0.72 L
[HA] ≈ 0.625 M
Since KOH is a strong base, it fully dissociates into K+ and OH- ions. As a result, the concentration of OH- ions will be equal to the concentration of KOH.
The concentration of A- can be calculated using the formula:
[A-] = moles of KOH / volume of solution
[A-] = 0.23 moles / 0.72 L
[A-] ≈ 0.319 M
Step 2: Calculate the molar ratio of HA to A-.
Since the reaction between HA and KOH has a 1:1 molar ratio, the concentration of HA and A- will be the same.
Step 3: Calculate the initial concentration of HA and A-.
Since HA and A- have the same concentration, their initial concentrations will be equal to [HA] and [A-], respectively.
[HA]initial = 0.625 M
[A-]initial = 0.319 M
Step 4: Calculate the concentration of H+ ions from the dissociation of HA.
Using the given Ka value for HA, we can calculate the concentration of H+ ions.
Ka = [H+][A-] / [HA]
6.2 × 10^-6 = [H+][0.319] / [0.625]
We need to solve for [H+]. Rearranging the equation:
[H+] = (Ka * [HA]) / [A-]
[H+] = (6.2 × 10^-6 * 0.625) / 0.319
[H+] ≈ 1.21 × 10^-5 M
Step 5: Calculate the pH.
The pH of a solution is given by the formula:
pH = -log[H+]
pH = -log(1.21 × 10^-5)
pH ≈ 4.92
Therefore, the pH of the buffer solution is approximately 4.92.