To find the pH of the buffer after adding LiOH, we need to calculate the concentration of the acid (HA) and its conjugate base (A-) in the final solution. Then, we can use the Henderson-Hasselbalch equation to determine the pH.
Step 1: Calculate the moles of acid and conjugate base in the original buffer solution.
Moles of HA = concentration of HA x volume of HA buffer solution
= 0.271 M x 0.650 L
Moles of KA = concentration of KA x volume of KA buffer solution
= 0.150 M x 0.650 L
Step 2: Calculate the moles of LiOH added.
Moles of LiOH = concentration of LiOH x volume of LiOH added
= 0.155 M x 0.130 L
Step 3: Determine the new volumes of the acid and conjugate base.
The moles of acid (HA) remain the same since its volume doesn't change. The volume of the conjugate base (A-) increases by the volume of LiOH added.
New volume of KA = volume of KA in buffer + volume of LiOH added
= 0.650 L + 0.130 L
Step 4: Calculate the new concentrations of acid and conjugate base.
New concentration of HA = moles of HA / new volume of HA
New concentration of A- = moles of KA / new volume of KA
Step 5: Determine the pH using the Henderson-Hasselbalch equation.
pH = pKa + log10([A-] / [HA])
The pKa is the negative logarithm of the acid dissociation constant (Ka) for the acid HA.
Now let's calculate the values:
Step 1: Moles of acid and conjugate base in the original buffer:
Moles of HA = 0.271 M x 0.650 L = 0.176 moles
Moles of KA = 0.150 M x 0.650 L = 0.098 moles
Step 2: Moles of LiOH added:
Moles of LiOH = 0.155 M x 0.130 L = 0.020 moles
Step 3: New volumes:
New volume of KA = 0.650 L + 0.130 L = 0.780 L
Step 4: New concentrations:
New concentration of HA = 0.176 moles / 0.650 L = 0.271 M
New concentration of A- = 0.098 moles / 0.780 L = 0.125 M
Step 5: pH calculation:
The pKa value is not provided in the question, so we cannot calculate the exact pH. The Henderson-Hasselbalch equation requires the pKa value. However, we can calculate the ratio [A-] / [HA] and use it to estimate the pH change.
[A-] / [HA] = (0.125 M) / (0.271 M) = 0.461
Now, we can estimate the pH change based on the ratio:
pH' = pH + log10(0.461)
Given that the initial pH is 2.85, we can calculate the final pH approximation:
pH' = 2.85 + log10(0.461)
pH' ≈ 2.85 - 0.336
pH' ≈ 2.514
Therefore, the pH of the buffer after adding LiOH is approximately 2.514.