A buffer solution is composed of 1.00 mol of acid and 3.25 mol of the conjugate base. If the pKa of the acid is 5.00, what is the pH of the buffer?
To calculate the pH of the buffer solution, we will use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where pKa is the logarithmic form of the acid dissociation constant (Ka), [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
Given:
pKa = 5.00
[A-] = 3.25 mol
[HA] = 1.00 mol
Plugging in these values into the Henderson-Hasselbalch equation:
pH = 5.00 + log(3.25/1.00)
Calculating this equation:
pH = 5.00 + log(3.25) - log(1.00)
= 5.00 + 0.511 - 0.000
= 5.51
Therefore, the pH of the buffer solution is 5.51.
To determine the pH of the buffer solution, one must first find the ratio of the conjugate base to acid.
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa of the acid and the ratio of the acid to its conjugate base:
pH = pKa + log([A-]/[HA])
Given:
- pKa = 5.00
- [HA] (acid) = 1.00 mol
- [A-] (conjugate base) = 3.25 mol
The ratio of [A-] to [HA] is:
[A-]/[HA] = 3.25/1.00 = 3.25
Now, substitute the values into the Henderson-Hasselbalch equation to calculate the pH:
pH = 5.00 + log(3.25)
Using a calculator, evaluate log(3.25), which is approximately 0.513.
pH = 5.00 + 0.513
Therefore, the pH of the buffer solution is approximately 5.513.