If a buffer solution is 0.170 M in a weak acid (Ka = 7.8 × 10-5) and 0.500 M in its conjugate base, what is the pH?
To find the pH of the buffer solution, we need to consider the equilibrium between the weak acid and its conjugate base.
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of the weak acid and its conjugate base:
pH = pKa + log([conjugate base] / [weak acid])
Here, pKa is the negative logarithm of the acid dissociation constant (Ka), which is given as 7.8 × 10^(-5).
Let's substitute the given values into the equation:
pH = -log(7.8 × 10^(-5)) + log(0.500 / 0.170)
To simplify the logarithmic calculations, we can rewrite the equation as follows:
pH = -log(7.8 × 10^(-5)) + log(2.9412)
Now, we can evaluate the equation step-by-step:
1. Evaluate the logarithm of the Ka value:
-log(7.8 × 10^(-5)) ≈ 4.11
2. Take the logarithm of the ratio [conjugate base] / [weak acid]:
log(2.9412) ≈ 0.47
3. Add the two values together:
pH ≈ 4.11 + 0.47 ≈ 4.58
Therefore, the pH of the buffer solution is approximately 4.58.
To find the pH of a buffer solution, you can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where:
- pH is the logarithmic measure of the concentration of hydrogen ions in a solution (acidic: pH < 7, basic: pH > 7)
- pKa is the negative logarithm (base 10) of the acid dissociation constant, Ka, of the weak acid
- [A-] is the concentration of the conjugate base
- [HA] is the concentration of the weak acid
In this case, the given values are:
- Ka = 7.8 × 10^-5
- [A-] = 0.500 M
- [HA] = 0.170 M
To calculate the pH, follow these steps:
Step 1: Calculate pKa
pKa = -log(Ka)
pKa = -log(7.8 × 10^-5)
Step 2: Calculate the logarithm of the ratio [A-]/[HA]
log([A-]/[HA]) = log(0.500 M / 0.170 M)
Step 3: Add pKa to the logarithm obtained in step 2
pH = pKa + log([A-]/[HA])
By substituting the values into the equation, you can find the pH.