```
pH = pKa + log([A-]/[HA])
```
where:
- pH is the pH of the solution
- pKa is the acid dissociation constant of HF
- [A-] is the concentration of the conjugate base of HF (F-)
- [HA] is the concentration of HF
The pKa of HF is 3.17. At equilibrium, the concentration of F- will be equal to the concentration of H+ produced by the dissociation of HF. Therefore, [A-] = [H+].
Substituting the values into the Henderson-Hasselbalch equation, we get:
```
pH = 3.17 + log([H+]/[0.5 M])
```
Solving for [H+], we get:
```
[H+] = 0.5 M * 10^(3.17 - pH)
```
The pH of the solution can be determined by measuring the concentration of H+ using a pH meter.
At 0.5 M, HF is partially dissociated, so we need to use the quadratic equation to solve for [H+] exactly:
```
[H+]^2 + 0.5 [H+] - 10^(-3.17) = 0
```
Solving for [H+] using the quadratic formula, we get:
```
[H+] = 0.25 M - √(0.0625 + 10^(-3.17))
```
```
[H+] = 0.25 M - 0.21 M
```
```
[H+] = 0.04 M
```
Therefore, the pH of a 0.5 M HF solution is:
```
pH = -log(0.04) = 1.39
```
