How would you determine the Ka value for an unknown weak acid just knowing two things?

At the equivalence point, the amount of titrant added equals the amount of analyte present. 12.5 mL is half way to the equivalence point. So after 12.5 mL of titrant have been added, half of the weak acid present has been converted to the conjugate base and so the amount of acid *equals* the amount of conjugate base. We can then use the Henderson-Hasselbalch equation to determine the Ka

pH = pKa + log([A-]/[HA])

The 2nd term on the right equals zero because the argument of the logarithm is 1 (the 2 concentrations are equal. Now we use the definition of pKa to get our answer

pH = -log(Ka)

Ka = 10^(-pH) = 10^(-4.74) = 1.8 * 10^-5