Esterification balance

You will write functions for the balance of the Fischer esterification. They give the fraction of the acid that becomes ester, the mass of ester, and the least amount of alcohol for a target yield.

The idea. Start with 1 mol of acid and $r$ mol of alcohol. At balance $K = \dfrac{x^2}{(1 - x)(r - x)}$. This is the quadratic $(K - 1)x^2 - K(1 + r)x + Kr = 0$, and the root below 1 is the one we want.

Your tasks.

1. Complete ester_fraction(r, K).
2. Complete ester_mass(acid_mol, r, K, molar_mass).
3. Complete least_alcohol(target, K) so that it returns the smallest whole number of moles of alcohol that gives at least the target fraction.