K, Q and the direction of change

You will write three functions that do the bookkeeping of an equilibrium.

The idea. For $\text{A} + \text{B} \rightleftharpoons \text{C} + \text{D}$, $K_c = \dfrac{[\text{C}][\text{D}]}{[\text{A}][\text{B}]}$. The same expression for any mixture gives $Q_c$. If $Q_c < K_c$ the reaction goes forward; if $Q_c > K_c$ it goes backward. Also, $K_p = K_c(RT)^{\Delta n}$.

Your tasks.

1. In quotient, return $Q_c$ for the four concentrations.
2. In direction, return "forward", "backward" or "equilibrium". Treat the two as equal if they differ by less than 0.1 %.
3. In kp_from_kc, return $K_p$, with $R = 0.0831$ L bar K$^{-1}$ mol$^{-1}$.