# Is K_c dependent on initial concentrations?

Dec 12, 2015

${K}_{C}$ is not dependent on initial concentrations because that's not how it is defined. It is only for equilibrium concentrations.

The constant for initial concentrations (or "current" concentrations) is reserved for the Reaction Quotient $Q$, the not-yet-equilibrium constant. It is defined precisely the same way as ${K}_{C}$; just replace $Q$ with ${K}_{C}$ and note that the concentrations are the initial concentrations at the time.

Suppose we have this general reaction:

$\textcolor{g r e e n}{2} A + B r i g h t \le f t h a r p \infty n s \textcolor{g r e e n}{3} C + \textcolor{g r e e n}{2} D$

It is always defined like this for this reaction:

$Q = \frac{{\prod}_{j} {\left[{P}_{j}\right]}_{0}^{\textcolor{g r e e n}{{\nu}_{{P}_{j}}}}}{{\prod}_{i} {\left[{R}_{i}\right]}_{0}^{\textcolor{g r e e n}{{\nu}_{{R}_{i}}}}}$

${K}_{C} = \left({\prod}_{j} {\left[{P}_{j}\right]}_{\text{eq"^color(green)(nu_(P_j)))/(prod_i [R_i]_"eq}}^{\textcolor{g r e e n}{{\nu}_{{R}_{i}}}}\right)$

where the $\prod$ symbol just means multiply the numbers that come after it, square brackets denote concentration (or if you know what activities are, use activities; no, I don't mean the activity series), $0$ means "initial", ${R}_{i}$ is each reactant of index $i$, ${P}_{j}$ is each product of index $j$, and $\nu$ is the stoichiometric coefficient.

So, you can write this as:

$Q = \frac{{\left[C\right]}_{0}^{\textcolor{g r e e n}{3}} {\left[D\right]}_{0}^{\textcolor{g r e e n}{2}}}{{\left[A\right]}_{0}^{\textcolor{g r e e n}{2}} {\left[B\right]}_{0}}$

${K}_{C} = \left({\left[C\right]}_{\text{eq"^color(green)(3)[D]_"eq"^color(green)(2))/([A]_"eq"^color(green)(2)[B]_"eq}}\right)$