Chapter 16, Problem 10P

For the reaction:

$2A+B\iff C$

equilibrium can be expressed as:

$K=\frac{\left[C\right]}{{\left[A\right]}^2\left[B\right]}=\frac{\left[C\right]}{{\left[A_0-2C\right]}^2\left[B_0-C\right]}$

$\text{If }K=2M^{-1}$, the initial concentration of A $\left(A_0\right)$ can be varied. The initial concentration of B is fixed by the process, $B_0=100$. A costs $1/M and C sells for $10/M. What would be the optimum initial concentration of A to use such that the profits would be maximized?