Consider a simple $pH$ indicator dye that changes color with $pH.$ Let's suppose that our dye absorbs

strongly at a given wavelength at $pH12$ while it has essentially no absorbance at $pH2$ as shown in the

table below

dye concentration $pH$ Abs

$10$ micromolar $2,0\mathrm{.}00$

$10$ micromolar $12,0\mathrm{.}90$

At $pH7$ you observe the absorbance of your $10$ micromolar solution to be $0\mathrm{.}3$

Calculate the pKa to $2$ significant figures

You can assume that our dye is a simple monoprotic acid that is fully deprotonated at $pH12$ and fully

protonated at $pH2.$