Five$-$gram samples of a low$-$organic$-$matter subsurface soil were equilibrated with $30-mL$ volumes of solution containing varying background electrolytes and initial concentrations $(c_{in})$ of the antibiotic chlortetracycline. The suspensions were equilibrated for $24h$ and the solid and solution phases separated by centrifugation. The solutions were then analyzed by HPLC for chlortetracycline to yield equilibrium concentrations $(($:$c_{eq}\}.$ The results are presented in the table below. Answer the following:

a$.$ On a single graph, plot the chlortetracycline adsorption isotherms for both the $10mMCaC{l}_2$ and $10mMKCl$ systems.

b$.$ For each isotherm answer the following:

i$.$ Fit the adsorption data with an appropriate adsorption isotherm model and generate the adsorption constants.

ii$.$ Examine the isotherms and the adsorption isotherm equations. The isotherms should indicate that chlortetracycline adsorption is a function of the background electrolyte.

Provide plausible explanations as to how the background electrolyte influences chlortetracycline adsorption.