Thermodynamics problem: You have a chemical that accumulates in blood and is excreted at a fixed rate. A man with a total blood volume of V (we assume that the chemical will only accumulate in the blood, so we do not consider the volume of other tissues and organs) and no initial chemical concentration in his blood is exposed to this chemical at a rate of ke = 90 ng/day. The chemical is excreted at a rate of 0.2 ng/day. The chemical can react with a certain metabolite, E, and in this process be converted into an inert chemical that can be effectively removed from the body. The reaction between the chemical and the metabolite E occurs with a rate constant krxn which has a value of 0.02 L/(ng*day). This reaction is irreversible. The metabolite E is initially present at a total mass of 100 ng, and it is produced at a rate constant kp = 10 ng/day. Finally, the metabolite E degrades with a rate constant kdeg = 0.1 ng/day.

Draw a diagram of the system, including all inflows, outflows, and reactions. (Hint: Remember, since we have two components in this system (the chemical and the metabolite), you need to specify which component each of the ins/outs/generation/consumption terms are affecting.) Then derive and simplify the the differential mass balance for this system:

dM/dt = ?

dE/dt = ?

where M represents the mass of the chemical in the blood (in ng), and E represents the mass of the metabolite in the blood (in ng).

Please explain your answer. Thank you