$K_{aw}=H^{\text{'}}=\frac{C_a}{C_w}$

$K_{sw}=K_d=\frac{C_s}{C_w}$

$K_{\text{b}\text{i}\text{o}\text{t}\text{a}}=\frac{C_{\text{b}\text{i}\text{o}\text{t}\text{a}}}{C_w}$

where $K_{aw}$ is the air$-$water partition coefficient $[-],C_a$ is the concentration in the air $[m\frac{g}{L}],C_w$ is the concentration in water $[m\frac{g}{L}],K_d$ is the soil$-$water partition coefficient $[\frac{L}{k}g],C_{\text{s}\text{o}\text{i}\text{l}}$ is the concentration in the soil $[m\frac{g}{k}g],K_{\text{b}\text{i}\text{o}\text{t}\text{a}}$ is the biota$-$water partition coefficient $\frac{L}{k}g,$ and $C_{\text{b}\text{i}\text{o}\text{t}\text{a}}$ is the concentration in biota $m\frac{g}{k}g.$ The equation for the total mass of a chemical in the unit world is given by:

$M_T=C_w{V}_w+C_{\text{s}\text{o}\text{i}\text{l}}{M}_{\text{s}\text{o}\text{i}\text{l}}+C_a{V}_a+C_{\text{b}\text{i}\text{o}\text{t}\text{a}}{M}_{\text{b}\text{i}\text{o}\text{t}\text{a}}$

where $M_T$ is the total mass $[$mg$]$ of the chemical constituent in the unit world, $V_w$ is the volume $[$L$]$ of water, $M_{\text{s}\text{o}\text{i}\text{l}}$ is the total mass $[kg]$ of soil, $V_a$ is the volume $[$L$]$ of air, and $M_{\text{b}\text{i}\text{o}\text{t}\text{a}}$ is the mass of biota $]$ in the unit world. Equations $(1),(2),(3),$ and $(4)$ can be combined and solved for $C_w$ to get:

$C_w=\frac{M_T}{V_w+K_d{M}_{\text{s}\text{o}\text{i}\text{l}}+K_{aw}{V}_a+K_{\text{b}\text{i}\text{o}\text{t}\text{a}}{M}_{\text{b}\text{i}\text{o}\text{t}\text{a}}}$

Using equations $(1),(2),(3),$ and $(5),$ the concentrations in all of the compartments can be calculated if the partition coefficients and the masses or volumes of the compartments are known.

In this exercise, you will calculate chemical concentrations in the various compartments when given values for the partitioning coefficients, volumes or masses of the compartments, and total mass of chemical. All variables on the right side of equation $(5)$ should be defined as input variables, and the concentrations $Cw,Ca,$Csoil, and Cbiota will be defined as functions of the other variables, and calculated.

Procedure:

Define input variables for the partitioning coefficients, volumes or masses of the compartments, and total mass of chemical; Calculate the concentrations in each of the environmental compartments by first solving equation $5$ for $Cw$ and then rearranging equations $(1-3)$ to solve for Ca$,$ Csoil, and Cbiota.

Test your formulas by inputting $1$ for all input variables. The output for all concentrations should be equal to $\frac{1}{\text{\#}}$ of compartments.

If file does not work correctly, debug. Otherwise continue with remaining steps.

Input partition coefficient values, appropriate values for compartment sizes, and total mass.

Assume that $60kg$ of hydrochloric acid and $10kg$ of sodium hydroxide are spilled onto a volume of soil containing $1,000$ L of water, $1,000$ L of air, $4,000$ kg of soil and $0\mathrm{.}005kg$ of biota. Given the known parameter values for $HCl$ and NaOH given below, answer the following questions.

Data Analysis and Questions:

How much of the total mass of $HCl$ is present in each of the four compartments: water, air, soil, and biota? Present your answer as $kgHCl$ in each compartment.

How much of the total mass of NaOH is present in each of the four compartments? Present your answer as kgNaOH in each compartment.

$\backslash$table$[[HCl,$NaOH