3.4. Final Concentration Calculation

We are doing mass balance of A in the system, so the mass balance of A in the system is initial and what we did in the calculation in the last class for the partitioning, we are doing partitioning. The assumption in partition is when we say partitioning constant we are saying it is at equilibrium always so initial and then we are saying that at equilibrium the total amount of A is conserved nothing is happening to, it stays as it is. So what is the total amount of A initially is this is 100 kilograms, this is what you are adding into the systems. So, if 100 kilogram of A is present you are now putting into your system and then you are seeing where is this 100 kilogram distributed. So, 100 kilograms will now distribute into at equilibrium it’s in the system, so it will distribute into mass of A it it can distribute into mass of A in water plus mass of A in the solids. These are 2 it can distribute in these 2 phases.

In this chunk, we begin by defining our system concerning the chemical A and the total concentration. The initial amount of the chemical introduced into the system is set at 100 kilograms. This total is crucial as it helps us understand how the chemical will be divided among different phases in the system—namely, between water and solids. Importantly, we operate under the assumption of equilibrium, meaning the system will reach a point where the total amount of A remains constant while the chemical adjusts between the two phases (water and solids).

Think of a sponge placed in a bowl of water. If you pour a certain amount of dye over the sponge and water, initially, all the dye is on the sponge. Over time, some of the dye will mix into the water, and some may stay in the sponge. Eventually, the dye concentration in both the sponge and water will reach a balance that reflects the initial amount you added.

Now what is the mass of A in the water? It is concentration of A in the water at equilibrium we will call this as ‘Rho A2 e’ into volume of water plus ‘WA 3e’ into mass of the, now here is the tricky part here. ok. Now, this m3 depends on what is the definition of w3, ok. w3 is loading of A on solids, now for the reasons I just mentioned it is convenient this thing is, this definition which means that here I have to put w3 dash, alright, so what is the definition of w dash here we have theta is m2 divided by the moisture content, m3 dash, yeah, now we want the m3 dash in terms of the moisture content, ok.

This chunk highlights the calculation of the mass of chemical A in water at equilibrium. We introduce terms like ‘Rho A2 e’ and ‘WA 3e’ for clarity. The loading of A on the solids, labeled w3, plays a critical role in the calculations. The concept of loading is essential as it relates the amount of A in the solid phase to the totality of solids present (m3). We must carefully choose definitions concerning moisture content and how we reference solids in our calculations to avoid confusion.

Imagine a wet sponge again, this time soaked in colored water. The water's concentration of dye can change depending on how long you leave the sponge in the solution. The sponge (solids) holds some of the dye (chemical A), and the ratio of dye in the sponge versus the dye dissolved in the water represents the loading concept. You can visualize loading as the sponge's ability to hold dye; if it's very saturated, more dye will stay in the water than in the sponge.

Now we do the final calculation, 100 * Rho A2 = (10^3) * (1) + (10^4) * 500. You can check the calculation...

Here, we perform the final calculation using previously established parameters and values. This calculation will yield the concentration of chemical A at equilibrium in the water phase. By plugging in the numbers associated with the system's components, we can arrive at an answer that informs us of how much of chemical A has dissolved into the water compared to how much remains in the solids. We also need to gauge that this calculated concentration does not exceed the known solubility of the chemical, verifying the accuracy of our calculations.

Using a simple concept, consider a cup of sugar in water. You can keep adding sugar until it won't dissolve anymore. If you want to know how much sugar is in the water, you'll perform a calculation based on how much sugar you started with and how it has distributed between the dissolved state and the undissolved state at the end, observing whether your final measurement aligns with what you know about the solubility of sugar in water.

Rho A2 star at equilibrium is greater than Rho A2 star solubility,...so we now redo the mass balance,...

In this segment, we assess a crucial anomaly: if our calculated concentration of A in the water exceeds its known solubility, we recognize an inconsistency. The concept of mass balance mandates that the total initial mass of A must account for what is dissolved in the water and what remains undissolved as a pure chemical. Therefore, any concentration greater than the solubility indicates some of the chemical remains purely intact. Thus, we must revise our calculations to accurately reflect this relationship.

Returning to our sugar analogy, if we find that our calculations suggest we could dissolve more sugar than known solubility allows, something is wrong. Just like how sugar will settle at the bottom of a glass after surpassing its solubility in water, we recognize the presence of the undissolved sugar (the 'pure chemical' in our scenario), signaling the need to adjust our calculations.

In a real scenario what may happen... This is the worst, ok.

In this final chunk, we discuss potential real-world scenarios that could affect our calculations. Here, the focus is on how external factors such as continuous flow, changes in system volumes, and reactions with other substances can impact the distribution and concentration of A between phases. We analyze how these adjustments guide us in making systematic worst-case scenarios for effective environmental assessments.

Picture a large lake where a chemical spill occurs. Water flow, temperature changes, and sediment interactions illustrate how the initial calculations might shift over time. The concept of a 'worst-case scenario' comes into play because, while the chemical might momentarily behave predictably, factors such as ongoing flow, evaporation, or chemical reactions can alter how much of it ultimately remains dissolved in the water versus settled in sediments.

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