When studying the environment, scientists and engineers draw from their extensive knowledge of the natural world to analyze pressing problems and offer solutions. Many of the tools in a scientist’s proverbial toolbox require an in-depth understanding of mathematics, physics, and chemistry to use. This is why an education in STEM takes years of persistence and hard work to complete (after all, the word “science” derives from the Latin verb “scire” – “to know”). Still, that knowledge is conquered one step at a time, and the basic concepts upon which science is built are accessible to everyone. In fact, some of the natural world’s most fundamental functions don’t require any knowledge of mathematics of physics at all to grasp.

One such concept is that of mass and energy balances. To understand what these balances entail, we must first discuss the law of energy and mass conservation. What this law boils down to is that energy cannot be created or destroyed in a closed system; it can only change form. But if that’s the case, how come we can generate energy at all? That is because we’re providing one form of energy to our closed system, say, a wind turbine, and converting it to another. That’s how we go from kinetic to electric energy, and from chemical to thermal energy. If you’ve followed so far,  you've understood the first law of Thermodynamics.

The same thing applies to mass: it cannot be created or destroyed, just removed from or placed into a closed system. Like energy, it can change forms, usually through a chemical reaction, but the sum total of the system’s mass remains the same (there is a notable exception when discussing nuclear reactions, but let’s leave that aside for now). The law of mass conservation basically means that the mass balance of a given system – say, a big container – is as follows:

(Mass Input) – (Mass Output)

=

(Accumulated Mass) - (Mass Produced from Reaction)

Now, let’s consider how these properties translate into the natural world by looking at a fairly common problem in environmental engineering: lake pollution. Let’s say the local government in a lakeside town keeps finding unsafe amounts of nitrate in water samples from the lake just out of town. The pollutant’s concentration appears to be increasing over time, which suggests that it’s accumulating – in other words, it’s being fed to the lake at a greater rate than it’s being removed. That is, of course, worrisome, as it can lead to eutrophication and even affect the quality of the town’s running water.

The local government conducts an extensive investigation to identify the source of the nitrate pollution. Their findings suggest that the extensive use of fertilizers in the town’s fields creates nitrate run-off that ends up in the lake, and the data suggest there is a specific rate at which this happens. The government also knows that some of the nitrate is constantly being removed from the lake as the water seeps into the soil and becomes groundwater.

Now, using the mass balance shown above, the municipality’s resident environmental scientist can calculate the rate at which the nitrate accumulates. This is important because it gives local leadership an estimate of how long they have to address nitrate pollution before its impact becomes severe. Or, to put it in a more politics-smart way, it lets the municipality know how much time they have before they are liable for hefty environmental fines.

This is only one out of countless examples of how scientists and engineers use mathematical models to tackle environmental issues. The process is also much more complicated than that: in truth, scientists take other factors into account, such as the way pollutants are absorbed throughout the food web, and create empirical equations to better model each system. Mass balances are only the foundation of a what is arguably one of the most complex and interconnected scientific fields. However, their simplicity lends itself to explaining environmental affairs to the public, which in turn serves to demystify the science involved and increase engagement.