Calculating Concentrations in ppm
At a well in a farming community in Guanajuato, the lab analyzes a glass of water and reports how many milligrams of nitrates it contains. But nobody drinks just one glass: the community uses thousands of liters a day. How do you go from what is in a small sample to what is in the whole well? With parts per million and a very simple calculation.
What a concentration in ppm tells you
ppm stands for "parts per million": how many parts of contaminant there are for every million parts of the sample. To make it easy to use, units are chosen that give the same number:
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In water: $1\ \text{ppm} = 1\ \text{mg/L}$ (a liter of water weighs about 1,000,000 mg).
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In soil: $1\ \text{ppm} = 1\ \text{mg/kg}$ (a kilogram is 1,000,000 mg).
That is why the concentration in ppm is a ratio: milligrams of contaminant divided by liters (or kilograms) of sample.
If you double the sample at the same concentration, the mass of contaminant doubles, but the ppm do not change. That is what lets you scale up.
Calculating the ppm of a sample
When you know how much contaminant there is and how much sample you analyzed, you divide.
When the result does not come out exact, round to the place value you are asked for.
In a 4 L water sample from a river, 12 mg of nitrates were detected. Calculate the concentration in ppm ($\text{mg/L}$) and round to one decimal place.
In a 4 L water sample from a river, 12 mg of nitrates were detected. Calculate the concentration in ppm ($\text{mg/L}$) and round to one decimal place.
Calculating the mass of contaminant
Now the other way around: the lab reports the ppm and you want to know how much contaminant there is in a certain amount of water or soil. You multiply.
Notice that you must use the unit that fits: liters for water, kilograms for soil. If the sample comes in grams or milliliters, convert it first ($1{,}000\ \text{mL} = 1\ \text{L}$; $1{,}000\ \text{g} = 1\ \text{kg}$).
Scaling from the sample to the whole site
A small sample represents the whole plot of land or body of water if it is representative. Then the concentration is the same and the mass grows in proportion.
Interpreting an analysis has three steps: measure (calculate the ppm), compare with the limit in the regulation, and decide what to do. Here you focus on the first step and on going from ppm to mass.
A 2.5 kg soil sample was taken from a farmland plot, and the laboratory reported a concentration of 40 ppm of a heavy metal. Calculate how many milligrams of that metal…
A 2.5 kg soil sample was taken from a farmland plot, and the laboratory reported a concentration of 40 ppm of a heavy metal. Calculate how many milligrams of that metal the sample contains and, at the same rate, how many milligrams there would be in one metric ton (1,000 kg) of soil from the plot.