we've learned about many different ways to express concentration but just like any other method of measuring and Reporting values we like neat and tidy values without lots of decimal places or extraneous exponents that's why we come up with conventions like the pH scale so that we can report hydronium concentrations which are typically tiny numbers with inconvenient exponents in a way that display a value that is equal to a small integer like seven it's easier to compartmentalize and rationalize that way this is why we need special ways to report concentrations that are extremely tiny but still relevant to our health and daily lives for example there are pollutants in our air and drinking water that can be harmful in even minuscule amounts concentrations that are so small that they barely register when measured in terms terms of marity or other conventional concentration units that's why we invented parts per million and parts per billion abbreviated as PPM and ppb respectively if a solute is present in a concentration of one PPM that means there is one gram of that solute for every 1 million grams of solution and one ppb would mean one gram of solute for every one 1 billion gr of solution for example sulfur dioxide is a pollutant in our atmosphere that can cause acid rain let's say at a particular time the concentration of sulfur dioxide in the atmosphere is 2 PPM what volume of atmosphere would contain one gram of sulfur dioxide if the density of the atmosphere is 0.0012 G per cubic ctim well if the concentration is 2 PPM then there are 2 G of sulfur dioxide in 1 million gram of air which means one gram of sulfur dioxide would be contained in half a million grams of air so what volume of air has a mass of 500,000 G well 500,000 gtimes 1 cubic cm over 0.0012 G gives us a volume of 4.17 * 10 9B CM if we were to convert this to cubic meters that would be about 4,170 this corresponds to a cubic area of atmosphere with a side length of around 16 M which is longer than a school bus to give just two gam of sulfur dioxide which is barely more than the mass of a cotton ball we can see how this tiny concentration would be inconvenient and even misleading to express in terms of normal concentration units which is why we have PPM and ppb to turn to when we look at lead concentration in our drinking water 15 ppb is the maximum level before precautions must be taken 15 is a convenient number to report and discuss whereas if this were expressed in a mass volume percentage or any other concentration unit we've learned the value would be inconvenient and ineffectual and now we know how to report concentrations in a wide variety of ways