“Parts per” notation is one way of expressing how much solute is in a solution. Common parts per expressions in aquatic science are parts per thousand (ppt), parts per million (ppm), and parts per billion (ppb). These expressions represent like units, such as grams per 1000 grams (ppt) or grams per 1000000 grams (ppm). For example, 35 parts per thousand salinity represents 35 grams of salt in 1000 grams of solution. Understanding parts per notation is useful when creating solutions. The following equation is for a 35 ppt salinity solution containing 35 grams of salt per 1000 grams of saltwater.
A scientist wants to make 400 mL of 35 ppt saltwater. The scientist must determine how much salt and how much water to use to make this solution. The density of pure water is approximately 1 g/mL, so the mass of 1 mL of water is 1 g. Thus, 400 mL of solution will have a mass of 400 g. In the following equation, the scientist solves for x to determine the amount of salt in grams needed to make 400 mL of a solution of 35 ppt.
Cross-multiplying the fractions gives
Multiply the values and cancel the units on each side of the equation, giving
So, the scientist needs 14 grams of salt to make 400 g of 35 ppt saltwater. However, the total mass of the solution is 400 grams. To calculate the amount of water needed
To make 400 grams of 35 ppt saltwater, the scientist will need to dissolve 14 grams of salt in 386 grams of water.
Updated March 30, 2020 By Kevin Beck Reviewed by: Lana Bandoim, B.S.
Parts per billion (ppb) and parts per million (ppm) both measure very small concentrations of substances. Scientists convert from ppb to ppm sometimes, because some substances can exert noticeable and even drastic effects on the human body and other biological systems, such as plant life, even in extremely low concentrations.
This means that an element or molecule can be hopelessly outnumbered in its chemical environment and still require careful monitoring. As a result, highly sensitive devices to measure concentration have been developed to ensure the ability to accurately measure very small absolute changes in concentration.
Since a billion is a thousand times a million, or three powers of ten (1 × 103) greater in magnitude than a million, one part per b_illion (1/1,000,000,000) is one thousand times less than one part _per billion 1/1,000,000). But both units crop up in a wealth of situations, typically related to the assurance of public health and safety.
When dealing with ppm and ppb values, be sure you know exactly what "parts" are involved. This is because the units can vary from situation to situation and usually depend on the physical state (solid, liquid or gas) or the substance being monitored.
For gases, measuring mass is possible but makes little practical sense. So the parts per million formula for gases within other gases (usually air) is a volume-to-volume relationship, e.g., millionths of a liter (microliters) per liter or μL /L. And ppb may be expressed as nanoliters per liter or nL/L.
For liquids, one part in mass per million or billion volume units is typical, so ppm is often expressed as milligrams per liter; this follows from a milligram (mg) of water having a volume of one microliter (μL), as many liquids are close to this density, and the comparison is in effect a volume-to-volume relationship, as with gases.
The parts per million formula for solids within other solids is a mass-to-mass ratio, e.g., μg/g or mg/kg both represent ppm. (You might experiment with division and multiplication of these quantities using exponents to reinforce the underlying math.)
The ppm-to-ppb conversion can be tricky if you are used to thinking of a billion as more than a million and significantly so (millionaires get little public attention these days, but billionaires tend to attract plenty). Because ppm and ppb are actually fractions when expressed as numbers, and the "million" and "billion" go in the denominator, so ppm needs to register in your mind as being a thousand times greater in concentration than ppb (regardless of the specific units used).
A number called the MCL, or maximum contamination level, represents the highest value that can be considered safe. It is often expressed as ppb (or μg/L) or ppm (or mg/L). Many common substances have MCL levels in the general range of one of these units.
The metal arsenic, for example, which can taint fish and other wildlife, was assigned an MCL of 0.010 ppm (or 0.10 mg/L) in the United States in the early 21st century, with the standard taking effect in 2006. Multiplying this value by 1,000 to get ppb, yields 10 ppb (or 10 μg/L). Another substance with potentially hazardous health effects, the element beryllium, has an even lower MCL than does arsenic, 0.04 ppm.
Another way to think of parts per million: If this were the concentration of space aliens in New York City, there would only be about eight of them secreted throughout all five boroughs and 300-plus square miles!
Now the #"moles of solute"# are a constant. The volume of solution MAY change substantially with increasing or decreasing temperature. In some calculations #"molality"# is used in preference, which is defined by the quotient.... #"molality"="moles of solute"/"kilograms of solvent"# ....this is temperature independent, and at lower concentrations, #"molarity"-="molality"#.
To get the molarity, you divide the moles of solute by the litres of solution. #"Molarity" = "moles of solute"/"litres of solution"# For example, a 0.25 mol/L NaOH solution contains 0.25 mol of sodium hydroxide in every litre of solution. To calculate the molarity of a solution, you need to know the number of moles of solute and the total volume of the solution. To calculate molarity:
EXAMPLE: What is the molarity of a solution prepared by dissolving 15.0 g of NaOH in enough water to make a total of 225 mL of solution? Solution: 1 mol of NaOH has a mass of 40.00 g, so #"Moles of NaOH" = 15.0 cancel("g NaOH") × "1 mol NaOH"/(40.00 cancel("g NaOH")) = "0.375 mol NaOH"# #"Litres of solution" = 225 cancel("mL soln") × "1 L soln"/(1000 cancel("mL soln")) = "0.225 L soln"# #"Molarity" = "moles of solute"/"litres of solution" = "0.375 mol"/"0.225 L" = "1.67 mol/L"# Some students prefer to use a "molarity triangle".  It summarizes the molarity formulas as #"Moles" = "molarity × litres"# #"Molarity" = "moles"/"litres"# #"Litres" = "moles"/"molarity"#
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What is the concentration of a chemical in ppb If 0.12 mg of it is found in 392 kg of solution your answer should have two significant figures?
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