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Practices of Science: “Parts per” notation

NGSS Science and Engineering Practices:

NGSS Crosscutting Concepts:

NGSS Disciplinary Core Ideas:

“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.


 

Question Set: 
  1. How much salt and pure water would you need to make 1000 mL of saltwater at each of the following salinities?
    1. 10 ppt
    2. 5 ppt
    3. 35 ppm
    4. 35 ppb
       
  2. A government agency recommends that the amount of arsenic in drinking water should not be above 0.01 ppm. At this concentration, how many grams of arsenic would you expect to find dissolved in 1000 mL of pure water?

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Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawaii, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.