Adapted from “One in a Million” 03-2007 by D. D. La Pointe, Nevada Bureau of Mines and Geology
Elisabeth Price aaejprice@att.net
Dana Sue Kimbal, Newmont Mining
Originally from USGS activity in Global Change: http://interactive2.usgs.gov/learningweb/teachers/globalchange_change_lesson.htm
The concentration of an acid or base in water is given in terms of moles of hydrogen ion per liter or moles of hydroxide ion per liter, respectively. These concentrations are then expressed as pH, the negative logarithm of the hydrogen ion concentration in moles per liter. The activity models the concentrations, expresses the concentrations in moles per liter, then converts to the logarithm.
SKILLS: Estimating, Counting,
Calculating, Observing,
Recording, Investigating,
TIME:
Modeling, Scientific notation,
Logarithms
30 minutes
AUDIENCE: Teachers and students, grades 5 –
8, but may be especially useful for students of grades 9-12. The activity can be adapted for younger students but requires a good understanding of fractions, and decimals.
To model the concept of concentrations as moles per liter, convert to scientific notation, then take the logarithm of the value.
No special precautions.
Concentrations in chemical applications are often expressed as moles per liter. A mole is merely an observable quantity of a chemical that can be measured by volume or by weight, depending on the state of the material. For example, a mole of water weighs 18 grams and takes up 18 milliliters (mL) of volume. The concentration unit of moles per liter makes it easy for the person working with chemicals to make dilutions and to figure out reaction relationships (called stoichiometry).
For acids, the concentration takes on a special form called pH, defined as the negative logarithm of the hydrogen ion concentration, written as pH = -log[H + ] where the square brackets mean concentration in moles per liter. The logarithm is a mathematical interpretation of a number that is the number to which
10 must be raised to get the original number. For example, 10 * 10 = 100 = 10 2 . So, the number to which 10 must be raised to get 100 is 2. So, the logarithm of 100 is 2.
In order to most easily figure out pH, it is most convenient to express the hydrogen ion concentration in scientific notation in which any number is expressed as a number between one and 10 times 10 raised to the appropriate power. So, a hydrogen ion concentration of 0.001 moles per liter is written as 1 *
10 -3 . The pH is then the negative of the power to which 10 must be raised to get 10 -3 , or
–(-3), or 3.
The model will provide the opportunity to practice these relations.
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2 gallon bucket, so be prepared with another container to hold the overflow.
Gather the materials together.

There is a lot of variation in the estimation of the individual quantities which can be magnified so in the end the million grains of rice may not fit into a 5

The estimation steps provide the opportunity for students to consider variation in sampling, measuring, and results. This is a good opportunity for them to consider significant figures: when one million rice grains are measured out, is that one million one grains or one million one hundred thousand?
notation as 1 * 10 -1 . If this were a hydrogen ion concentration in moles per liter (where the

One 50 pound bag of small uniformly-sized grain such as rice, big enough to be counted quinoa represents the hydrogen ion and each grain of rice represents a liter of water), the pH would be 1. Very concentrated. Remove the individually.

A small amount of a small grain to represent the hydrogen ion.

10 small cups (2-oz bathroom cups are OK)

10 paper plates to keep grain in one place

2 clear plastic vials to hold 1000 grains

2 clear plastic cups (about 8 - 10 ounce)

2 clear plastic containers at least one half gallon
(a gallon sized plastic milk or juice jug with the non-rice particle.
4.
Then continue to have each group count out exactly 100 grains. Assign jobs: counter,
“quality control” checker, transporter, etc., depending on the number in each group. Again, add the non-rice grain to represent the hydrogen ion and express that grain as 1 in one hundred, expressed in scientific notation as 1 * 10 -2 . The pH would be 2, less concentrated hydrogen ion top cut off works fine)

Two large plastic containers such as plastic 5 gallon buckets with covers, for storage and final container. If measurements are done carefully, with a grain no larger than rice, one million concentration.
5.
Have the students return exactly 100 grains to the paper cup without dropping any.
6.
One person takes the 100 grains into a single clear plastic cup while the whole group keeps track of the total number of grains. If desired, should barely fit into a 5-gallon bucket, but it may take two.
1.
Engage students by discussing fractions, and then focus on decimal forms of the fractions.
Compare a couple of fractions to decide which one represents a larger quantity of material. For example, which is larger, 1/3 or 1/5; or 1/10 or
1/100?
2.
Divide class into ten groups of approximately equal numbers of members per group. Have each group guess how much space a million grains of rice will take up and record their guesses.
3.
Give each group a paper plate and a small paper cup with about ¼ inch of grain in it. Initially, have each group count out exactly 10 grains onto the plate. Then, add one grain of the smaller grain (such as quinoa) and identify that as 1 out of 10, 1/10 or 0.1. Express that in scientific time how long it takes to put all 10 groups of 100 into the cup. Students can calculate how long it will take to get a million grains if this process is repeated. Students can discuss ways to get to one million more quickly.
7.
A student now carefully levels, marks and labels the 1000 grain line on the outside of the plastic container with a grease pencil or permanent marker. Add (or set near the cup) the one grain of non-rice. Identify it as 1 in 1000, expressed in scientific notation as 1 * 10 -3 . What would the pH be? Is this more or less acidic than the previous step?
8.
Then, a student from each of the 10 groups comes up and fills the container to the 1000 line and dumps it into another plastic cup while the whole group keeps a careful record of the total number of grains. (10,000 grains should fit into an 8 - 10 ounce cup unless a larger grain size than rice or barley is used.) Write the concentration of one grain of the non-rice in the

whole mass, express in scientific notation, then as pH. Discuss the acidity.
9.
Students carefully level, mark, and measure the
10,000 grains. One student from each of the 10 groups dumps 10,000 grains into the larger clear container. (100,000 grains). Repeat the analysis of pH as above.
10.
Repeat the marking and labeling, and the final round of filling to the 100,000 line with the 10 groups, dumping into the 5 gallon bucket.
(1,000,000 grains). Again, repeat the analysis of pH.
1.
The relationship between the reaction of the hydrogen ion and the hydroxide ion to form water defines the relationship between the concentration of hydrogen and the concentration of hydroxide ions. HOH (or H
2
O) → H + + OH .
These two ions come together such that the concentration of one times the concentration of the other is always a constant (the dissociation constant) of 10 -14 . [H + ][OH ] = 10 -14 . When the concentrations of hydrogen ion and hydroxide ion are equal, the water is neutral, neither acidic nor basic. If the hydrogen ion predominates, then the solution is acidic. If the hydroxide ion predominates, then the solution is basic.
2.
What is the range of pH for an acidic solution?
For a basic solution?
3.
Have participants note instances when they have heard or used the measure of hydrogen concentration called pH.
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