Summary

In this lesson, students will be introduced to a base-10 logarithmic scale and use it to calculate pH from hydrogen ion concentration. Often students are able to calculate pH by pushing the correct buttons on their calculators, but they don’t understand what the values mean. This lesson attempts to bridge that gap using a guided inquiry model.

Grade Level

High School

NGSS Alignment

This lesson will help prepare your students to meet the performance expectations in the following standards:

• Scientific and Engineering Practices:
  • Using Mathematics and Computational Thinking

Objectives

By the end of this lesson, students should be able to

• State to purpose of using logarithms to express pH.
• Estimate pH value from hydrogen ion concentrations using knowledge of logarithms.
• Using a calculator, compute pH from hydrogen ion concentrations and vice versa.
• Classify a substance as acidic, basic, or neutral based on pH or hydrogen ion concentration.

Chemistry Topics

This lesson supports students’ understanding of

• acids and bases
• pH and pOH
• acid/base theories
• logarithms
• concentrations

Time

Teacher Preparation: 5 minutes

Materials

• Copies of student handout (1 per student)
• Copies pre-quiz and post-quiz number values (1 per group; optional)
• Scientific or graphic calculators

Safety

• No specific safety precautions need to be observed for this activity.

Teacher Notes

• Students should be introduced to various theories of acids and bases, such as Arrhenius, Bronsted-Lowry, and/or Lewis, as well as the autoionization of water before completing this lesson. They should also be able to understand that H⁺ and H₃O⁺ can be used interchangeably.
• Though I prefer to use this lesson as a group activity, it may also be used as an individual or whole-class activity.
• In my experience, student math levels vary within a class. I suggest surveying the class by asking who has used logs in math class. I then group those kids together and group together the ones who have never heard of logs. The ones who have already been introduced to logs get through the activity quickly, but get stuck on the significant figure portion of it. I spend most of my time facilitating the groups for which logs are a new topic. The practice problems offer an opportunity for students to figure out which equations to use in order to solve for the unknown. In some cases, there are various pathways to the correct answer.
• Suggested values for the pre-quiz (in order, so mix them up when written on the board/sharing with students): 7.89 x 10 ^-9, 9.5 x 10^-8, 5.8 x 10 ^-5, 6.45 x 10^-5, 0.00089, 7 x 10^-3, 0.0995, 8.4 x 10 ^-1. Instead of writing them on a part of the board that can be covered, you could also write them on sheets of paper that get distributed to each group. The teacher should time each group when they raise their hand (and compare this with the time it takes for the post-quiz). Values for post-quiz (in order, so mix them up when written on the board/sharing with students): 0.08, 1.002, 2.2, 3.05, 4.190, 4.24, 7.02, 8.10. The teacher should also time the groups with putting these values in order. The pre and post quizzes should be done at the same time for the entire class.
• Be sure to look at each student’s calculator and explain how to enter log/antilog on it. (This is entered on most graphing and scientific calculators similarly; older versions sometimes differ.)
• For lower level classes, leave off the significant figure portion. Have students report all pH values to 2 decimal places.
• A suggested extension activity: Write the following problems on the board and have students predict answers without the use of a calculator. Log 0.0001, -log 1 x 10^-13, log 0.05, log 6000, log 4000.
• Answer Key document is available for this activity.