Students will be able to use hydronium and hydroxide concentrations to calculate pH.

The pH is derived from the negative log of hydronium concentrations and the pH of bases can be found from adding the log of hydroxide concentrations to 14.

In this lesson students will learn how to convert hydronium and hydroxide ion concentrations into pH using the log function on their calculators.

This lesson does not align to an NGSS Disciplinary Core Idea; NGSS does not have a unit dedicated to acids and bases. Nonetheless, I do believe this unit is important for a number of reasons. First, it corresponds to Massachusetts Chemistry Framework 8.2, which asks students to “relate hydrogen ion concentrations to the pH scale and to acidic, basic, and neutral solutions.” In addition to complying with my state standards, I also believe that it is important to teach students this material because acid-base theory is an integral part of chemistry. Students will see this material in college and so for these reasons I include this unit in my introductory chemistry course.

This lesson aligns to the NGSS Practices of the Scientist of Using mathematics and computational thinking because students will need to grapple with using a calculator to derive pH’s from ion concentrations.

It aligns to the NGSS Crosscutting Concept of *Scale, Proportion, and Quantity: Using the concept of orders of magnitude allows one to understand how a model at one scale relates to a model at another scale*. Knowing the concentration of hydronium and hydroxide concentrations is useful when using stoichiometry, but in every day usage the pH scale was derived as a more practical tool for assessing the acidity or alkalinity of a substance.

In terms of prior knowledge or skills, students should at this point have an understanding of what acids and bases are; this material can be found in a previous lesson.

The only materials needed for this lesson are calculators.

10 minutes

**Do Now**: After settling into class students read the first paragraph on p. 417 of their textbook and answer questions 21-23 from the Acids and Bases Reading Questions. I reason this is a good way to start class because I want students to begin to introduce themselves to the work that we will be doing today. This page explains the meaning of pH and the relationship between exponents and pH.

**Activator**: After students have done this work I greet them and check in on the answers to these questions. The answers students share are in parentheses:

21. In addition to describing whether something is an acid or a base, what else does pH indicate? (the molarity of the H^{+} ions)

22. How does pH relate to molarity? (pH is a way of describing molarity)

23. What does the negative exponent indicate in this expression? 4.32 x 10^{-5} (that this number is a number less than 10)

15 minutes

**Mini-lesson**: Once students are comfortable that they understood the reading, I note that today is a good day to have patience and to help each other out as we grapple with converting between ion molarities and pH.

Before teaching students about logs and pH, I first want to contextualize what students are learning by relating these topics to topics students have experienced. Because pH and molarity can be fairly abstract concepts for many students, I believe that dedicating time to making the topics less abstract is an important first step in helping students understand the material.

I start the discussion by showing two beakers of water. One has several drops of food coloring in it, and the other is a tenfold dilution of the first beaker. I ask students to make observations about each beaker. They note that one is more colorful. I then discuss Kool-aid, in that concentration is based on how much powder you put in the water. A weak, lightly flavored Kool-aid is like my diluted beaker, and "sickly-sweet" Kool-aid is like my higher concentration beaker.

Acids and bases, I note, can also have different levels of concentration. When I buy acid from the chemical supply company, I get concentrated HCl, and it is 35% HCl, with the rest being water. I dilute it significantly with water before students use it so that the final concentration is about 3%.

I then discuss swimming pools. I ask students if they have ever had to test the pH of a swimming pool? A few students have, and I ask them to discuss it. They note that they use pH paper (litmus paper) and if the pH is too high or too low they have to add chemicals to the pool and wait before using it. At this point I note that pH is simply another way of expressing the H^{+} concentration in a substance. I remind them that acids typically give off an H^{+} in solutions.

I then explain that a pH value is calculated using a log. Most of the students do not remember how to calculate using logs, and so I first model how to do this using a calculator that I project using a document camera. On my calculator I enter 100 and then hit the log button, and get an answer of 2. As I do each of these steps I name explicitly what I am doing. If a student misses a step I backtrack and repeat the step. I then ask students to find the other logs and record them in the Log Practice sheet.

After they have had a chance to do this work, and we have discussed it, I then ask them to record a few notes. The notes can be seen at the bottom of the first page this student's work. I explain to them that to convert from ion concentration to pH, they simply need to find the log and multiply it by -1. I model this for the first problem, and then slowly release students to practice this skill using the pH Worksheet.

**Guided Practice**: For the log work and for the pH work, I ask students to do a problem or two and then check their answers. I have answers posted around the room so they can get up and check their work.

25 minutes

**Student Activity**: During the bulk of the class student grapple with the log sheet and the pH sheet. The classroom is buzzing with students grappling and trying to help one another. One of the biggest challenges students have is figuring out how to use their calculator. During this time I am walking around helping students. This using the calculator video shows how I support a student who is struggling with this challenge.

The other big mistake students make during this time is forgetting to multiply the log of the H^{+} concentration by -1, which is easily remedied by reminding them.

10 minutes

To wrap this lesson up I encourage students to keep wrestling with this challenge. Students are in very different places with this skill at the end of class. I encourage them to get help from me during my office hour, before school, or during lunch, but I suspect that many students will need additional help with this skill at the start of next class.

I remind students that there have been many things over the course of this year that seemed difficult and then became easy, and that this is no exception.

Ending class this way allows me to address both content and character skills that were the learning objectives for today’s class.