Students will be able to calculate the concentration of an acid or a base using titration data.

The molarity of an acid or a base can be derived from a balanced chemical equation, a mole ratio that compares the acid and the base, and titration data.

In the previous lesson students learned how to write neutralization reactions between acids and bases. In this lesson students build on that knowledge by learning how to identify an unknown concentration of a base using titration data.

This lesson aligns to the NGSS Disciplinary Core Idea of *HS-PS1-7: Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction*. It does this because students balance chemical equations as part of their titration problems.

It aligns to the NGSS Practices of the Scientist of *Using mathematics and computational thinking* because students need to conduct a series of math-based steps in order to derive the unknown concentration.

It aligns to the NGSS Crosscutting Concept of Cause and Effect: Mechanism and Prediction because students will better understand the neutralization reaction (an effect) by examining what is happening at the molecular level.

In terms of prior knowledge or skills, students should have an understanding of what a neutralization reaction is going into this lesson, as shown in this previous lesson. They should also understand how to derive the number of moles in a solution given the molarity and volume of the solution, as found in this lesson.

There are no special materials needed for this lesson.

10 minutes

**Do Now**: Students walk into class with this problem on the projection screen: In a liter of human blood there are 9 grams of salt. What is the NaCl molarity of human blood? Fun fact: adult bodies contain about 5 liters of blood. I reason this is a good warm-up activity because it recaptures the work with molarity that students have been working on over the past two classes, and molarity is a key part of today’s lesson.

**Activator**: I first ask a student to tell me what the NaCl molar concentration of blood is. A student notes that 9 grams of NaCl is equal to 0.154 moles, and so 0.154 moles divided by 1 liter is 0.154 M.

15 minutes

**Mini-lesson**: I begin the lesson by explaining to students that the rest of the unit is going to use everything we have learned so far in a process called titration. I then show this video to give a brief visual overview of what titrations are.

I then ask the class some questions, and students share out answers in an informal environment:

- What is a titration? (a controlled acid-base neutralization reaction)
- What is an indicator dye? (a dye that changes from clear to pink in color depending on whether the solution is acidic or basic)
- What is a burette? (a measurement tool that contains an acid or a base)
- What color are you trying to make the solution? (a light pink)
- What do you do when the solution becomes light pink? (take a reading from the burette)
- What is the significance of the light pink color? (the moles of acid equal the moles of base; the solution has been neutralized)

I then explain how to figure out the unknown molarity based on the information gathered. I use a titration graphic organizer and fill it in as I go through the steps. Step 1 is to have a balanced chemical equation for the neutralization reaction. Step 2 is to figure out how many moles of the known chemical you have using the molarity formula. I emphasize that the known chemical (acid or base) is the chemical that lists a volume and a molarity. Step 3 is to use a mole ratio to figure how much of the acid or base is needed to neutralize the other. Step 4 combines the answer from Step 3 with the volume from the problem into the molarity formula. While giving this information students copy down what I am showing them with my document camera.

**Guided Practice**: I then ask students to use this model example from the mini-lesson to attempt the first problem in the Titration Practice Problems. This allows students the chance to see what they understood and retained from the mini-lesson, and it also starts students on the journey of learning this material. Only by doing practice problems, I reason, will students really learn how to do them.

After the class has struggled with the problem, I reteach at a faster pace, using the graphic organizer again. I call out for ideas from the class about how to solve the problem so that my voice is not the only voice leading class.

25 minutes

**Student Activity**: Once the class has worked a problem together, I ask them to work on the remaining Titration Practice Problems. I explain that that they will ultimately need to be able to solve this type of problem independently and without notes, but for now they should use both of these resources as needed.

I want students doing this work because I know that the best way to learn how to solve titration problems is for students to work the problems and discuss their misunderstandings and mistakes as they go.

While students are doing this work I walk around the room in the role of coach. If I see a mistake, I offer suggestions about what is wrong. I answer student questions, and I offer words of encouragement. Students are free to check their answers against the Titration Practice Problem Answers which are posted around the room.

**Catch and Release Opportunities**: This walking around also has another purpose. I learn what I need to do to efficiently support the class as a whole. My class sizes are too large for me to have the luxury to engage in a 5-minute conversation with each student. Rather, I take what I learn from observing student work and I spend a few minutes re-teaching the whole class, as shown in this teaching video. This serves as reinforcement for some students, and re-teaching for others.

This time also serves as a chance for students to stop working on problem solving and instead try to make connections between the different steps. In this discovery video a student does just that--he realizes the importance of a mole ratio and a balanced chemical equation in the titration problem process.

10 minutes

To wrap this lesson up I first explain where we are heading as a class—why does this work matter. My explanation is captured in this video called Clear Expectations. I then discuss the character strengths and weaknesses that I observed in class today in this video called Growth Mindset. I love how a student thanks me for offering him respect because he struggled with material that was difficult. Finally, I give students a Titration exit ticket so I can see how they are doing individually.

This work reveals a few things that will help me focus in the next lesson. Exit ticket 1 shows that I need to keep reiterating the importance of converting ml to L. Exit ticket 2 shows that some students still do not know how to set up the problem. Perhaps I need to show them that paying attention to units is a good way to get at this challenge. Exit ticket 3 is struggling with setup as well, but also I see that the student does not know how to solve the math involved (0.45 x 0.45 does not equal 0.0045). Finally, Exit ticket 4 shows that while this student knows how to set up the problem, they do not know what to do mathematically. All of these challenges will be addressed in the next class.

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