# Graphing Equilibrium Reactions

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## Objective

SWBAT interpret experimental data to identify when a chemical reaction reaches equilibrium..

#### Big Idea

Equilibrium can be determined as the point when the rates of the forward and reverse reactions are equal, or when the concentrations of the reactants and products becomes constant.

## Background

This lesson took place during PARCC testing.  As a result, the classes were shortened to 35 minute periods.  Due to the short period, this lesson bridged two full days in class.  It could likely be accomplished in one full 50 minute period.

After taking notes on equilibrium and practicing on reversible reactions the day before, I wanted the students to work with some reactions to round out their understanding prior to giving a quiz.

One of my co-workers found the original of this assignment last year, and it has been modified some to our local needs.  I can not give credit, as I don't know the originator, but would love to if someone reads this and can point me in the right direction.

This assignment allows me to continue to work with the students on their graphing skills (discovered during the Reversible Reactions lesson) while building a stronger understanding of equilibrium.  This lesson ended up taking nearly two whole days: one to graph and one to analyze the graphs and complete the conclusions.  Students who were absent the first day were directed to answer the questions purely based on the data as presented in the charts during the second day.

I generated the graph paper at Math-Aids.Com.  You can customize the paper in a lot of ways, which makes it an invaluable resource.

This is a heavily standards aligned lesson due to the graphing and data analysis:

• HS-PS1-6Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium.
• Science and Engineering Practice 2  Develop and use models.
• Science and Engineering Practice 4 Analyzing and interpreting data
• Science and Engineering Practice 5  Using mathematics and computational thinking
• High School Patterns Cross Cutting ConceptMathematical representations are needed to identify some patterns
• High School Stability and Change Cross Cutting Concept  Much of science deals with constructing explanations of how things change and how they remain stable
• High School Stability and Change Cross Cutting Concept  Change and rates of change can be quantified and modeled over very short or very long periods of time.

## Opener and Instructions

12 minutes

When students enter the room, I have written "What makes a quality graph?" on the whiteboard.

When students are in the room, I tell them we will be continuing our work with reactions reaching equilibrium today by looking at data sets from experiments.  We will be graphing the data, and want to improve on our graphs from the previous week.  I ask them to tell me what needs to be on a graph for it to be considered of high quality.

• Axes
• Scale
• Key for colors used
• Title
• Labels for each axis
• Data points

My senior students who have done a lot of graphing in economics this year really lead the discussion in each period.  Once we have generated the list, I leave it on the board and pass out the Equilibrium Reading and Graphing packet.

I ask students to read the front page, and give them 5 minutes to do so.

I ask what the purpose of this activity is, and students explain that we want to find out what happens to both the rates of the reactions and concentrations of chemicals when we get to equilibrium.

I ask what molarity is.  Students struggle, as this is the first time outside of lab they have encountered molarity.  If no one refers back to the text to provide the answer, I ask someone to read the first two sentence of the concentration section aloud.  After they finish, if no one will still explain it, I explain that it is simply the unit for concentration, or how much chemical is in the sample.

I remind students of the qualities of good graphs on the board, and tell them they can work with a partner and each make two graphs, or work alone and make all four.  I explain that they are responsible for analyzing ALL four graphs, but can work together on the task.

## Data Graphing and Analysis

23 minutes

At this point, I set out the colored pencils and markers, and pass out the Equilibrium Graphing paper so students can begin. The students are presented with four data sets.  The first set presents the rates of the forward and reverse reaction vs time.  The remaining three sets present the concentration of both a reactant and product versus time.

Most of the student questions are in relation to labeling and scaling the axes properly.  Some students need to be reminded that time is nearly always on the X-axis to help them get unstuck.

Students graphing the rate data have a difficult time with the decimals.  Many students insist that 0.085 is greater than .16, so throughout the day I had to reinforce proper number sense.  The best strategy I discovered was adding the third decimal as a zero to the other numbers, so that students compared 0.085 with 0.160 and could see the difference.  Unfortunately, we didn't arrive at this until the middle of the third class (of four).

Student graphs were much improved over the previous efforts, as seen in these two student examples.

There is still room for improvement, as partner #1 mislabeled the second graph as rate instead of concentration, and partner #2 did not label the graphs as concentration at all.  There are still some issues with number sense as the graphs are not smooth, but buck when they struggled with the decimals.  This was endemic to about 70% of the graphs my students made.  For this year, I decided to let it go since the remainder of the graphs, and the overall patterns were observable.

One of the reasons I really like this assignment is that graph 1 shows the rates MUST become equal to reach equilibrium, but that the concentrations in graphs 2-4 all become constant in different relationships at equilibrium.  In graph 2 the product is favored, in graph 3 the reactants and products are equally favored, and in graph 4 the reactants are favored.  This provides examples of all the various ways equilibrium can be presented graphically.

If students are working with a partner and do not finish the analysis by the end of the period, I collect all the work so if a partner is absent the following day, there is nothing missing.  Students who are working alone and need to complete multiple graphs may take their work home.

The following day students use their graphs and data tables to answer the analysis and conclusion questions.  I spend the day circulating the room to answer questions, listening to student discussion, and entering progress report codes while students work independently.

Below are samples of student answers for each section.  They are not perfect, but overall are indicative of how the assignment went in class.

Experiments 1 and 2

Experiments 3 and 4

Final summary