Trends in Alkane Boiling Points
Summary
Students will develop a mathematical model of alkane boiling points by graphing the number of carbons in the alkane chain against its boiling point. The data for carbons 1 through 10 are in their text book and in my attached Excel spread sheet. Students will determine the degrees of boiling point increase for each carbon added to the alkane chain.
If the graph is done by hand, students are directed to draw a linear regression and determine the linear equation. If the graph is done on the computer, students will find that a quadratic regression best fits their data, resulting in lower percent errors when they compare their extrapolation prediction from their graphs to the actual boiling points of longer alkane chains.
CollapseLearning Goals
This activity is is designed for students to determine the relationship between number of carbons in an alkane chain and its boiling point. Students will complete a mathematical regression on data, then use that equation to extrapolate beyond the range of data. Concluding the acitivity are percent error calculations that open the discussion of the dependability of their model and extrapolation.
Students will be critically thinking as they determine the best regression for their data and determine the reliability of their model.
Vocabulary to be reviewed: linear regression, mathematical model, percent error
Vocabulary to be discovered: extrapolation, quadric regresssion
Students will be critically thinking as they determine the best regression for their data and determine the reliability of their model.
Vocabulary to be reviewed: linear regression, mathematical model, percent error
Vocabulary to be discovered: extrapolation, quadric regresssion
Context for Use
This activity is written for a high school chemistry class involved in an organic unit. It is a self directed student activity that builds a mathematical model. The activity is adaptable to the equipment you have. The data can be graphed by hand and a linear best fit line drawn, and slope calculated from that. If computers are available, students can do multiple regressions, finding that a quadratic regression fits their data better... giving them lower percent errors when they extrapolate the data. Students would have already done graphs and linear models by hand and on the computer if available. Students would already know what an alkane chain is and how it is named. I think it would be very easy to adapt into any organic unit.
Description and Teaching Materials
Students will determine the relationship between the number of carbons in an alkane chain and its boiling point. The lesson is introduced after learning what alkanes are and building molecular models from ball and stick kits. I have a typed hand-out that explains the activity. Students have the option to graph by hand or on the computer. The teacher could decide that for the students in advance. When graphing by hand, students are limited to a linear regression. When graphing on the computer, students will find that a quadratic regression is a better representation of their data trend than a linear regression. The data are in their notebooks. I have included the data in the Excel spread sheet that shows both linear and quadratic analysis. For closure, we calculate percent errors of their extrapolated data to actual data of alkane chain boiling points beyond their data. Actual data is included in the typed assignment sheet for error calculations.
This activity is adapted from a text
Chemistry in the Community 5th Edition
W.H. Freeman and Company
page 228 Assignment hand out (Microsoft Word 156kB Aug23 07) Data and Mathematical Models: Linear and Quadratic (Excel 20kB Aug23 07)
This activity is adapted from a text
Chemistry in the Community 5th Edition
W.H. Freeman and Company
page 228 Assignment hand out (Microsoft Word 156kB Aug23 07) Data and Mathematical Models: Linear and Quadratic (Excel 20kB Aug23 07)
Teaching Notes and Tips
Common area's of confusion are putting units on slope and writing the equation with units. If this was not practiced in the past, you can use this as a lesson to teach that.
How much assistance your students need depends on how much time you have spent on mathematical regressions of data.
If this were to be done directly from the text, the students would only do linear regressions. I have found that a quadratic regression yields smaller percent errors when they extrapolate to determining the boiling points of alkane chains beyond 10 carbons.
How much assistance your students need depends on how much time you have spent on mathematical regressions of data.
If this were to be done directly from the text, the students would only do linear regressions. I have found that a quadratic regression yields smaller percent errors when they extrapolate to determining the boiling points of alkane chains beyond 10 carbons.
Assessment
Students will hand in completed analysis including their mathematical model (the equation). Students will estimate by hand reading their graph and by using their mathematical equation, and then completing an error analysis on their estimations.
To assess students' grasp of the data, I will give them a set of regressed data and ask them to identify the slope and the y intercept, and then to use the regression equation to predict. Lastly, the students will do an error analysis of their prediction.
To assess students' grasp of the data, I will give them a set of regressed data and ask them to identify the slope and the y intercept, and then to use the regression equation to predict. Lastly, the students will do an error analysis of their prediction.
Standards
9-12 I. B. 2,3,4