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CAST---Module 5A: More on Interactive Animated Excel ©Pittsburgh Supercomputing Center Page 1 Module 5A More on Interactive Animated Excel: The Boyle’s Law Simulator This module will introduce the interactive features available in Excel by constructing a multivariable simulation of Boyle’s Law. Boyle’s Law is the classic inverse relationship between pressure, P and volume, V of a trapped amount of gas at constant temperature, so mathematically PV = k, where k is constant. It finds itself introduced in chemistry, physics, and general physical sciences plus it is the basis of air exchange in the lungs. It is a simple experiment to perform with a syringe and pressure probe. The objectives for this module: To construct a multivariable simulation to help you become a model builder To introduce the use of the forms tools and if statements To demonstrate how errors influence power regression results To strengthen your computational skills and use naming variables To show how a simulation can extend a simple laboratory experiment and its data analysis Let’s construct this spreadsheet by setting up the worksheet to simulate Boyle’s Law. Since Boyle’s Law is part of the Ideal Gas Law, PV = nRT, we see that k = nRT and we have two variables (n is the amount of trapped gas in moles, R is the gas constant, and T is Kelvin temperature) normally held constant that can enter our simulation. The other two variables, noise and V tubing are errors and will be discussed later. We are assuming you have completed modules 2 and 3. Constructing the basic simulation Boyle’s Law holds if temperature (T) and the amount of trapped gas (n) are constant or considering the Ideal gas law: PV = nRT where R is the gas constant (0.0821 L-atm/mole-K). We want to create a column of volume data for a syringe and then we will calculate the pressure as: PV = k k nRT P = = V V Now we have two more variables to change to see how they influence the pressure and change the graph.

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CAST---Module 5A: More on Interactive Animated Excel ©Pittsburgh Supercomputing Center Page 1

Module 5A More on Interactive Animated Excel: The Boyle’s Law Simulator

This module will introduce the interactive features available in Excel by constructing a multivariable

simulation of Boyle’s Law. Boyle’s Law is the classic inverse relationship between pressure, P and

volume, V of a trapped amount of gas at constant temperature, so mathematically PV = k, where k is

constant. It finds itself introduced in chemistry, physics, and general physical sciences plus it is the basis

of air exchange in the lungs. It is a simple experiment to perform with a syringe and pressure probe.

The objectives for this module:

To construct a multivariable simulation to help you become a model builder

To introduce the use of the forms tools and if statements

To demonstrate how errors influence power regression results

To strengthen your computational skills and use naming variables

To show how a simulation can extend a simple laboratory experiment and its data analysis

Let’s construct this spreadsheet by setting up the worksheet to simulate Boyle’s Law. Since Boyle’s Law

is part of the Ideal Gas Law, PV = nRT, we see that k = nRT and we have two variables (n is the amount of

trapped gas in moles, R is the gas constant, and T is Kelvin temperature) normally held constant that can

enter our simulation. The other two variables, noise and Vtubing are errors and will be discussed later.

We are assuming you have completed modules 2 and 3.

Constructing the basic simulation

Boyle’s Law holds if temperature (T) and the amount of trapped gas (n) are constant or considering the

Ideal gas law: PV = nRT where R is the gas constant (0.0821 L-atm/mole-K). We want to create a column

of volume data for a syringe and then we will calculate the pressure as:

PV = k

k nRTP = =

V V

Now we have two more variables to change to see how they influence the pressure and change the

graph.

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When you do this experiment it can be difficult to hold the syringe at constant volume especially at high

pressures. So let’s add some random error to the volume measurement. This will be done by the

equation below, where “noise” is the random variation in the volume data:

'V = V + noise*(RANDBETWEEN(-10,10)/10)

The “noise” varies from 0 (no error) to some positive value that is multiplied by a random number

between -10 to +10 using the RANDBETWEEN function in Excel.

Another error in this experiment is due to the tubing connecting the syringe to the pressure gauge or

other measuring device. The tubing adds some extra volume that is not accounted for without applying

a correction. So let’s add this in to the equation for volume above and convert it to liters. To get:

'tubingV = (V + noise*(RANDBETWEEN(-10,10)/10) + V )/1000

The final calculation of pressure then becomes:

tubing

nRTP =

((V + noise*(RANDBETWEEN(-10,10)/10) + V )/1000)

Now we have four variables to adjust in this simulation. Okay to the spreadsheet…

Set up the worksheet to look like the screen shot below. If you use the same cells as illustrated here, all

the formulas will be the same as we work through this module.

Now we need to place a formula to

calculate in cell B5. To make the formula

look more like a real formula and not

spreadsheet notation, let’s name the

variable. Go to the Formula tab and

select Define Name and then Define

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Name… again. This will open the New Name pop-up menu. Click on D2 and the “n” will appear in the

name box as seen below.

Repeat this process for the other variables. Click

on F2, I2, and then K2 to get the four variables

named.

A named variable is automatically made an

absolute reference. It will keep its cell reference

on dragging down a formula. See absolute

reference for more information.

To compose the formula to calculate the pressure, click on cell B5. In B5 start the formula with an equal

sign and type this (you can get the variable by clicking on the appropriate cells):

=n*0.0821*T/((A5+noise*(RANDBETWEEN(-10,10)/10)+Vtubing)/1000)

After typing the formula in, click on B5 and then the formula bar (see below). Notice the colors of the

boxes around the cells that appear and the variable names in the formula bar.

Here is another way of showing how the calculation is done using the variables. This uses the Formula

Auditing tools on the Formula tab.

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Now drag the formula down the column to complete the calculation of pressures.

Set up a graph by highlighting the data to plot, go to the Insert tab and select Scatter. This is the only

plot in Excel where the x-variable is a numerical scale, all others are categories.

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Now select the “Scatter with markers only” plot type from the menu as

seen to the right. Your graph should appear.

If you click on the graph, it will highlight the data as shown below. Note the colors of the boxes that

highlight the x and y variables of the data to the left of the graph below. The x-data or V is purple while

the y-data or P box is blue.

With the graph highlighted, you will see the Chart Tools as three new tabs appear on the right end of the

ribbon bar (see screenshot of the ribbon bar on next page).

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You can add a trendline (power regression) from the Layout tab. This tab also allows you to label axes,

title, etc.

If you select trendlines (really regressions) and go to the bottom and click on More Trendline Option…

the Format Trendline menu seen to the right appears.

Select Power as the trendline option and select the display equation on chart and display R-square value

on chart too. If you move the Format Trendline menu from on top the graph, you can select through

the various trendline to explore fits.

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Now if you change one of the variables on row 2, the data recalculates, the graph adjusts, and the

regression recalculates as well. Wow, you built a simulation!

Adding the interactive features

Now we are going to add the ‘bells and whistles” to the simulation to increase the level of interactivity.

We will use the Forms toolbar from the Developers Ribbon (to get the Developer ribbon, see the

Developer’s Guide to Excelets for Excel 2010, 2007, or even 2003). Once the Developer tab is turned on

it remains on the ribbon bar on the right end.

The forms controls are under Insert on the Developer ribbon. We use the Forms Controls because they

operate on both PC and Mac platforms.

Now if you cursor over any of the tools they are identified. Find the scroll bar and then click on it. Move

to the worksheet just under the yellow temperature cell then click and drag to the right (this sizes the

scroll bar).

When you release the click, the scroll bar will appear

in the box. Now right click on the scroll bar and go

to the Format Control... Click on it.

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When the Format Control menu pops us, click in the box

labeled cell link and then click on the yellow cell next to T =

(the cell reference will appear in the cell link box).

Now we need to set the minimum and maximum values for the temperature scroll bar.

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We will use a range of Kelvin temperatures from 250K to 1000K. Click in the appropriate box and set the

values.

For all the forms tools, the minimum and maximum values and incremental change must be whole

positive numbers. Hence to get the forms tools to control values that are negative values and/or

decimals, we must write a formula.

First let’s copy the original scroll bar for temperature and paste it two cells below each of the other

variables (this maintains the same size for all four scroll bars). Notice that the color of the temperature

has been changed as well since this is now a cell controlled by a scroll bar and not one for typing in!

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Now to get the scroll bar to control “n =”, right click and select Format Control… Link in the cell link box

and reset the cell to the cell right below the yellow “n =” cell. Reset the minimum and maximum values

too.

Once you have set the control click OK.

Then go to the yellow cell, D2 and enter

this formula:

=D3/100000

Press the enter key and you should see

the value when the scroll bar is set to 50:

=0.0005

This value of n = 0.0005 moles is for a volume of 12.3mL trapped air in a syringe at 298K and 1.0 atm.

Now repeat this process for the other two remaining variables, which are errors, as shown below.

For the noise variable:

For the Vtubing variable:

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Now reposition the scroll bars to cover the cells where they are linked and you are ready to simulate

with interactive tools.

Let’s add a comparison line based on the initial conditions of the simulation (n = 0.0005, T = 298, noise

and Vtubing both set at zero). To do this we will need to copy the P data and do a Paste Special of just the

values (we do not want the formula to copy). This data then

remains constant when other variables are adjusted. Copy and

Paste Special (green highlight on screenshot) the data into D5 (this

will hide it under the graph).

Next we will need a Check Box to allow the comparison data to be

plotted and moved on the plot out of sight. To get a Check Box, go

to the Developer ribbon and click on it in the Form Controls. Then

click on the worksheet, to the right of the graph, to place it.

Once placed, right click on the

Check Box, select Format Control…

and check the 3-D shading box and

click in the cell link box and then

click on the cell next to the box as

shown. You can click on the Check

box and edit the text. The Check

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box returns a true to the cell when checked and false when unchecked.

We will use this in combination with an “if statement” to control the position

of the comparison line. Go to cell E5 and add the following:

=IF($N$5=TRUE,D5,-10)

By placing the $ signs on N5 we have made this an absolute reference (it will remain N5 when we drag

the formula down the column). The if statement functions as follows- when N5 is true, the value of D5

will be placed in the cell, when N5 is false, the value of -10 will be placed in the cell. You should see this

by checking and unchecking the Check Box.

Next we want to plot this on the existing graph. First step is to lock the y-axis so the minimum remains

at zero. Go to the graph and click on the y-axis. When the Format Axis menu pops up, select Fixed for

the Minimum under Axis Options as shown below.

Now click on the graph and then right click and click on Select Data… in the pop-up menu. This will get

you the Select Data Source menu to pop up (see next page) where you click on Add.

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The Edit Series menu pops up and you can name the series, highlight the series x-values (volume) and

then the series y-values (the pressure data in column E). Be sure it looks just like it is shown here on the

Edit Series pop-up window below (watch the formatting of the Series X values and the Series Y values

boxes).

Click the OK button twice on the two menus. Now go to the graph and select the “compare” data on the

graph (may need to move cursor around the data points to get it). Double click to get the Format Data

Series and follow the series of screenshots below.

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Now you should have a smoothed dashed line with no markers. You can go to line color to change the

color.

Here is the final product, your Boyle’s Law Simulator with a 2mL tubing error to show how the

regression is influenced and shifts compared to the comparison line. The tubing error is a systematic

error while the addition of noise causes more scatter in the data about the curve and is a random error.

Can you think of questions to have your students investigate?

Resources for more information

Developer’s Guide to Excelets – http://academic.pgcc.edu/~ssinex/excelets

For more information on the Boyle’s Law simulator, see The Boyle’s Law Simulator: A Dynamic

Interactive Visualization for Discovery Learning of Experimental Error Analysis, which appeared

in Spreadsheets in Education 3 (1) 20-26 (http://epublications.bond.edu.au/ejsie/vol3/iss1/2/).

Derive the ideal gas law for observational behavior and Excel, see

http://academic.pgcc.edu/psc/chm101/ideal_gas/

More on the tubing error and how the correction is derived -

http://academic.pgcc.edu/~ssinex/PV_tube.xls

For more about random and systematic errors, see Investigating Types of Errors, which appeared

in Spreadsheets in Education 2 (1) Article 7 (http://epublications.bond.edu.au/ejsie/vol2/iss1/7/)

See the other CAST professional development modules at

http://www.psc.edu/index.php/cast/professional-development-program.