Check attached files for instructions.
Graphical Analysis Introduction: Graphs are often used to represent numerical observations (measurements). For example, consider the motion of a rocket. We could measure the distance that the rocket has traveled over time. If we made many measurements it would be difficult to analyze the meaning of the data. To understand the data, we could produce a graph that shows how the distance traveled depends on time. Consider the two graphs shown below and note their similarities and differences: Graph 1: · The title does not give much information about what the graph is showing. · The axes are labeled, but without units. Does the time show mean seconds or minutes or years? · Only a small portion of the graph paper is used. This bunches everything in one corner. · A straight line was not used as the line of best fit. Connecting the dots does not indicate whether there is a simple mathematical relationship between distance and time. Graph 2: · The title explains what is shown in the graph. · The axes are labeled with units drawn in parentheses. · Round numbers are used to give an idea of scale on both axes. The numbers follow a linear pattern and are regularly spaced. · Most of the graph area is used. · The data points are clearly shown with open circles. · The line of best fit is shown Linear Regression It is often necessary to make predictions or draw conclusions based on experimental data. Graphical analysis can often help in this goal. Consider the data shown in Table 1: Based on the pattern of this data we can estimate that at 50 seconds the distance should be 60 meters because the distance appears to increase by 12 meters every 10 seconds. However, this type of estimate is difficult to make with most sets of data. A graphical representation of the data can sometimes make the process of estimation easier. To predict the distance at 50 s we could draw a graph of the data shown in the table. In this graph we plot distance on the vertical axis and time on the horizontal axis (Graph 1). Notice that each point on the graph represents a paired set of data (one for distance and one for time). In the graphs that we will draw, it is always the case that each point on the graph corresponds to a paired set of data. One variable often depends on another. For example, the distance traveled depends on how long you have traveled. In this case, distance depends on time. In general, when one variable depends on the other, the one that is independent is drawn on the horizontal axis. The one that is dependent is drawn on the vertical axis. For Graph 1 we would say that it is a graph of "distance versus time" because distance is the dependent variable and time is the independent variable. To project the value of distance when the time is 50 seconds is made easier by drawing a straight line through all the points and extending it to 50 s. When we do this, we get Graph 2. By looking at the line, it is easy to see that at 50 seconds, the distance is 60 meters. The process of using a line to project the values of distance for given times is often called linear fitting. The line is drawn based on the actual data values. But where there are no data values, we can use the line to determine what they would be. In the data for Graphs 1 and 2, the line fits the data perfectly, meaning that the line overlaps with all the data points. This rarely happens with real experimental data. Usually, there is no line that perfectly fits over all the data points. So, we must draw a line that comes as close to all the points as possible. This line is often referred to as the line of best fit. The line of best fit can be drawn with a pencil and a ruler. Graph 3 shows the case in which there is no line that can perfectly fit all the data points. We draw a "line of best fit." Even though the line of best fit does not perfectly fit the data, we can still use it to project data values we have not measured. There is a mathematical analysis that can be used to calculate the line of best fit. It is not based on estimation with a pencil and a ruler. It is based on calculation and is called linear regression. The calculation is extensive and is usually done using computer software. Equation for a Line: The equation for a line is given by y = mx + b where y is the data that corresponds to the vertical axis, x is the data that corresponds to the horizontal axis, m is the slope of the line, and b is the y-intercept (the value of y when x is equal to zero). Sample Calculation: Suppose that a graph of distance versus time (y versus x) gives a slope equal to 10 m/s and a y-intercept equal to 5 m. If the distance is equal to 55 m what is the time equal to? For many of your future chemistry labs you will be required to input your data in Excel. Watch the following videos to learn how to produce a proper graph: Video: Creating a Line of Best Fit in Excel https://www.youtube.com/watch?v=d65jx4BhslA Video: Copy and Paste a Graph from Excel into Word 3 minutes and 33 s https://www.youtube.com/watch?v=Q-xVHilWJWs Procedure: All these steps are done in the first video, watch it before attempting the graph. Watch it again while doing the graph. Part 1: · Enter the values into Excel. Column 1 = time (minutes) Column 2 = CO Content micrograms Time (minutes) CO content (micrograms) 0 1320.25 8.50 1225.44 17.50 1183.90 34.50 1023.21 53.00 887.42 74.00 777.89 91.50 609.11 108.00 477.20 127.00 368.43 · Format the cells to have 2 decimal places. This is explained and done in the first video. · Produce a line scatter graph. · Label the x and y axis. x-axis = time (min)y-axis = CO content (micrograms) · Title the graph. Carbon Monoxide Concentration as a Function of Time · Add line of Best Fit Make sure to display the equation on the graph. · Format the axis using minimum and maximum bounds. x-axis = boundary: minimum 0.00maximum 130.00 y-axis = boundary: minimum 350maximum 1340 · At the end of the first video the removal of the grid lines is described. Just leave the graph in the default setting. Do not change the lines. · Copy and paste the graph into your lab report. The second video describes the process. · Using the line of best fit information from your graph determine how long it takes for carbon monoxide to reach zero concentration. Part 2: · Using the data below construct two graphs using excel. Use the previous graph as a model. · In the first graph plot volume (cubic inches) versus pressure(inHg). · In the second graph plot volume (cubic inches) versus 1/Pressure (inHg-1). You will need to calculate 1/ Pressure for each value of pressure. Keep three significant figures for each calculation. · Compare the two graphs. Only one of these graphs is suited to be used for a line of best fit. For only the graph that you decide is better for the best fit line, take the line of best fit. For the other graph leave it as is. · Copy and Paste both graphs into your lab report. Items to keep in mind when producing your graphs in part 2: · Appropriate title for each graph · What goes on the x-axis and what goes on the y-axis? · Units must be indicated on both x and y axis · For the second graph, you must physically do the math for the 1/pressure. For example, the first set has the pressure at 6.00 inHg. To obtain 1/pressure take 1 and divide by 6 which equals 0.167 inHg-1. · Modify the ranges on each axis as needed. Keep in mind your line must take up most of the space on the graph. · When deciding on the graph that should have the line of best fit, see which one would allow for more points to be close to the best fit line. Table of Volume and Pressure Data: Volume (cubic inches) Pressure (in Hg) 118 6.00 0.167 87 8.00 71 10.0 59 12.0 44 16.0 35 20.0 29 24.0 Lab Report: Part 1: Copy and paste your excel graph into a word document. Show the calculation used to determine how long it takes for carbon monoxide to reach zero concentration. Part 2: Copy and paste the Table of Volume and Pressure Data with all values transferred. Show the seven calculations for the last column. Copy and Paste both excel graphs.