__Experiment
1: Graphical Representation of Data__

A line graph shows the relation between two variables in the form of a curve. Graphs are often useful in determining the mathematical relationship between two variables. Line graphs are used to compare values of two variables using two orthogonal straight-line scales called axes. The vertical or y-axis is referred to as the ordinate, and the horizontal or x-axis is referred to as the abscissa. If we have two variables x and y, and y is a function of x, expressed as y = f(x), y is referred to as the dependent variable, and x as the independent variable. Values of y, the dependent variable, are plotted on the ordinate. Values of x, the independent variable, are plotted on the abscissa. When plotting experimental data one should be careful in choosing the appropriate variable and thus the appropriate axis. In general, the independent variable is altered in regular intervals in the experiment, and the dependent variable is the quantity measured or calculated for each regular step of the independent variable. When drawing a graph, observe the following rules:

1. Mark the scales along the axes and label each scale with the variable being plotted. Units should be included in parentheses. The graph should be easy to read. Make each large division equal to an appropriate scale to facilitate plotting a readable graph. Plotted data should fill most of the graph, and should not be confined to small area of the graph. Where appropriate, error bars should be included. Last, the point (0,0) need not appear on the graph as a point unless it is a relevant point on the graph.

2. Plot points carefully. Use suitable symbols for each point. When two different sets of data are plotted on the same graph, use different data symbols for each data set. Indicate in a legend what experimental conditions correspond to each data set.

3.
If appropriate, fit a curve to the plotted points. Most graphs will be for the purpose of
verifying a law or determining a functional relationship. Graphs will show either a uniformly smooth
curve or a straight line. Many graphing
programs will automatically draw a curve for your data set. Include on the graph the equation of the
best fitting curve and the R^{2} value. The closer the R^{2}
value is to unity (one) the better the data set.

4. Give the completed graph a title. The title should take the form of “Y versus X under the conditions Z”.

Many graphs you encounter will have variables chosen so that the graph itself is a straight line, and the linear relationship:

y= **m**
x + **b**

where m is the slope of the line
and b is the y-intercept. In graphs
drawn from experimental data, the constants **m** and **b** have physical
significance and may have specific units associated with them. Note that plots of this type have value in
that they may be used to predict data values given certain input data.

Sometimes graphs may be used to
explore a trend, or discover a relationship between two variables. The plots may not necessarily be linear in nature. It is up to the investigator to decide what
type of function best fits the data points.
This can be done by trial and error. A function that fits the data well
will have an R^{2} value close to unity. In exercises 3 through 5
you will explore data trends for the periodic table of the elements.

**Exercise 1**.

The following relationship allows you to convert from the Fahrenheit scale to the Celcius scale:

^{O}C
= 5/9 ^{o}F – 5/9(32) note
that it takes the form y= mx +b

A student records the following
data. Determine the ordinate and abscissa, dependent and independent
variables. Plot the following data set
and cite appropriate units. Include a
title, and show the R^{2} value and formula on the plot. How well does this data set correspond to
the formula? Compare the intercept and slope to the theoretical equation
above. Do the equations match
exactly? What limits are there in
precision? How well does the trend line
fit the data? Explain in detail.

## Fahrenheit |
## Celcius |

-40 |
-40 |

-20 |
-28.9 |

-15 |
-26.0 |

-5 |
-20.9 |

0 |
-17.9 |

5 |
-15.0 |

20 |
-6.9 |

80 |
26.9 |

200 |
93.5 |

400 |
204.5 |

**Exercise 2. **

Plot the following data for thermal expansion of a sample of oxygen gas at 1 atmosphere constant pressure. Plot the data citing units and using appropriate labels. Determine the slope and intercept and write the equation for this line plot.

Volume in Liters |
Temperature in Celcius Degrees |

25.00 |
31.50 |

30.00 |
92.39 |

35.00 |
153.30 |

40.00 |
214.17 |

45.00 |
275.20 |

50.00 |
336.11 |

65.00 |
? Predict this value using your plot |

Refer to the periodic table for the following exercises.

**Exercise 3. **

Plot the atomic mass vs. the atomic number for all elements
in column 1 of the periodic table.
Assume that the plot passes through (0,0). Cite appropriate units and
include a title. Show the R^{2}
value and formula on the plot.

**Exercise 4. **

Plot the atomic mass vs. the atomic number for all elements
in period 4 of the periodic table. Assume that the plot passes through
(0,0). Cite appropriate units and
include a title. Show the R^{2}
value and formula on the plot.

**Exercise 5. **

Plot the density vs. the atomic number for all elements in
period 4 of the periodic table. Cite
appropriate units and include a title.
Show the R^{2} value and formula on the plot. Do a similar plot for all elements in period
5 of the table and compare your results.

** **

- Is there a general trend in the molar mass vs. atomic number plot? The slope of the plot is not equal to 1. Why does the molar mass increase by more than one unit when the atomic number increases by one unit?

- Is
there a general trend in the density vs. atomic number plot? Does the
pattern of the plot repeat? What does the term periodicity mean to you?
Explain in detail.

**Graphing with Excel**:

- Open Excel – a worksheet should open.
- Type in your data points – X axis is usually in column A and Y-axis is usually in column B.
- Click on the chart wizard button on the toolbar. (It looks like a bar graph.)
- To plot you points as on single line, click on the XY Scatter choice for chart type.
- Under chart sub-type, choose either the curved line or straight line choices. Click on the next button.
- Under data range and series, leave at the default values and click next.
- Under the titles tab, add the chart title and titles for the X and Y axis.
- Under the axes tab, make sure that under primary axis both value x axis and value y axis are checked.
- Under the gridlines tab, choose the configuration of gridlines that you are looking for.
- Under the legends tab, choose the placement of your legend information.
- Under the data labels tab, choose show label. This will give each data point value for the x-axis. If you choose show value, it would show the x-axis value for each data point. Click next.
- Under place chart, choose as a new sheet – chart 1. This will save the graph as a full page and not a smaller version of the graph. If you choose “as object in – sheet 1”, the graph will show up as a smaller graph right on your data sheet. Click finish.
- If you right click on any of the titles (chart title, axis titles, legend), you can modify them to suit how you want your graph to look.
- If you right click on the x-axis numbers, you can change the scale or modify the information shown on the x-axis.
- If you right click on the y-axis numbers, you can change or modify the y-axis information.