Procedure: Graphical Analysis of Mass and Volume Data of an Unknown Solid

1. Collect a ruler and obtain a sample containing cylindrical pieces of an unknown solid material from your instructor. Record the ID Code of the unknown solid in your data table.

2. Using the ruler, measure the dimensions (diameter and height) of each cylindrical object. Start with the smallest object first and progress in order of increasing object size. Calculate and record the volume of the objects using the formula for the volume of a cylinder:

V= π*r2*h

3. Confirm these calculations by measuring the volume of the object using the displacement method learned in Lab Activity 2. Record these volumes.

4. Measure the mass of each cylindrical object using an electronic balance. Again, start with the smallest object first and progress in order of increasing object size.

5. Analysis: Using excel (or another graphing software approved by your instructor) create one graph with two lines displayed. One line should be the mass (Y) versus the volume (X) of each object, using the volume you calculated from the measured dimensions. The second line should be the mass (Y) versus the volume (X) of each object, using the volume you found from the displacement method. Add a best- fit line to each data set on this plot. Include the equation for each best fit line AND the correlation coefficient (R2) for each line on the graph. Choose the line with the best correlation (or the R2 closest to 1) to determine the density of the sample. The slope of this line, which is ∆ ∆ , is the density of your unknown material. Use this density to identify the unknown material analyzed. Your unknown material is one of the substances listed in the table below.

Lab Activity 3 – Research Skill Summary

1. Show your graph of mass vs. volume here. Explain which you volume measurement procedure ultimately used to determine the density of your unknown material and explain why you made that decision.

2. What is the likely material of your unknown? What is your percent error between the experimental density and the known density of this material?

Lab Activity 3 – Communication Skill Summary Presenting data in graphical form (rather than in table form) can be useful for several reasons. It allows the audience to take in a large amount of data in a small amount of space and time. Graphs are particularly useful at showing trends in the data, specifically, in highlighting possible relationships between dependent and independent variables being studied in a particular experiment. For this lab, follow these rules below and generate a graph for the relationship between mass (Y axis) and volume (X axis) for this experiment.

Here are some crucial rules for designing a good (basic) graph:

1. Give your graph a descriptive title. E.g.: A Graph to show the effect of x on y 2. Ensure you have put your graph the right way around. Your x axis should always show the independent variable – this is the variable you are changing. Your y axis should always plot the dependent variable – this is the variable you are measuring. For example, when looking at the effect of temperature on rate of reaction (a classic chemistry investigation), you change the temperature and measure the rate. As such, temperature goes on your x axis (it is independent) and rate goes on your y axis (it is dependent) 3. Ensure you plot your data thoughtfully, choose a data point graphic that is legible and takes up a reasonable amount of space on the graph. If you are plotting multiple data sets on one graph be sure to select data markers that will allow the viewer to quickly and easily distinguish between data sets. 4. If plotting multiple data sets, INCLUDE KEY/LEGEND! 5. Do not play connect-the-dot. Only very rarely are data points connected in this way. More often, we are seeking the trend or pattern that our results show, for that we need… scatter in experimental data is expected, and the use of an actual line on the graph connecting the points is meaningless. 6. DRAW A LINE OF BEST FIT (if your data/trend is supposed to be linear!). These lines pass through or near as many data points as possible. Excel and other graphing programs do the statistical analysis for you to minimize the least square fit. 7. Show R2 (linear correlation coefficient) and the equation for a line of best fit (if your data is supposed to be linear): if you use a line of best fit on your graph, be sure to include it in your legend.