Density and Graphing Data Assignment | Online Assignment

I have 13 page of chemistry assignments. Every page has minimum 2 questions and maximum 5. There are no long answers or a paragraph requires. All the answer should be numbers or briefly explain

Name _____________________________

Experiment 3: Density and Graphing Data

 

DATA RECORD 

Use permanent black or blue ink to record data. Calculations may be completed in pencil.

 

Part I: Clear liquids

Raw Data from Direct Observations

Unknown Liquid #	Mass of empty grad. cylinder	Mass of grad. cylinder + liquid	Volume of liquid	Qualitative Observations

 

Calculate mass and density of each unknown liquid using the data above. Show work below, keeping units with all numbers. Enter final values with correct significant figures in the data table below.

 

 

 

 

 

 

 

 

Results Table

Unknown Liquid #	Mass of liquid	Density of liquid	Identity of Liquid

 

 

 

 

Part II: Solid Cylinder

Qualitative observations:

 

 

 

 

 

Mass of solid cylinder    m  = _______________

 

Volume of solid cylinder (record in the units of the instrument)

Method 1:  Ruler/Calipers

Height from ruler: h = ________________   diameter from calipers:  d = ________________

 

Show calculations for mm to cm using dimensional analysis, for volume using the formula for a cylinder and for density using d=m/V. Include units with each number, showing how the final units were determined. Example of tracking units: 2.00 cm x 3.00 cm = 6.00 cm²

 

 

 

 

 

 

 

 

 

 

 

Method 2: Liquid Displacement

Initial water volume: V_i =__________________  Final water volume: V_f = __________________

 

Volume & density calculations (show work!):

 

 

 

 

 

 

 

 

 

 

 

Identity of the substance: ____________________  Actual density from table: _______________

 

 

 

 

DATA ANALYSIS  Pencil may be used. 

Part II: Solid Cylinder

1. Enter your team’s density data for the Solid Cylinder on the class spreadsheet.

 

2. Once all class data is entered, record the average density values from the class spreadsheet forPart II: Solid Cylinder.

Average density found by class with ruler method = ______________________

Average density found by class with displacement method = ______________________

 

 

3. Compute the % error of the average density of the class data found by the ruler method and by the volume displacement method. Show your calculations, keeping units with each number. Report your answer with the correct significant figures. **multiple operations!**

 

 

Density % error, ruler method:

 

 

 

 

 

 

Density % error, volume displacement method:

 

 

 

 

 

 

 

4. The following table shows the raw data collected in an experiment like the one you did this week. On the following page, hand graph the mass and volume data given below for the Solid Cylinder using graphing criteria learned in previous labs. Graph volume on the x-axis and mass on the y-axis. Refer to the Appendix for “How to Construct a Scatter Plot on Paper.”

volume (cm3)	mass (g)
0.53	3.79
2.35	8.78
4.81	15.70
8.45	24.25
11.29	33.65
16.45	46.25

 

 

 

 

 

 

Let’s look at the relationship between the graphed variables.

1. State the general relationship between variables illustrated in this graph (e.g. what happens to mass as volume increases).

 

1. Does this relationship make sense based on the physical quantities graphed? Briefly explain.

 

 

9. Now assume you’re no longer in the lab, but you want to know the mass of an object made of the same substance that has a volume of 9.55 cm³. Use the graph to approximate the mass. Show your work by drawing lines directly on your graph above (refer to the Background section for an example).

mass = ______________

Now we will quantify this relationship between the two variables using the best-fit line. Refer to the Background section “Equation of a Best-Fit Line of Graphed Data.”

y-intercept =

• On your graph, use a ruler to draw a best-fit line for the data points. Note that the best-fit line will probably NOT go through the origin (0,0) since it is an average of all points. Give your y-intercept numerical value with units in the box. Note: For y-intercept, give only the y-axis value, not an xy point.

 

1. Circle two points on the line for which you can easily read the x and y values (do not use the points you just graphed).

 

• Use these circled points to calculate the slope of your best-fit line using the equation shown below. Show your calculation, including units with all numbers. Give your slope with units in the box.

 

 

 

1. The general equation for a line is given as “y = mx + b.” In science we use graphs to represent data on matter. Each symbol has meaning for data analysis! Now we need to translate this general equation to one that has some meaning for our data. See the Background section for an example.

 

You have already determined numerical values for m (slope) and b (y-intercept) for the data on the previous page. Add them to the table below. Fill in the rest of the table by looking at the axis labels (physical quantity + unit) for this graph.

 

Equation component	Meaning	Number or Physical Quantity	Unit
y	name of physical quantity graphed on y-axis
m	numerical slope
x	name of physical quantity graphed on x-axis
b	numerical y-intercept

 

1. Substitute the numbers/symbols and units above for the symbols given in the general equation for a line: y = mx + b. Note that the letters x, y, m and b should NOT appear in your equation.

 

 

 

9. Suppose another unknown solid of the same substance has a mass of 9.55 cm³. Use your equation with units from the previous question to calculate the expected mass of this unknown solid. Show all work with units.

 

 

 

 

5. Check here if your instructor has directed you to complete this tutorial this week. _____ Each student will complete either the Excel or GoogleSheets Graphing tutorial found in Appendix B. Attach your graph from this tutorial to the end of the lab report after the Post-lab Questions. Use these guidelines to complete the next question.

 

6. Each team member will INDIVIDUALLY use Microsoft Excel or GoogleSheets to graph the data given in Data Analysis #4. Computers with Excel software are available on campus. Use proper graphing criteria (see Experiment 2). Add the best-fit line and the equation for the line generated by the software (and the R² value if directed by your instructor) to the graph. Change the equation for the line on the graph to one appropriate for this scientific data (it must match the format in #4H). Attach YOUR graph to the end of your lab report after the tutorial graph.

 

7. Compare your hand graph (#4) to your computer-generated graph (#6) of the same data.
   • How are they similar and different?

 

 

 

• Is there anything you could do to improve either of them?

 

 

 

1. Now compare the equations for the best-fit lines, which should be largely the same.

• How are they similar and different?

 

 

 

• Assuming the data was graphed accurately, the computer-generated equation for the best-fit line is accurate for that set of data. How could you improve your hand-drawn best-fit line, if at all?

 

 

 

 

Analysis of a Graph

So far you’ve completed the mechanics of creating a graph and best-fit line for raw scientific data. The next step is to think more deeply about what that graphical data, including the best-fit line, can tell us.

8. Answer the following questions for your computer-generated graph (#6).
9. The formula for slope is Dy/D Look at the physical quantities graphed on the x and y axes. In this case, what physical property is indicated by the slope of this graph?

 

1. Is the slope from your computer-generated graph (#6) greater than, less than, or the same as the class density value from direct measurements (#2, 3)? Use the class data average value with the smallest percent error.

 

 

 

1. How should they compare? Why?

 

 

1. As stated in the pre-lab, the numerical value of y at the y-intercept of a best-fit line will vary depending on the specific graph. For the computer graph of mass vs. volume (#6 above), what should be the numerical value of the y-intercept? Briefly explain using the physical quantities graphed.

Hints: what is the value of x at the y-intercept for any graph, what is the physical quantity graphed on the x-axis on this graph, and what are the implications for the associated value of y at this y-intercept?

 

 

 

 

 

1. The y-intercept may indicate discrepancies between the measurements and expected values, which may be due to experimental setup parameters such as instrument calibration, incorrect (though consistent) measurement errors, etc.

Based on your answer to D, is there evidence for these discrepancies in this data?

 

 

 

 

 

Extension: Accuracy and Precision 

Refer to the Background: Experimental Uncertainty section to answer the following questions.

 

9. Imagine an experiment in which students are measuring the density of ethanol. The accepted density of ethanol is 0.789 g/mL. Label the set that is most precise, least precise, most accurate, and least accurate.

 

Group 1 0.959 0.958 0.958 0.959 Mean = 0.959 Range = 0.001

Group 2 0.799 0.805 0.810 0.795 Mean = 0.802 Range = 0.015

Group 3 0.791 0.788 0.786 0.785 Mean = 0.788 Range = 0.006

Group 4 0.689 0.692 0.691 0.695 Mean = 0.692 Range = 0.006

Group 5 0.891 0.852 0.915 0.867 Mean = 0.881 Range = 0.063

Note: Average is calculated by adding all values and dividing by the number of values.

Range is calculated by subtracting the lowest value from the highest value.

	Group number
most precise
least precise
most accurate
least accurate

 

10. Which gives a better indication of accuracy of the data, the mean or the range? __________
11. Which gives a better indication of the precision of the data, the mean or the range? __________
12. Does the R² value for a best-fit line of experimental data give an indication of accuracy or precision?

Circle one:       accuracy          precision

Briefly explain.

 

 

 

 

13. Does the value of the slope for a best-fit line of experimental data give an indication of accuracy or precision? Briefly explain. Note that this is only true when the slope indicates a physical property of the substance such as density.

Circle one:       accuracy          precision

Briefly explain.

 

 

 

 

 

 

 

Post-lab for Experiment 3: Density and Graphing

1. In addition to density, list two specific qualitative observations that helped identify your unknown solid cylinder. Quote the observation and give the page number from your lab report where you made the observation.

 

 

 

 

2. The following pressure/temperature graph includes the software-generated equation for the line. Convert the software-generated equation to one that has meaning for the scientist (as you did in data analysis #4H).

• The letters x, y, m and b should NOT appear in your equation.
• Include units with all numbers.

• Place your answer in the box.

 

 

 

Pressure-Temperature Relationship for a Gas

 

 

3. The percent error calculation gives an indication of how “correct,” or close to the known value, the data is. In science, the true value is not always known. It is only established through years of multiple experiments by many scientists that are shown to be in agreement. Therefore, in many cases of original research, percent error cannot be calculated. Fortunately, this week we are working with well-established densities of materials.

 

According to the percent error calculations for density of a solid cylinder (Data Analysis #3), which method of determining volume resulted in better experimental results? Circle one and briefly explain how % error informed your answer:

 

Ruler method        Volume displacement method      Neither

 

 

 

 

 

 

 

4. Calculate the percent error for the density of copper determined from the experiment that generated the following equation. Show work. Place your final answer with correct units and significant figures in the box. Hint: what additional information is needed to calculate % error? Where can you find it?

mass, g = (8.7409 g/cm³)(volume, cm³) – 0.0822 g

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. Use dimensional analysis with the density of mercury as a conversion factor (see Table 2) to calculate the mass in nanograms of mercury of a 2.000 microliter sample of mercury. Remember that you must go through the base unit! Place your final answer with correct unit abbreviations and significant figures in the box.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. Read the experiment objectives listed on the first page of the lab handout. Consider whether you achieved each objective, what difficulties you encountered, and how you got to your current level of understanding. Then answer the following questions using full sentences.

 

1. Rewrite the one experiment objective (or portion of the objective) from the first page of the lab handout that was the most difficult to achieve.

 

 

 

1. Explain how you achieved or did not achieve this objective. What steps did you take? What barriers to learning did you encounter?

 

 

 

 

 

 

 

 

 

 

1. If you achieved this objective, what steps can you apply to future labs? If you did not achieve this objective, what steps can you take to master this topic?

 

 

 

 

 

 

 

1. Choose either this objective or some other aspect of this week’s experiment and describe how it is related to your everyday life or the world around you.

 

 

 

 

 

 

 

 

 

 

Extension Questions

7. According to the definitions given in the Background section of this experiment, label the following as accurate and/or precise beneath each picture.

 

 

 

 

 

 

 

 

 

 

 

 

 

8. Is percent error an indication of accuracy or precision? Briefly explain.

 

 

 

 

9. In order to determine the density of five pieces of iron, two students each determined the mass and volume of each piece (volume was determined by water displacement). Each student plotted their five data points; the resulting plots are shown below.

 

 

 

1. Which student collected more accurate data? Student #______

Which graph feature informed your answer? (circle one): slope        R²

 

1. Which student collected more precise data? Student #______

Which graph feature informed your answer? (circle one): slope        R²

 

 

 

 

 

Extra Credit

10. Benjamin Franklin showed that 1.00 teaspoon of oil would cover 0.50 acres of still water. What was the thickness of the layer of oil in nm? Hint: how is area related to volume? Show all work using dimensional analysis, keeping all units and proper significant figures with each number. Place your final answer with correct units and significant figures in the box.

1.00 tsp = 5.00 cm³      1.0 x 10⁴ m² = 2.47 acres