Density, Accuracy, Precision And Graphing

  1. The determination of the density of water
  2. A comparison of the accuracy and precision of a graduated cylinder and a pipet

EXPERIMENTAL MATERIALS

Part A

A 50mL graduated cylinder A balance 50.0mL deionized water A rubber policeman

Part B

A 100mL beaker A 50mL graduated cylinder A volumetric pipet 120.0mL deionized water A thermometer A rubber policeman

EXPERIMENTAL METHODS

Part A:

Density of water

  1. An empty, dry 50mL graduated cylinder was obtained.
  2. The mass of graduated cylinder with using a balance.
  3. 10.0mL of deionized water was added to the 50mL graduated cylinder.
  4. Mass of 10.0mL of deionized water + the cylinder was measured with balance.
  5. To take only mass value of the 10.0mL deionized water, the mass value of the graduated cylinder was subtracted from the mass value of the 10.0mL of deionized water + the cylinder.
  6. Density of 10.0mL of deionized water was calculated by its’ mass and volume. (d=m/v)
  7. The exact density of the 10.0mL of deionized water was recorded on the data sheet.
  8. Deionized water was added up to the 30.0mL mark of the 50mL graduated cylinder and Steps 3 to 7 were repeated for 30.0mL.
  9. Deionized water was added up to the 50.0mL mark of the 50mL graduated cylinder and Steps 3 to 7 were repeated for 50.0mL.

Part B:

Accuracy and Precision Using a graduated cylinder

  1. An empty, dry 100mL beaker was obtained and measured its’ mass with a balance.
  2. 10.0mL of deionized water was added to a graduated cylinder and transferred it to the 100mL beaker.
  3. Mass of 10.0mL of deionized water + the beaker was measured.
  4. To take only the mass value of the 10.0mL deionized water, the mass value of the beaker was subtracted from the mass value of the 10.0mL deionized water + the beaker.
  5. Density of 10.0mL of deionized water was calculated by its’ mass and volume. (d=mv)
  6. The exact density of the 10.0mL of deionized water was recorded on the data sheet.
  7. The water in beaker was measured by using a thermometer.
  8. Steps 2 to 6 were repeated for 20.0mL and 30.0mL.
  9. Average density and average deviation were calculated by density values of the three trials.

Using a volumetric pipet

  1. An empty, dry 100mL beaker was obtained and measured its’ mass with a balance.
  2. 10.0mL of deionized water was pipetted to the 150mL beaker.
  3. Steps 2 to 9 were repeated by using a volumetric pipet instead of a graduated cylinder.

DATA AND CALCULATIONS

Part A:

Density of water Mass of an empty, dry 50mL graduated cylinder = 23.607g

Volume of water (mL)

10.0 30.0 50.0 Mass of graduated cylinder + water (g) 33.1003 52.8690 72.985 Mass of water (g) 9.4933 29.262 49.378 Density of water (g/mL) 0.94933 0.9754 0.98756

Part B:

Accuracy and Precision Mass of a 100mL beaker = 31.058g / Temperature of water in beaker = 24.6˚C

Graduated Cylinder Pipet After First addition (g) 40.7 41.0 After Second addition (g) 50.0 50.9 After Third addition (g) 60.0 60.8 Mass of 10mL (g) 9.65 9.93 Mass of 20mL (g) 19.0 19.8 Mass of 30mL (g) 28.5 29.8 Density of Water (g/mL)

a. Trial 1 b. Trial 2 c. Trial 3

0.965 0.946 0.950

0.993 0.991 0.993 Average density (g/mL) 0.954 0.992 Deviation from average: (g/mL) a. Trial 1 b. Trial 2 c. Trial 3

0.0115 0.00738 0.0041

0.00083 0.00132 0.00049 Average deviation (g/mL) 0.00766 0.00088 % Error of average density (%) 4.353 0.484

In these experiments:

Accepted value for the density of water at 24˚C = 0.997g/mL

Sample calculation for Graduate Cylinder: Percentage error of average density measurement (%) = |Accepted Value - Experimental Value| \ Accepted value x 100% = |0.997g/mL – 0.954g/mL| \ 0.997g/mL x 100% = 4.353%

DISCUSSION

Results Obtained Part A: Density of water Density is defined as a measure of the quantity of mass per unit volume of a substance. In the experiment, the density of water was successfully determined by a formula that d=m/v. As it is showed in the table, each samples of water has the different density of water. However, those results are expected because the each values of the mass and volume of water are different. Also, the slope of the graph is defined as density of water. Therefore, the average of those results are showed in the graph (y=0.9833x). Part B: Accuracy and Precision

Accuracy is determined by how close a measurement comes to an existing. In this experiment, it can be observed that which one is more accurate with the comparison of the graduated cylinder and the volumetric pipet. As a result, the volumetric pipet is more accurate than the graduated cylinder because the percentage error of the average density measurement of using volumetric pipet is lower than using the graduated cylinder.

Precision is how close a measurement comes to another measurement. Precision is determined by a statistical method called a standard deviation. Standard deviation is how much, on average, measurements differ from each other. High standard deviations indicate low precision, low standard deviations indicate high precision. Mathematically the average deviation is not as significant as the standard deviation.

However, in this experiment, average deviation is a measure of the precision of the measurement. As a result, the volumetric pipet is more precise than the graduated cylinder because the average deviation of using volumetric pipet is lower than using the graduated cylinder. Errors

There were factors that affected the accuracy of these experiments. First, there was no way to ensure that the volume of water was very accurate because of tiny water drops except measured value in graduated cylinder. Also, there was little left over of the water in a volumetric pipet when the water was transferred from the volumetric pipet to a beaker. Precautions

To reduce the error in the volume of water, the graduated cylinder should be dried except the part of water. Also, wait about 20 seconds to drain the water when transferring the water from the volumetric pipet to the beaker. Therefore, the volume and mass values of the water were more accurate.

CONCLUSION

Part A: Density of water

The density of water was determined to be 0.94933g/mL for 10.0mL, 0.9754g/mL for 30.0mL, and 0.98756g/mL for 50.0mL. The slope that was showed on the graph was 0.9833g/mL defined as the rate of density of water.

Part B: Accuracy and Precision

Using a graduated cylinder

  1. Precision: the average deviation measurement was determined to be 0.00766g/mL.
  2. Accuracy: the percentage error of average density measurement was determined to be 4.353%

Using a volumetric pipet

  1. Precision: the average deviation measurement was determined to be 0.00088g/mL
  2. Accuracy: the percentage error of average density measurement was determined to be 0.997g/mL. The degrees of both of precision and accuracy are higher when using a graduated cylinder than a volumetric pipet.

REFERENCES

  • Miller, Dionne A. (Third Edition.); SCC201 Fundamentals of Chemistry Laboratory Manual; CENGAGE Learning, 2009, p 29 – 31