Density experiment - Lab Report Example

Density Lab Report Charnelle Palama and Tanya Ono (Group H) Chaminade This experiment aims at using the Archimedes principle to determine the density of post-1985 pennies. The experiment used water determined corresponding masses and volumes of pieces of pennies. This was then used to determine the pennies’ average density. The results yielded a significant relationship between mass and volume at ‘0.05 level of significance’ and a corresponding p value of 0.0009. The results also identified an experimental density of 7.

54 g/mL for the pennies. This was different from a theoretical density of the pennies that is 7.18 g/mL. The experiment therefore yielded a percentage error of 5 percent that can be attributed to inaccurate measurements. Density lab Introduction Density is an intensive property of matter and is defined in terms of mass and volume of a substance. It is the mass of a substance per unit volume. Archimedes’ approach is one of the applicable techniques for determining density of a substance. Under the method, displacement of water is used to obtain volume of the subject material whose density is to be determined while a mass balance is used to determine the material’s mass.

The material should however be insoluble in the applied liquid, water. Displacement that defines the immersed substance’s volume is calculated from the difference between the final volume of water after immersion and the volume before immersion. The mass is similarly determined by the difference between the masses after and before immersion (Boyd, 2012; Roessle, n.d.). This experiment seeks to ascertain the relationship between mass and volume of the pennies and compare the established value with the literature density of the post-1985 pennies that is reported at 7.18g/ml. It therefore explores the following research question.

‘Is there a significant relationship between mass and volume of post-1985 pennies?’ In order to answer the question, the experiment tests the following set of hypotheses, H0: The density of post-1985 pennies is not related to its mass and volume H1: The density of post-1985 pennies is related to its mass and volume The sets of hypothesis therefore claim a defined relationship between mass and volume of the pennies to yield a constant density that is reported at 7.18g/ml. Methods and materials Materials The experiment’s applied materials were 10 post-1985 pennies, 50 ml graduated cylinder, water, and a top loading balance.

Methods A 50 ml graduated cylinder was filled with 20.0 ml of water that was carefully measured. Using a top loading balance, the initial mass of the cylinder and the water was determined and recorded as the initial mass reading. The volume was similarly recorded. Ten post-1985 pennies were immersed into the cylinder, in pairs, and the new volumes and masses recorded. Results The following table shows the results for the experiment Initial Volume of Water (ml): 20.0 ml, Initial Mass of Cylinder + Water: 105.

06 g Table 1: experimental results Discussion From the results, corresponding values of each set of pennies, mass and volume, were obtained by subtracting initial values from final values upon each addition of pairs of pennies. The following table summarizes the cumulative masses and volumes for each addition of the pairs of pennies. Table 2: Corresponding mass and volume for each addition Volume (ml) Mass (G) Rep A 1 5.03 Rep B 1.5 9.94 Rep C 2 14.97 Rep D 3 19.97 Rep E 3.5 24.96 The following graph illustrates the corresponding masses and volumes for pennies.

Graph 1: Graph of mass against volume From the graph, the line of best fit can be used to determine the experimental value for the pennies’ densities. The second and the fifth points can be used as follows. Density, ρ = [ Mass(5) - Mass(2) ] / [ Volume(5) - Volume(2) ] (in g/ml) = (24.96- 9.94)/ (3.5- 1.5) = 15.02/2 = 7.51 g/mL. A linear regression model as shown by the following regression model can more accurately determine the relationship. Table 3: Table of regression coefficients   Coefficients Standard Error t Stat P-value Intercept -1.621163 1.367378 -1.1856 0.321133 X Variable 1 7.5432558 0.572731 13.17067 0.000946 The following ANOVA table supports the model.

Table 4: ANOVA table ANOVA   df SS MS F Significance F Regression 1 244.673 244.673 173.4665 0.000946 Residual 3 4.231474 1.410491 Total 4 248.9045       From the regression model, the graph has a slope of 7.54 that estimates the experimental density. The small p value, 0.0009, relative to the level of significance identifies the significance of this relationship between mass and volume. The low significance value from the ANOVA table leads to rejection of the null hypothesis to the conclusion that the density of post-1985 pennies is related to its mass and volume, and that density is 7.54 g/mL. This yield the following experimental error, based on the literature value of 7.18 g/mL. Percentage error= = {(7.54- 7.18)/7.

18}*100 = (0.36/7.18)*100 = 5 % Conclusion The experiment identifies a significant relationship between mass and volume to define density. The experimental density for the pennies is 7.54 g/mL. This identifies a five percent experimental error relative to the literature value of 7.18 g/Ml. The error can be attributed to inaccurate readings. The identified relationship between mass and volume to define density means that the Archimedes method can be used to determine densities of other substances, including liquids that are insoluble in water.

The experiments therefore recommend the approach for estimating density of substances. References Boyd, A. M. (2012). Density via displacement. Retrieved from http://www.middleschoolchemistry.com/atomsworld/2012/03/density-via-displacement/ Roessle, P. A. (n.d.). Density of regular solods. Retrieved from: http://doc.istanto.net/pdf/1/determine-the-density-of-each-solid-figure.html