For a given sample of matter, density denotes the mass contained per unit volume. The unit volume often equals to 1.0mL for numerous samples of matter. Density units are often represented in grams per milliliter (g/mL) or g/cm3 for several liquid and solid samples of matter. Density is applicable in determining the concentration of solutions in diverse occasions. Often, when a solvent is used to dissolve a solute, the solution density tends to differ with that of the pure solvent. Existing kinds of literature offer comprehensive information about the densities of various solutions as a function of their concentration, mainly in terms of solute percentage in the solution. A solution’s concentration is often displayed in terms of the percentage composition depending on weight. The purpose of this lab report is to establish a linear regression and graphical model for the concentration of Sodium Chloride in relation to its density. The models will then be used to determine the concentration of sodium chloride of unknown concentration from using the resulting (calculated) densities.
Data Results
|
Concentration |
5% |
10% |
15% |
20% |
25% |
Unknown #1 |
Unknown #2 |
| Mass (g) |
9.955 |
10.34 |
10.78 |
11.4 |
11.54 |
10.25 |
10.9 |
| Volume (mL) |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
| Density (g/mL) |
0.9955 |
1.034 |
1.078 |
1.14 |
1.154 |
1.025 |
1.09 |
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Density/Concentration Graph
The graphical analysis and representation of the variables indicate the values of the unknowns are 30% and 35%, respectively (that is, Unknown #1 and Unknown #2).
Linear Regression Results
Performing the linear regression using the excel data analysis function produced the following results:
Linear Regression Statistics |
|
| R |
0.976026 |
| R-Square |
0.952627 |
| Adjusted R -Square |
-2 |
| Standard Error |
0.017207 |
The equation used in the linear regression model was designed for predictive analysis; that is, to quantify the correlation between solution concentration and density. The equation is outlined below:
Y = c +a X ; where c represents a constant (that is, the value of dependent variable – Y – when the value of X is 0) and a represents the slope or gradient.
From the findings used in the regression model, the following equation is adopted:
Y = 0.9955 + 1.13 X
Discussion of Findings
The graphical and linear models highlight that as the concentration of sodium chloride rises, the density also increase linearly. The data used in this lab also supports this occurrence, within the appropriate margins of error. The linear regression model demonstrates that the standard error is 0.017. The lower level of standard error is an indication that the measures or data have great degree of accuracy. The objective of the lab was achieved when the calculations and modeling predicted the solution concentrations of unknown concentation using the given densities. Error analysis has not demonstrated any serious concern because the experiment considered the mass of the cylinder when determining the mass of the sodium chloride samples. As a result, the solutions’ mass matched the expected densities found after calcultation using the given volumes.
Conclusions
The linear regression and graphical models indicated the existence of a linear relationship between the concentration and density of sodium chloride solutions. Additionally, the findings demonstrate that the correlatioon can be applied in making predictions of the properties of solutions that have unknwon concentations.
