Determination of the Density of a Sodium Chloride Solution Lab Report PDF

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Determination of the Density of a Sodium Chloride Solution Lab Report...

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Determination of the Density of a Sodium Chloride Solution

Hannah Strickland

January 29, 2018

Chemistry 355 Section JW

Experiment 1

Introduction: The main goal of this experiment was to determine the density of a sodium chloride solution, given a weight percent of 11. The volume of the solution was determined by using a pipette and graduated cylinder. Then, it was weighed using a balance scale. Then, the data acquired from these two methods were put into the density formula, shown as equation 1. Equation 1:

Density = mass (g) / volume (mL)

Another goal for this experiment was to learn how to properly use important analytical tools (a pipette, graduated cylinder, and scale). Proper use of these tools is vital to obtaining accurate results. Density is the measure of mass per volume for a substance. Mass is in grams and volume is in milliliters.1 Typically, the density of a liquid can be directly related to the concentration of the solution. The concentration of a substance is moles per volume, in milliliters. Density can be useful in identifying substances. It can also be used to determine the purity of a substance. If the material is pure, then the density should be the same as the mass concentration.2 Impurities can occur due to contamination or when dealing with solutions. Variation can also occur with differences in pressure and temperature. These differences are usually small with liquids and solids, but more differential with gases.2 In addition to the use of analytical tools, statistical tools were also used in this lab. To determine if the two methods differed greatly (pipette or graduated cylinder), several tests were done. Using a statistical computer program, the Grubb’s test, F-test, and T-test were performed. If the calculated value for t falls between the critical value for t, then the null hypothesis is accepted (the two means are equal). If the calculated t value does not fall within the critical t value range, then the null hypothesis is rejected and the alternative hypothesis is accepted (mean 1 does not equal mean 2).3 Experimental: Preparation of 11% Sodium Chloride Solution First, an 11% sodium chloride solution was made. The mass of the sodium chloride needed to make an 11% sodium chloride solution in 250 mL of water was calculated, and is shown as equation 2. The obtained value from the calculation was 30.8988 g NaCl. Then 30.8981 g of NaCl was placed into a 500 mL beaker, and 250 mL of deionized water was added to the beaker. The mixture was stirred until all of the NaCl was dissolved. Equation 2:

Density Measurements Using a Graduated Cylinder Next, a 10 mL graduated cylinder was obtained and weighed. After weighing, 10 mL of the 11% NaCl solution were pipetted into the graduated cylinder using a plastic pipette. The weight was obtained and recorded. Next, the solution was disposed of, the graduated cylinder was dried, and the process was repeated four more times. Next calculations were done. First, the mass of the solution was obtained by subtracting the mass of the graduated cylinder from the total mass. Next, equation 1 was used to determine the density. The mass obtained was divided by 10 mL, which was the volume of the solution. These values were recorded as Dgrad. Lastly, the average for all the calculated densities were calculated. All of these values can be found in table 1. ! Density Measurements Using a Volumetric Pipet Next, a 50 mL beaker was obtained and weighed. Then, a 10 mL pipette was used to pipette 10 mL of the 11% NaCl solution into the weighed 50 mL beaker. The mass was obtained and recorded. The solution was poured out and the beaker was dried. This process was repeated 4 more times. Next, equation 1 was used again to determine the density. First, the mass of the beaker was subtracted from the total mass, thus giving the mass of the solution. Then, using equation 1 for density, the mass was divided by the volume (10 mL). These values were recorded as Dpip. Then, the 5 densities were averaged together. These values can be found in table 2.

Results: Table 1 shows the values obtained for the trials using a graduated cylinder as the analytical tool. It shows volume, given in milliliters. It also shows the weight of the graduated cylinder in grams, the weight of the solution and the graduated cylinder in grams, and the weight of just the solution in grams. The value for the mass of the solution was calculated by subtracting the mass of the graduated cylinder from the mass of the graduated cylinder and solution. The table also shows the density values, which was calculated by dividing the mass of the solution by the volume of the solution. Lastly, the table also shows the average density, calculated by using Excel’s average function. It also shows the standard deviation, which was calculated using Excel’s standard deviation function. Table 2 shows the values obtained for the trials using a volumetric pipette as the analytical tool. tool. It shows volume, given in milliliters. It also shows the weight of the pipette in grams, the weight of the solution and the pipette in grams, and the weight of just the solution in grams. The value for the mass of the solution was calculated by subtracting the mass of the graduated cylinder from the mass of the graduated cylinder and solution. The table also shows the density values, which was calculated by dividing the mass of the solution by the volume of the solution. Lastly, the table also shows the

average density, calculated by using Excel’s average function. It also shows the standard deviation, which was calculated using Excel’s standard deviation function. Table 1: Density Measurements Using a 10 mL Graduated Cylinder Trial

Volume (mL)

Graduated Cylinder (g)

Solution + Graduated Cylinder (g)

Solution (g)

Dgrad (g/mL)

1

10

25.3299

35.9990

10.6691

1.06691

2

10

25.5279

36.0124

10.4845

1.04845

3

10

25.3876

35.9850

10.5974

1.05974

4

10

25.4601

35.9499

10.4898

1.04898

5

10

25.3901

36.0390

10.6489

1.06489

Average Density

1.057794

Standard Deviation

0.00869250424216192

Average Density with Error

1.058 ± 0.008693

Table 2: Density Measurements Using a 10 mL Volumetric Pipette Trial

Volume (mL)

Graduated Cylinder (g)

Solution + Graduated Cylinder (g)

Solution (g)

Dpip (g/mL)

1

10

27.5526

37.7022

10.1496

1.01496

2

10

27.5584

38.2722

10.7138

1.07138

3

10

27.5557

38.2941

10.7384

1.07384

4

10

27.5567

38.4871

10.9304

1.09304

5

10

27.5574

37.9901

10.4327

1.04327

Average Density

1.059298

Standard Deviation

0.0304906628330708

Average Density with Error

1.059 ± 0.03049

Discussion: During the course of this experiment, two densities were obtained for the 11% NaCl solution. The first density was obtained using a graduated cylinder, which was 1.058 ± 0.008693 g/mL. The second density was obtained using a volumetric pipette, which was 1.059 ± 0.03049 g/mL. To determine if the two values were significantly different, the F-test, t-test, and Grubb’s test were performed. First, the Grubb’s test was performed. This is shown in table 3. The data for all the trials, for both Dgrad and Dpip, fell under the T value which was 1.67. This concludes that there was no outliers in the data for 95% confidence. Next, the F test was performed to determine which t test would be best to use. The F stat value was obtained and then compared against the F critical values (95% confidence, α=0.05). The F stat obtained was -0.10607, which is smaller than the F critical of 6.39. This data is shown in table 4. Because the obtained value was smaller than the critical value, the t-test chosen was equal variances. Next, the null and alternative hypotheses were set up which were: Null hypothesis: H0 = x Dgrad = x Dpip Alternative hypothesis: HA = x Dgrad ≠ x Dpip After the F test was performed, the equal variances t-test was performed using the Excel Data Analysis for the t-Test Two-Sample Assuming Equal Variances. This data is shown in table 5. The t stat obtained was 0.918, which was smaller than the t critical two tail (2.306004135). Because the calculated t stat is smaller than the critical t value, the null hypothesis is accepted and the alternative hypothesis is rejected. Thus, the measurements are not significantly different.5 The null hypothesis was accepted with a 95% confidence level. So, with 95% confidence, the two analytical tools, the pipette and graduated cylinder, do not differ significantly.

Table 3: Grubb’s Test Trial

Dgrad

Dpip

Result

1

1.0249626135972

1.44440800262382 Keep

2

1.09858506844587

0.406034765496886 Keep

3

0.20016104911999

0.48671695637914 Keep

4

1.0376164730243

1.11643161692358 Keep

5

0.792591740480854

0.515906854706469 Keep

1.67

T (0.5, n=5)4

1.67

Table 4: F-Test Dgrad Variances

Dpip 0.000075568249

0.0009296401

-0.10607

-0.10607

T Calculated T (df=4, df=4) with α=0.05 5

6.39

Table 5: t-Test: Equal Variances

Average

Variable 1

Variable 2

1.058

1.059

Variance

0.000075568249

0.0009296401

5

5

Observations Pooled Variance

0.0005

Hypothesized Mean Difference

0

df

8

t Stat

0.918137317748678

P (T< 1) One Tail

0.192705

t Critical One-Tail

1.859548038

P (T < t) Two-Tail

0.38541

t Critical Two-Tail

2.306004135

Conclusion: The average density of the 11% sodium chloride solution was measured in two ways. First by using a graduated cylinder, and the results were 1.058 ± 0.008693 g/mL. The second density was obtained using a volumetric pipette, which was 1.059 ± 0.03049 g/mL. Then, these results were analyzed using the Grubb’s test, F-test, and ttest using Excel. The results confirmed that the null hypothesis was accepted, which indicates that there is not a significant difference between the two analytical tools. Even though the calculations were similar, there were still some differences. This could be due to the fact that the pipette and graduated cylinder were not dried out completely in between weighs. This would affect the weight of the glassware, thus affect the final density calculations. Another error could have occurred in recording the data, or calculating the data. One major improvement for this lab would be to add more trials, which could possible decrease the slight error in the results.

Citations: 1. Harris, D. C. Quantitative Chemical Analysis; W.H. Freeman: New York, 2010. 2. Moore, J.; Stanitski, C.; Jurs, P. Chemistry The Molecular Science, 4th ed.; Brooks/ Cole, Cengage Learning: California, 2011, pg. 403-404, 678-680, 840- 846. 3. Vyazovkin, Sergey. Department of Chemistry. CHEM 355: Quantitative Analysis Student Laboratory Manual. [Online] (accessed Jan 29, 2018). ! 4. University of Gottingen. Grubbs test. [Online] 2014, 3-9 http://www.sediment.unigoettingen.de/staff/dunkl/software/pep-grubbs.pdf (accessed Jan 29, 2018). ! 5. Dinov,Ivo. UCLA Statics Online Computational Resource. F Distribution Tables. [Online] 2002, http://www.socr.ucla.edu/applets.dir/f_table.html (accessed Jan 29, 2018). !

Questions: 1:

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