Lab 7. Free Energy Lab

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Helen Tian CHEM 11200 2 Lab Partner: Mason Wright Lab 7. Free Energy of a Cobalt Complex Introduction The purpose of this laboratory experiment is to better understand free energy, solubility, enthalpy, and entropy through spectrophotometric analysis of nitropentaamminecobalt (III) chloride. The ultimate goal of this experiment is to determine the enthalpy (∆H) and entropy (∆S) of the reaction. The absorbance of the cobalt solution, prepared through dilutions with varying amounts of distilled water, was measured using spectrophotometry. Spectrophotometry is useful for measuring light intensity at different wavelengths, gauging the amount of photons absorbed as the light traverses the sample solution. With a spectrophotometer, the concentration of a chemical substance can be deduced by evaluating the detected light intensity, indicative of the light either re-emitted or absorbed. In this experiment, a UV-vis spectrophotometer was employed to expose a sample to light across the UV to visible wavelength range (190 to 900 nm). 1 Subsequently, the instrument recorded the light absorbed by the sample at each wavelength. Furthermore, the absorbance of four saturated solutions of the cobalt solution, available at temperatures of 0.0 °C, 6.0 °C, 12.0 °C, and 18.0 °C, was determined using the spectrophotometer. Finally, by applying Beer’s Law, a calibration curve was constructed through conversions between absorbance and concentration, facilitating the calculation of enthalpy and entropy (82780 J mol -1 and 163 J K -1 , respectively). Procedure Our procedure did not stray from the lab manual provided to us. Other than the usual environmental and human error factors, there weren’t any notable issues that would’ve altered the results. As such, we measured our solutions with the spectrophotometer a few times to make sure our data was accurate. Data Analysis Note: In our calculations, we ignored significant figures until the end to get the most precise results Weight of cobalt salt (grams) = 0.1018 g Table 1. Concentration (M), r i , Absorbance (A), and of solutions 0-3 Sol. # Concen. (M) C i / C 0 Absorb. (A) 0 2.654*10 -3 1 0.168 1 8.845*10 -4 1/3 0.081 2 1.327*10 -3 1/2 0.087 3 1.769*10 -3 2/3 0.098 (should be close to 0.1500) 𝐴 ?𝑒𝑎? = 0.168+0.081+0.087+0.098 4 = 0. 1085

Figure 1. Spectrophotometry results of solutions 0-3. Peak absorbance observed at ~548 nm. Table 1.1 Concentration (M), Absorbance (A), and Path length of solutions 0-3 Sol. # Concen. (M) r i = C i / C 0 Absorb. (A) A i / r i 0 2.654*10 -3 1 0.168 0.168 1 8.845*10 -4 1/3 0.081 0.243 2 1.327*10 -3 1/2 0.087 0.174 3 1.769*10 -3 2/3 0.098 0.140 𝐴 0 = 0.168+0.243+0.174+0.140 4 = 0. 181 Table 1.2 Verification of Beer’s Law (lowkey not verified) 𝐴 0 𝐶 0 = 𝐴 1 𝐶 1 = 𝐴 2 𝐶 2 = 𝐴 3 𝐶 3 Sol. # Concen. (M) Absorb. (A) A i / C i 0 2.654*10 -3 0.168 63.3 1 8.845*10 -4 0.081 91.5 2 1.327*10 -3 0.087 65.5 3 1.769*10 -3 0.098 55.4

𝑅 ?𝑒𝑎? = 𝐴 0 𝐶 0 = 63.31+91.57+65.57+55.40 4 = 69. 0 Table and Figure 2. Temperatures ( o C) and absorbances (A) of second set of solutions A-D Sol. # Saturated at (°C) Absorbance (A) A 0 0.164 B 6 0.214 C 12 0.266 D 18 0.329 Table 2.1 Temperatures ( o C), Absorbance (A), Concentration (M) using R mean , and K sp of solutions A-D Sol. # Saturated at (°C) Absorbance (A) Concentration (M) K sp A 0 0.164 0.00238 5.37 * 10 -8 B 6 0.214 0.00310 1.19 * 10 -7 C 12 0.266 0.00386 2.29 * 10 -7 D 18 0.329 0.00477 4.33 * 10 -7 Table 2.2 Temperatures ( o C), Absorbance (A), Concentration (M), and K sp of solutions A-D Sol. # Temp (°C) Temp (K) 1/T (K -1 ) K sp ln (K sp ) A 0 273 1/273 = 0.00366 5.37 * 10 -8 -17.0 B 6 279 1/279 = 0.00358 1.19 * 10 -7 -15.9 C 12 285 1/285 = 0.00351 2.29 * 10 -7 -15.3 D 18 291 1/291 = 0.00344 4.33 * 10 -7 -14.7

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Figure 3. ln(K sp ) vs. 1/T of solutions A-D. Close to a linear regression Calculations for ΔH and ΔS. Discussion In this experiment, we measured the absorbance of the colored cobalt salt solution on a UV-vis spectrophotometer. We looked at the differences of absorbance based on concentration and temperature, which you can see in Tables 1 and 2. As noted in Table 1 , the higher the concentration (with the stock solution 0 being the highest) the higher the absorbance. The absorbance of the stock solution (concentrated at 2.654*10 -3 M) had the highest absorbance of 0.168. From there, based on the ratio of stock solution and distilled water, the absorbance decreased. With ratios (C i / C 0 ) of ⅓, ½, and ⅔ (solutions 1, 2, and 3) the absorbance increases accordingly—0.081, 0.087, and 0.098. This works because solutions that are more concentrated have a larger number of molecules that interact with the light that enters, thus increasing its absorbance; by

Beer’s Law, the two are directly proportional. Now, for Table 2 , the higher the temperature, the more absorbant the solution was; the two are also directly proportional. Increasing by increments of 6 o C (starting from 0), solutions A, B, C, and D increase in absorbance—0.164, 0.214, 0.266, and 0.329, respectively. When a system (the solution in our case) is heated, the electrons get more excited, creating different excited states which lead to transitions between them. This results in a higher absorption of UV. 2 From the data that we collected, we were able to find A 0 and R mean = A 0 /C 0 ; please refer to Tables 1.1 and 1.2. Using a concentration ratio of C i / C 0 and our collected absorbance, we solved for A i / r i , all of which we averaged to find A 0 . While someone could use this to find the concentration of Table 2.1 , we continued to find R mean through Table 1.2. Here, we averaged all of our values of A i / C i ; you could also use the solved-for A 0 divided by the stock solution’s concentration. In addition, Table 1.2 is a verification of Beer’s Law; it speaks to the accuracy of our experiment, which unfortunately was not the greatest (will be discussed more in the errors section of this discussion). Moving on, we used our R mean to solve for the concentrations of our A-D solutions, as seen in Table 2.1 ; the equation for this is C A =A A / R mean . Here, we find that the higher the absorbance of a solution, the higher the concentration; therefore, temperature, absorbance, and concentration are all directly proportional. Now, using our solved-for concentration, we solve for the K sp which is 4x 3 , which also increases as concentration increases. We can conclude that as absorbance and concentration increase, K sp will also increase. Now, we want to determine the enthalpy and entropy of these systems. To solve for the two, we must look at the correlation between ln(K sp ) and 1/T; you can see the values of these in Table 2.2 . As K sp and temperature both increase, ln(K sp ) increases (albeit being in the negative values) and 1/T decreases. Their correlation to one another, based on our experimental data, is y = -9956x + 19.6 (mx+b); the trendline of the points from Table 2.2 and its slope are shown in Figure 3 . Using the solved-for function, we can find enthalpy (∆H = -mR) and entropy (∆S = bR) — 82780 J mol -1 and 163 J K -1 , respectively. Since the accuracy of most spectrophotometric studies is generally in the range of 3% to 5%, 1 I’d say our results are somewhat within that range of accuracy. However, while the increase/decrease in absorbances and concentrations made sense to the other data, I’d say our experiment does not follow Beer’s Law. Looking at Table 1.2 , we see that the ratios A i / C i of the different solutions don’t equate to each other. They should consider that molar absorptivity and path length are constant throughout. Therefore, we can conclude that our experiment isn't perfectly accurate. There are multiple factors that would have contributed to this inaccuracy. The solutions are light sensitive and must be stored in a dark place (i.e. the cabin under the stock solution fume hoods); while we worked as fast as we could, it is possible that the little light that it was exposed to affected the result. Some of the cuvettes we used were scraped, so the first trial we ran resulted in completely inaccurate data; although we redid it, the additional light exposure could have affected our results.These are experimental errors that could’ve been improved through a darker environment and brand new cuvettes with softer handling. In addition to this, there were multiple human errors such as not rinsing off the cobalt from the magnetic stirrer when we took it out of the volumetric flask. This means that there was possibly less dissolved cobalt salt than recorded in our solution; as such, our calculated concentrations would be a bit higher (from Table 1) than what the absorbance values tell us. We also didn’t wait for the cobalt salt to

completely dissolve; although we kept the stirrer in for over 30 minutes, there were still little solid bits and pieces in the solution. This again would have affected our concentration, leading to inaccurate data and calculations. Post-Lab Discussion Questions 1. Inorganic reactions in solution often have a ΔS° between -20 and 20 (J·mol –1 ·K –1 ). Why does ΔS° have such a significant value in the current experiment for this dissolution? When we consider normal inorganic reactions in solution, we think of aqueous reactants becoming aqueous products; as such, the entropy (which is defined as a measurement of disorder is near 0). For our experiment, we dissolve a salt, meaning our reaction’s state of matter goes from solid (reactant) to aqueous (product). Solids are a lot more ordered than aqueous solutions, meaning that the entropy will increase drastically compared to aqueous to aqueous reaction where the reactants and products have similar entropy values/levels of disorder. 2. Comment and suggest ways to improve this experiment. See above. 3. Why is it permissible to use the simplified beer’s law, A1/C1=A2/C2, in this experiment? Beer’s law is defined as A = ɛbC . A stands for absorbance, ɛ is molar absorptivity, b is the path length, and C is concentration. In this experiment, we only used one compound—cobalt salt—such that molar absorptivity ( ɛ ) would stay constant throughout the experiment and calculations; therefore, we do not need to include it in the equation. Similarly, path length ( b ) is defined by the thickness of our cuvettes, all of which should be the same. 4. If your cuvettes were dirty or stained, how might you expect this to affect your results? Why? The absorbance should be higher because the dirtiness/stain on the cuvette will also absorb light. ILess light would pass through the glass and the machine would interpret this as the solution absorbs more light, resulting in a higher absorbance value.Therefore, in addition to the solution absorbing light, the stain will also falsely increase the absorbance. References 1 Zhao, M. Z.; Dragisich, V. General Chemistry Experiments; MacMillan Learning: ISBN-978-1-5339-0949-7, 2018. 2 Welcome_Green ( https://physics.stackexchange.com/users/288027/welcome-green ), Why does a higher temperature increase absorption / optical density?, URL (version: 2022-01-12): https://physics.stackexchange.com/q/688259

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