Determining the Equilibrium Constant of a Chemical Reaction

Determining the Equilibrium Constant of a Chemical Reaction- SIMULATION 23/09/2020 INTRODUCTION Reactions go in both the forward direction as well as the reverse direction A +B↔C . When the forward rate and the reverse rate are equal, the reaction is at equilibrium (dynamic equilibrium), and all reactants as well as product concentrations are constant. There are multiple different techniques that can be utilised to determine the equilibrium constant, however, due to the high coloured nature of this experiment, spectrophotometry can be used to determine the concentrations of the varying solutions. The Fe 3+¿¿ −¿ ¿eq ¿ SC N ¿ ¿ N 2 +¿¿ FeSC ¿ ¿ K eq =¿ eq formula to determine Keq for this experiment is as follows: eq The aim of the experiment was to determine the equilibrium constant Keq of the reaction: Fe3+ + SCN⁻ ⇌FeSCN2+ by first measuring the equilibrium concentrations of the reacting species as well as the overall equilibrium concentration which can be determined by calibrating the spectrophotometry’s absorbance response to the varying concentration, thus creating a calibration graph. The graph’s line of best fit will the equilibrium concentration for FeSCN2+ for the different solutions. Beer’s Law states that there is a relationship between the attenuation of light through a substance as well as the properties of that substance, and thus, absorbance of a solution is directly proportional to the concentration of the absorbing species. It is defined as: “The path length and concentration of a chemical are directly proportional to its absorbance of light” (Beer 1852). The equation for Beer’s Law is: A=εbc where ‘A’ is the absorbance (no units), ‘ ε ’ is the Greek letter ‘Epsilon’ and represents the molar absorption coefficient (Mol-1 cm-1) and finally, ‘c’ represents the concentration of the compound in solution (M). Ultimately, in this experiment, absorbance will be directly proportional to the concentration of FeSCN2+ A real-life application of spectrophotometry’s is often seen in the commercial as well as industrial fields. The technique is often applied to plastics, paper, metals, fabrics and liquids to ensure that the chosen colour for the item remains constant from the initial conception, throughout the developmental stages, into the final, finished product. PROCEDURE The Keq Simulator.swf. was downloaded from D2L and opened. The equation M1V1=M2V2 was used to calculate the initial values of [SCN-]I and the dilution factor (V2/V1) was also taken into account. The volume of each component from the table (0.004 M SCN-, 0.10 M Fe3+, 1.0M HNO3 and H2O) were entered into the Part I portion of the Keq Simulator.swf. and the “Take Scan” button was clicked. The absorbance readings were then collected and recorded into a table. The input of data and recording of absorbance values were done separately for all six samples of the data. The next step was to graph Absorbance (x-axis) against Concentration (y-axis) in Excel. The line of best fit was added to the graph by clicking “add chart element”, and the equation of the line as well as R 2 value were added by clicking on the trendline. In Part II, the initial concentrations of SCN- and Fe3+ were calculated using the M1V1=M2V2 formula, and the dilution factor was also taken into account. The values were then recorded into a table. The volumes (mL) for each component (0.004 M SCN -, 0.10 M Fe3+, 1.0M HNO3 and H2O) were imputed into Part II section of the Keq Simulator.swf. and the “Take Scan” button was clicked. The input of component volumes were inputted into the simulator until an absorbance value was recorded for all six samples. Using the absorbance value of each sample as well as the equation of the line calculated using excel, [FeSCN2+]equil was solved for using the slope-intercept form y=mx + b and solving for x . From this value, the ICE box technique was used to calculate the equilibrium concentrations of all species. The final step was the calculate the K eq value by using the equilibrium concentration [FeSCN2+]equil divided by the equilibrium concentrations of the two species (Fe3+ and SCN-) Fe 3+¿¿ −¿ ¿eq ¿ SC N ¿ ¿ N 2 +¿¿ FeSC ¿ ¿ K eq =¿ eq multiplied by each other. value eq DATA PART I Sample 1 2 3 4 5 [SCN]i 0 0.00006 0.00012 0.00024 0.0004 [FeSCN2+]eq 0 0.00006 0.00012 0.00024 0.0004 Absorbance 0 0.18 0.41 0.70 1.39 Table 1: The initial concentrations (M) of SCN are equivalent to the equilibrium concentrations of FeSCN2+ as the equilibrium has been forced to the far right by having the Fe3+ much higher than the SCN- Concentration (M) vs. Absorption 1.6 1.4 f(x) = 3406.65 x − 0.02 R² = 0.99 Absorption 1.2 1 0.8 0.6 0.4 0.2 0 0 0 0 0 0 0 0 0 0 0 Concentration(M) Graph 1: The Concentration (M) on the x-axis, is graphed against the Absorption on the yaxis. PART II Sample SCN- (M) Fe3+ (M) 1 0.0004 0.0016 2 0.0008 0.0012 3 0.001 0.001 4 0.0014 0.0006 5 0.0004 0.0006 6 0.0015 0.0015 Table 2: Concentrations (M) of SCN- and Fe3+ calculated using the equation M1V1=M2V2 for M2 Sample Absorbance [FeSCN2+]equil 1 0.35 0.000109405 2 0.60 0.000182792 3 0.57 0.000173986 4 0.52 0.000159308 5 0.15 0.000050696 6 0.75 0.000226824 Table 3: Calculated absorbance values using the Keq Simulator.swf. for each of the six samples as well as the [FeSCN2+]equil value obtained by solving for “x” using the slopeintercept form of the line. Sample [FeSCN2+]equil [Fe3+]equil [SCN-]equil Keq 1 0.000109405 0.001419 0.0002906 252.506 2 0.000182792 0.001017 0.0006172 291.155 3 0.000173986 0.000826 0.0008261 255.008 4 0.000159308 0.000441 0.0012407 291.359 5 0.000050696 0.000549 0.0003493 264.220 6 0.000226824 0.001273 0.0012731 139.969 Table 4: Sample results for reactant equilibrium and product equilibrium as well as the calculated equilibrium constant (Keq) Sample Keq 1 252.506 2 291.155 3 255.008 4 291.359 5 264.2199 6 139.969 Average = 249.036 Table 5: The Keq value calculated for each sample as well as the average Keq value. The average Keq across the six different samples is: 249.036 CALCULATIONS SAMPLE CALCULATION PART II SAMPLE 2: 2+¿ −¿ ⇌ FeSC N ¿ Fe 3 ++SCN¿ M 1 V 1= M 2 V 2 M 2= M1 V1 V2 M 2= ( 0.004 )( 4 ) 20 M 2=0.0008M SAMPLE CALCULATION PART II for [FeSCN2+]equil (1a) (1b) (1c) Y = Absorbance x = Concentration of FeSCN2+ y =3406.6 x −0.0227 (2a) 0.35=3406.6x− 0.0227 (2b) x= 0.35+0.0227 3406.6 (2c) x=0.000109405M SAMPLE CALCULATION PART II: SAMPLE 1 ICE BOX SCN- (M) Fe3+ (M) FeSCN2+ (M) Initial 0.0004 0.0016 0 Change -0.000109405 -0.000109405 0.000109405 Equilibrium 0.000290595 0.001491 0.000109405 Table 6: ICE box calculations using the initial concentrations of the two species to calculate the equilibrium concentrations. SAMPLE CALCULATION PART II: SAMPLE 1 Keq Fe 3+¿¿ −¿ ¿eq ¿ SC N ¿ N 2 +¿¿ FeSC ¿ ¿ K eq =¿ eq K eq = (3a) eq (3b) 0.000109405 ( 0.000290595)( 0.001491 ) K eq =252.506 DISCUSSION Our Keq value should be very reliable as the experiment was done through a simulation thus limiting the chances of systematic and random errors which may have occurred during an actual lab experiment. The calculated Keq average value was 249.036, and all Keq values for the six samples centred around that mean value with no extreme outliers present. Ultimately, if the value of Keq is > 1, the products in the reaction is > than the reactants, and the reaction favours the formation of products (forward reaction). In contrast if Keq is < 1, there are more reactants than products, and the reaction favours the formation of reactants (reverse reaction) and if Keq = 1, the products = the reactants. Ultimately, our calibration curve is reliable as the initial concentration of [SCN -] and the equilibrium concentration of [FeSCN2+]eq were calculated using the Keq Simulator.swf. which decreases the chances of random errors (adding the incorrect volume of SCN -). The absorbance of each sample was also calculated using the simulator, further decreasing the chances of random errors such as human perception. The concentration (M) and absorbance were graphed against each other to create the calibration curve. The line does pass through the origin where [FeSCN2+] =0 and Absorbance=0, as it should. Beer’s Law states that: absorbance of a solution is directly proportional to the concentration of the absorbing species. So therefore, absorbance is directly proportional to [FeSCN 2+] and if [FeSCN2+] = 0, absorbance will also be equal to 0. The calculated R 2 value for the line of best fit was 0.9894 (on a scale of 0 to 1), which means that there is a very strong, positive correlation between concentration (M) and absorbance, so therefore, the graph is highly accurate and the trendline, fits our observations. A spectrophotometer works by shining a specific wavelength of light through a liquid sample. This apparatus consists of two main components- a spectrometer which has a lens that sends a straight beam of light through a prism, to split it up into its individual wavelengths. A wavelength selector then filters out the specific wavelength/s and sends it towards the photometer which detects the number of photons that are absorbed and displays the value on a digital display. The wavelength (nm) is set to a specific value for the compound that is being measured. A spectrophotometer is able to quantify how much a given substance (in this case, the substance is our solution of [FeSCN 2+]equil) reflects of absorbs light. By using a specific measurement to detect absorbance and colour, decreases the chances of random errors such as human perception, as differences in human perception of a specific colour (violet) may appear differently to different people due to colour blindness, eye-fatigue or another limiting factor. (more blue or more purple). Ultimately, the specific wavelength is determined by determining the maximum absorbance of the compound. As Beer’s Law states, “the path length and concentration of a chemical are directly proportional to its absorbance of light” (Beer 1852). Ultimately basing our experiment on Beer’s Law, the absorbance will be directly proportional to the concentration of FeSCN2+ and this is shown in Graph 1 as Concentration (M) and absorbance are basically proportional (shown by the line of best fit and a R 2 value of 0.9894). Subsequently, the spectrophotometer is the perfect piece of apparatus to use for this experiment, as it utilises light (wavelengths) to calculate absorbance and thus equilibrium concentrations of our solutions. Wavelengths between 400-800nm are in the visible range and include colours from red (longest wavelength) to violet (shortest wavelength). If values such as 325nm or 600nm were chosen, the experiment may not be accurate, as some solutions may surpass these values and impact the accuracy of the experiment as the results would be inaccurate. Therefore, the max wavelength of light should be used. In Part I of the experiment, the equilibrium was forced to the far right as there was a much higher volume (mL) of Fe3+ than the SCN- so at equilibrium, [SCN-]I was equivalent to [FeSCN2+]eq and the reaction favoured the products. In Part II, the aim was to measure a different set of samples will reach an equilibrium without having to force the equilibrium to the far left or to the right. This means that the reaction favours nor the reactants, or the products. Since Keq is a constant, its value depends on equilibrium concentrations of the reactants using their relative ratios which stay constant, so therefore, Keq also stays constant at a particular Fe 3+¿¿ −¿ ¿eq ¿ SC N ¿ ¿ N 2 +¿¿ FeSC ¿ ¿ K eq =¿ eq temperature. eq Consequently, the Keq values for the solutions should not drastically vary. If the value of Keq is > 1, the products in the reaction is > than the reactants, and the reaction favours the formation of products (forward reaction). In contrast if Keq is < 1, there are more reactants than products, and the reaction favours the formation of reactants (reverse reaction) and if Keq = 1, the products = the reactants. In all samples of our experiment, the K eq was greater than one, demonstrating that the reaction favours the formation of products and is thus a forward reaction. There are not many potential sources of error in this experiment, as it was done through a simulation, which drastically decreases the chances of systematic (inaccurately calibrated instrument) and random errors (human perception error) which may have occurred during an in-person experiment. However, a range of random errors may have occurred during the process of the simulation. Incorrectly entering values such as the volume (mL) into the simulation will produce an incorrect absorbance value which will then impact the accuracy and reliability of values such as Keq, [SCN-]equil, [Fe3+]equil in further steps. According to Beer’s Law: A=εbc , under specific conditions, a substances’ concentration (M) and its absorbance are directly proportional. If a sample is too concentrated, more light will be absorbed. In contrast, a solution of a lower concentration will absorb less light. For the linearity of Beer’s Law to be maintained, absorbance values must range between 0.2 and 0.5. No, a maximum absorbance value of 2.0000 should not be used as it varies drastically from the ideal values between the ranges of 0.2 and 0.5 for Beer’s Law to take effect. Using a absorbance value of 2.000 will result in extreme outliers, and thus the R 2 value of the graph will weaken. Absorbance values either below 0.2, or above 0.5, would affect our lab results, as they are not ideal values. CONCLUSION According to Beer’s Law: A=εbc , under specific conditions, a substances’ concentration (M) and its absorbance are directly proportional. This is seen in Graph 1, as there is a very strong correlation between Concentration (M) and absorbance, as shown by the R 2 value of 0.9894. For the linearity of Beer’s Law to be maintained, absorbance values must range between 0.2 and 0.5 (Graph 1). Values below 0.2, or above 0.5 will result in a loss of linearity, and a weaker R 2 value. The main objective of the lab was to calculate the equilibrium constant Keq of the reaction: Fe3+ + SCN⁻ ⇌FeSCN2+. The average Keq was calculated to be 249.036 using a variety of techniques to determine equilibrium concentrations of reactants and products such as the ICE box. Overall, the Keq values of all six samples, centred around the mean Keq value of 249.036, with no outliers present in the data. Overall, this lab was a success as the graph showed a very strong correlation between concentration (M) and absorbance, confirming the accuracy of Beer’s Law. Overall, our results were very reliable as the experiment was completed through a simulation, limiting the chances of systematic and random errors which would affect our results. If the lab was to be repeated, more samples with varying reactant volumes (mL) could be added to produce more data points, which would potentially increase the R 2 value of the graph and result even more precise and accurate results. REFERENCES N/A