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Lab report experiment 1 Introduction The objective is to experimentally determine the order of the reaction between crystal violet and sodium hydroxide, and write rate law based on the data obtained. Additionally, the change in rate constant is to be examined at different temperatures. The values of the rate constant obtained are to be used to calculate the activation energy of the reaction, as well as to evaluate the half-life of the reaction at different temperatures [1]. The reaction includes two reactants, which are solutions of crystal violet and sodium hydroxide, and the color change occurs due to reaction between crystal violet and hydroxide ion (equation 1) [1]. The solution of sodium hydroxide (NaOH) is a colorless translucent solution, with basic pH, highly corrosive in higher concentrations. Crystal violet (CV) is an organic compound with the formula C 25 H 30 N 3 Cl. It is a basic dye that displays different colors depending on the pH and is used in histology and microbiology as a stain, as well as a cytotoxic agent, as a component of antifungal and antiparasitic medications [3]. CV +¿+ OH –^ ( aq ) → CVOH ¿ (^) (1) The rate law is an equation that describes the rate of the reaction depending on the rate constant of the reaction at specific temperatures and concentrations of the reactants. Depending on the impact of the concentration, the reaction can be 0th, 1st, or 2nd^ order. If the concentration is doubled and it does not affect the rate, the reaction is of 0th^ order. If the concentration is doubled and the rate doubles as well, the reaction is of 1st^ order. If the concentration is doubled and the rate of reaction quadruples, the reaction is of 2nd^ order. To determine the rate law, the absorbance over time was measured for the reaction between CV and NaOH. The absorbance was measured using the method of spectroscopy. The principle of spectroscopy is that the ray of light passes through the sample and is absorbed by particles in the solution. The remaining light is captured by an array detector and analyzed a by computer with the output in the form a of graph providing information about absorbance depending on the wavelength, or absorbance over time, which was mainly utilized in this experiment [2]. To achieve temperature below and above room temperature, cold and warm water bath were used under constant temperature control to ensure the constant temperature of the probe place in the water bath. The results were graphed in accordance with integrated laws of 0th, 1st,^ and 2nd^ order. The 0th order reaction general rate law form is presented in equation 2 and its integrated form is presented in equation 3. The plot for integrated form of 0th^ order is received by graphing Absorbance (y-axis) over Time (x-axis). rate=k (2)
At =− kt + A 0 (3) The 1st^ order rection general rate law form is presented in equation 4, and its integrated form is presented in equation 5. The plot for integrated form of 1st^ order is received by graphing natural logarithm of absorbance (y-axis) over Time (x-axis). rate=k[A] (4) ln ( A ¿¿ t )=− kt +ln ( A 0 )¿ (^) (5) The 2nd^ order reaction general rate law form is presented in equation 6, and its integrated form is presented in equation 7. The plot for integrated form of the 2nd^ is received by graphing 1/Absorbance (y-axis) over 1/Time (x-axis). rate=k[A]^2 (6) 1 A (^) t = kt +
A 0
The suitable rate law can be determined based on the value of R^2 , which shows the degree of correlation between data points. The plot with R^2 closest to 1 has the strongest correlation between data points and indicates the order of the reaction. The plot of the integrated rate law allows to determine k, which is a negative slope for 0th and 1st^ order reactions and a positive slope for 2nd^ order reactions. Rate constant obtained at different temperatures allows to obtain Arrhenius plot by graphing ln of rate constant on y-axis and 1/temperature on x-axis. The line obtained corresponds to the integrated form of Arrhenius equation (equation 8), where k is rate constant, Ea is the activation energy, R is gas constant, T is temperature, in Kelvin, and A is a pre-exponential factor. Arrhenius plot allows to calculate activation energy of the reaction, as well as the pre-exponential factor. Lastly, rate constant and order of the reaction allow to determine the half-life of the reaction, which is the time over which the concentration of the reactant decreases by 50%. ln ( k )= − Ea RT +ln ( A ) (^) (8) Data and observations The reaction occurred between equal amounts (10.00 mL) of 0.020M NaOH (colorless translucent solution) and (^) 2.5 ∙ 10 −^5 M crystal violet solution (dark violet translucent solution). At the start of the reaction the obtained mixture was bright violet with no precipitate, and got colorless after 13 minutes of reaction at room temperature (20.4◦C) and 10 minutes of reaction at a higher temperature (27.6◦C). The reaction at a colder temperature (14.2◦C) was still light violet and translucent at the end of 13 min.
0 100 200 300 400 500 600 700 800 -1. -1. -1. -1.
-0. -0. -0. -0. 0 f(x) = − 0.00130134933686861 x − 0. R² = 0. Time, sec Ln (absorbance) Figure 3. Change in absorbance over time for a first-order reaction at room temperature. For the second order, the graph of 1 over absorbance at 1 over time t was created. 0 0.005 0.01 0.015 0.02 0.025 0.03 0. 0 1 2 3 4 5 6 f(x) = − 92.3139902897773 x + 3. R² = 0. 1/time, 1/sec 1/absorbance Figure 4. Change in absorbance over time for second-order reaction at room temperature. Out of the three graphs, orders 0 and 1 provided a straight line, which immediately allowed excluding the second order as a possibility for the rate law of this reaction. R^2 for the zeroth order was 0.9913, while for the first order, R^2 was 0.9976. R^2 closer to 1 shows a stronger correlation between data points, which allowed for a conclusion that the reaction between crystal violet and NaOH is of the first order with regard to CV. The concentration of NaOH was not accounted for, so the reaction is of zeroth order in regards to NaOH. Since the reaction between CV and NaOH was determined to be first order, data for temperature above and below room temperature was plotted in accordance to the integrated first- order law. The temperature for the cold bath was 14.2◦C being below room temperature (20.4 ◦C) by 6.2◦C. The data obtained was graphed with x being the time of reaction, in seconds, and y being Ln of absorbance.
0 100 200 300 400 500 600 700 800 900 -1. -1. -1.
-0. -0. -0. -0. 0 f(x) = − 0.000816455054171339 x − 0. R² = 0. Ln absorbance Time Figure 5. Change in absorbance of the reaction over time at the temperature 6.2◦C below room temperature. The temperature for the warm bath was 27.6◦C being above room temperature (20.4 ◦C) by 7.2◦C. The data obtained was graphed with x being the time of reaction, in seconds, and y being Ln of absorbance. 0 100 200 300 400 500 600 700 800 -2.
-1.
-0. 0 f(x) = − 0.00187913285372019 x − 0. R² = 0. Ln (absorbance) Time Figure 6. Change in absorbance of the reaction over time at the temperature 7.2◦C above room temperature. The equations of the integrated rate law obtained are in y=mx+b form, which corresponds to the integrated first order rate law with ln[At] being y, -k being m, t being x, and y-intercept b being ln[A 0 ]. The rate constant is equal to the negative of the slope. Rate constant k for temperature 20.4◦C is 0.0013, k for temperature 14.2◦C is 0.0019, and k for temperature 27.6◦C is 0.0008. The rate law with respect to CV is rate=k[CV]. For room temperature, the rate law is rate=0.0013[CV]. For the temperature 6.2◦C below room temperature, the rate law is rate=0.0019[CV]. For the temperature 7.2◦C above room temperature, the rate law is rate=0.008[CV].
Ea =46.2 kJ To calculate pre-exponential factor A, the y-intercept b was the following approach was utilized. A = e b A = e
A =209190.37=2.09 ∙ 10 5 Half-time was calculated for each setting of the reaction using the half-life formula for the first order rate law t 1 / 2 = ln( 2 ) k For room temperature, k was determined to be 0.0013. t 1 / 2 = ln( 2 ) kroom t 1 / 2 = ln ( 2 ) 0.0013 1 / sec t 1 / 2 =533.1 sec For temperature above room temperature, k was determined to be 0.0019. t 1 / 2 = ln( 2 ) kroom t 1 / 2 = ln ( 2 ) 0.0019 1 / sec t 1 / 2 =364.7 sec For temperature below room temperature, k was determined to be 0.0008. t 1 / 2 = ln( 2 ) kroom t 1 / 2 = ln( 2 ) 0.0008 1 / sec t 1 / 2 =866.3 sec Discussion The objective of the experiment was to determine the order of the reaction between CV and NaOH experimentally and examine how the rate constant is affected by the change in temperature. Based on the changes in k, the Arrhenius plot was created, activation energy and pre-exponential factor were calculated from the plot, as well as half-life of the reaction at three different temperatures was determined. The integrated rate law plots were utilized because the strength of the connection between concentration (or absorbance, like in this case) and time, plotted in accordance with three integrated
laws of different orders, allows to experimentally determine the order of the rate law of the reaction. The closer the correlation factor, R^2 is to 1, the stronger the connection exists between data points. For 2nd^ order, R^2 for all three temperatures was below 0.5. which indicated on correlation between data points. R^2 for 0th^ and 1st^ order were above 0.9 for all three temperatures, with R^2 of the 1st^ order plot being closer to 1, which allowed to conclude that the reaction is of 1st^ order with regards to CV. Rate constant k was determined from the equation describing the 1st^ order plot as -m. Value k was the highest (0.0019 s-^1 ) for temperature above room temperature and lowest for temperature below room temperature (0.0008 s-^1 ). Rate constant describes how much the concentrate changes over time t, with lower k indicating a slower change in absorbance, and higher k indicating faster change in absorbance. According to the data obtained, increasing the temperature increases k, consequently increasing rate of reaction (presented as faster change in absorbance in Figure 1). Decreasing the temperature decreases k, consequently decreasing the rate of reaction (presented as slower change in absorbance in Figure\ 1). Using different values of k obtained at different temperatures, the Arrhenius plot was created. The plot shows that with decrease in temperature value of ln(k) also decreases, indicating linear connection (Figure 6). The equation describing the plot obtained allowed to determine activation energy of the reaction and pre-exponential factor A. Activation energy is the amount of energy need to break the bonds in the reactants and initiate the reaction. It was determined to be 46.2 kJ (^) , and was not affected by change in temperature. Pre-exponential factor A describes the number of collisions and orientation of the molecules at the time of collision that is needed to achieve the rate constant k at the activation energy Ea. It was determined to be (^) 2.09 ∙ 105 and was not affected by change in temperature. Values k at different temperatures were also used to determine half-life of the reaction at different temperatures. The longest half-life was calculated to be 866.3 sec at 14.2◦C because the rate of the reaction was the slowest at the lowest temperature in the setup. Slower reaction rate was the result of decreased number of collision and longer time needed to accumulate enough energy needed to break down the bonds in reactants and initiate the reaction. The shortest half-life was 364.7 sec for the reaction at 27.6◦C because the rate of the reaction was the fastest in this set up. The number of collisions was the highest as speed of particles increases with temperature, as well as their kinetic energy being higher, which results in reaction accumulating activation energy faster and having a higher overall rate. The results obtained are highly precise and accurate as indicated by R^2 above 0,9, which is an indication of high degree of correlation between data point. Due to that, the equations describing the trend lines of the plots are highly reliable, and so are the value of k, t1/2, and Ea calculated using them.
- The order of the reaction at all three temperatures in the experiment is same (all reactions are of the 1st^ order), which indicates that elementary steps likely remain the same and the mechanism of reaction does not change with the change in temperature. The only thing that likely changes is the rate of slow step. The rate of the slow step decreases with decrease in temperature as the number and strength of collisions becomes lower and it takes longer to accumulate enough energy to overcome Ea. The rate of the slow step increases with increase in temperature as the number and energy of collision increases, the Ea is reached sooner, and the overall reaction run to compilation faster than it would at a lower temperature. Sources Garces, Fred O. Chemistry 201 L Laboratory Packet ; San Diego Community College District: San Diego, CA, January 2023 ; pp 95- “Go Direct® Spectrovis® plus Spectrophotometer.” Vernier , https://www.vernier.com/product/go- direct-spectrovis-plus-spectrophotometer/. “CHEBI:41688 - Crystal Violet.” ChEBI , EBI Web Team, www.ebi.ac.uk/chebi/searchId.do? chebiId=CHEBI%3A41688. Accessed 23 Sept. 2023.
