Experiment #4:Chemical Kinetics

By: Simon Hagos7767295

Partner: Patrick Ding7426216

CHM 1311 Section C3

Demonstrator:Philip Dumouchel

DON’T PRINT THIS PAGE BECAUSE IT IS NOT COVER PAGE

October 22, 2014

Department of Chemistry

University of Ottawa

Experiment 4. Chemical Kinetics

Introduction:

A chemical reaction is a process by which new substances are formed due to chemical changes. These reactions occur at particular rates, which are thoroughly studied in the area of chemistry known as chemical kinetics. Chemical kinetics is all about studying particular factors that affect reaction rates. These particular factors are catalysts, surface area, concentration of reactants and their chemical nature and temperature. Temperature is an important factor of reaction rates in this experiment. When the temperature is increased, reaction rates increase because of really large increases in high energy collisions (Clark). Graphical analysis can be used to find the rate of reaction. Generally, the rate of a chemical reaction can be expressed as follows.

Reaction rate (average) = r = Δc/Δt = change in concentration/elapsed time [1]

Yet, the initial rate of a reaction can be determined using the following equation where [X] and [Y] are the reactants initial concentration, k is the rate law constant, m and n (powers) are the orders of reaction which describe how the reactants concentration affects the rate.

r=k [ X ]m¿ [2], where X+Y –> Products

The overall order of the reaction is equal to m+n. All of the variables in the rate law equation are determined experimentally.

In this experiment, the rate of reaction is measured empirically analyzing reactions that change color. The important analytical tool known as spectrophotometry is used in order to properly measure the size of the quantity (substance) present based on its light absorption. This spectrophotometric analysis is also known as Beer-Lambert’s law and is expressed in the following equation where absorbance of a solution is equal to the products of the molar absorptivity coefficient, the (path) length of solution the light passes through and the concentration of the solution.

A=εbc [3]

For the reaction of the Cr(III) salt and the EDTA solution, the rate expression can be expressed as follows.

Rate = -d[Cr(III)]/dt = d[Cr(III) – EDTA]/dt = k[Cr(III)]a[H+]b [4]

The equation above can be simplified because the change in concentration of the EDTA can be neglected.

When using spectrophotometry, transmittance and absorbance are the two important measurements used in determining the rate of a reaction. Transmittance is the ratio of the intensity of light after passing the studied medium (I), to the light intensity before hitting the medium (IO). Absorbance is a logarithmic ratio describing the measure of the amount

of light absorbed by a sample, which is related to transmittance as expressed by the following equations.

T=I/IO [5]%T = [(I)(IO)] x 100% [6]

A = - log T = - log (I/IO) [7]

During the experiment, the percent transmittance is given from the modern spectrophotometers and the absorbance can be determined using the equations above. Next, the absorbance of the Cr(III) salt can be determined by the absorbance amount at time infinity where all of the salt has been completely reacted, and subtracting that by the absorbance amount at any specific point in the elapsed timing of the experiment.

ACr(III) = A∞ - AT [8] Overall, the log rate equation (in form y=mx+b) is used in order to determine the partial order of the reaction with respect to Cr(III) as follows.

Log Rate = alog[Cr(III)] + logK [9], where a=partial order

Procedure: As described in the lab manual (If it Were Done… Then ‘Twere Well it Were Done Quickly, Dr. Rashmi Ventateswaran, 2013, Exp. 4, p. 52-54).

Data Table:

Table 1: Raw Data

pH = 4.0 pH = 4.5 pH = 5.0

Volume of EDTA Solution (mL)

50.0 50.0 50.0

Temperature of Water Bath (°C)

22.1 22.1 22.1

Number of Drops of Cr(III) into EDTA Solution

7 6 5

%T = 5 mins 78.0 87.0 82.0%T = 10 mins 74.0 85.5 81.0%T = 15 mins 67.5 83.5 78.5%T = 20 mins 62.5 81.5 77.5%T = 25 mins 59.0 79.0 74.0

%T = 30 mins 55.0 77.5 71.5%T = 35 mins 51.0 75.0 70.0%T = 40 mins 47.5 73.0 68.0%T = 45 mins 45.5 71.0 63.5%T = 50 mins 43.5 69.5 63.0%T = 55 mins 41.0 68.0 62.5%T = 60 mins 40.5 68.0 62.0%T = 65 mins 39.0 66.5 61.0%T = 70 mins 39.0 65.0 60.0%T = 75 mins 36.0 62.5 57.5%T = 80 mins 36.0 62.5 56.5%T = 85 mins 36.0 62.5 56.0%T = 90 mins 35.0 62.0 56.0%T = 95 mins 34.0 61.0 55.0%T = 100 mins 34.0 61.0 54.0Time when cuvette solution cooled after heated

11.0 16.5 5.0

Observations:

Initially, the EDTA solutions consisting of pH’s 4.0 and 4.5 were transparent, whereas the 5.0 pH solution was a dark-greyish color (slight mix of black and purple). Once mixed with the added drops of the darkish blue Cr(III) solution to the EDTA, the following qualitative (color) observations were noticed respective to the pH, slight purple, moderate mix (sufficiently between both colors) and dark purple. Overall, all the solutions in the cuvettes were gradually turning purple throughout their time in the water bath and as well in hot bath. A trend observed was that the color of the cuvettes appeared more concentrated as the pH of the EDTA solutions observed increased.

A decrease in the percent transmittance throughout the first 75 minutes of the experiment occurred and after, the percent transmittance remained relatively constant for the remaining 25 minutes before the ten-minute hot bath. However, the percent transmittance significantly decreased after placed for ten minutes in the hot bath and cooled in the initial water bath placed. The reaction with the EDTA solution and the Cr(III) solution appeared complete once the tone of the cuvette appeared significantly concentrated (dark).

Table 2: Data and Results in analysis of cuvette solution over elapsed time for pH of 4.0.

Time (mins)

%T AT ACr(III) log[ACr(III)]RateInstantaneous

(m-1

)Log[RateInstantaneous]

5.0 78.0 0.108 0.851 -0.070 0.425 -0.37110.0 74.0 0.131 0.828 -0.082 0.414 -0.38315.0 67.5 0.171 0.788 -0.104 0.394 -0.40520.0 62.5 0.204 0.754 -0.122 0.377 -0.42325.0 59.0 0.229 0.729 -0.137 0.365 -0.43830.0 55.0 0.260 0.699 -0.156 0.349 -0.45735.0 51.0 0.292 0.666 -0.176 0.333 -0.47740.0 47.5 0.323 0.635 -0.197 0.318 -0.49845.0 45.5 0.342 0.617 -0.210 0.308 -0.51150.0 43.5 0.362 0.597 -0.224 0.299 -0.52555.0 41.0 0.387 0.571 -0.243 0.286 -0.54460.0 40.5 0.393 0.566 -0.247 0.283 -0.54865.0 39.0 0.409 0.550 -0.260 0.275 -0.56170.0 39.0 0.409 0.550 -0.260 0.275 -0.56175.0 36.0 0.444 0.515 -0.288 0.257 -0.58980.0 36.0 0.444 0.515 -0.288 0.257 -0.58985.0 36.0 0.444 0.515 -0.288 0.257 -0.58990.0 35.0 0.456 0.503 -0.299 0.251 -0.60095.0 34.0 0.469 0.490 -0.310 0.245 -0.611

100.0 34.0 0.469 0.490 -0.310 0.245 -0.611 . ∞

11.0 0.959 0.000

Table 3: Data and Results in analysis of cuvette solution over elapsed time for pH of 4.5.

Time (mins)

%T AT ACr(III) log[ACr(III)]RateInstantaneous

(m-1

)Log[RateInstantaneous]

5.0 87.0 0.060 0.722 -0.141 0.361 -0.44210.0 85.5 0.068 0.714 -0.146 0.357 -0.44715.0 83.5 0.078 0.704 -0.152 0.352 -0.45320.0 81.5 0.089 0.694 -0.159 0.347 -0.46025.0 79.0 0.102 0.680 -0.167 0.340 -0.46830.0 77.5 0.111 0.672 -0.173 0.336 -0.47435.0 75.0 0.125 0.658 -0.182 0.329 -0.48340.0 73.0 0.137 0.646 -0.190 0.323 -0.49145.0 71.0 0.149 0.634 -0.198 0.317 -0.499

50.0 69.5 0.158 0.625 -0.204 0.312 -0.50555.0 68.0 0.167 0.615 -0.211 0.308 -0.51260.0 68.0 0.167 0.615 -0.211 0.308 -0.51265.0 66.5 0.177 0.605 -0.218 0.303 -0.51970.0 65.0 0.187 0.595 -0.225 0.298 -0.52675.0 62.5 0.204 0.578 -0.238 0.289 -0.53980.0 62.5 0.204 0.578 -0.238 0.289 -0.53985.0 62.5 0.204 0.578 -0.238 0.289 -0.53990.0 62.0 0.208 0.575 -0.240 0.287 -0.54195.0 61.0 0.215 0.568 -0.246 0.284 -0.547

100.0 61.0 0.215 0.568 -0.246 0.284 -0.547 ∞ 16.5 0.783 0.000

Table 4: Data and Results in analysis of cuvette solution over elapsed time for pH of 5.0.

Time (mins)

%T AT ACr(III) log[ACr(III)]RateInstantaneous

(m-1

)Log[RateInstantaneous]

5.0 82.0 0.086 1.215 0.085 0.607 -0.21710.0 81.0 0.092 1.210 0.083 0.605 -0.21815.0 78.5 0.105 1.196 0.078 0.598 -0.22320.0 77.5 0.111 1.190 0.076 0.595 -0.22525.0 74.0 0.131 1.170 0.068 0.585 -0.23330.0 71.5 0.146 1.155 0.063 0.578 -0.23835.0 70.0 0.155 1.146 0.059 0.573 -0.24240.0 68.0 0.167 1.134 0.054 0.567 -0.24745.0 63.5 0.197 1.104 0.043 0.552 -0.25850.0 63.0 0.201 1.100 0.042 0.550 -0.25955.0 62.5 0.204 1.097 0.040 0.548 -0.26160.0 62.0 0.208 1.093 0.039 0.547 -0.26265.0 61.0 0.215 1.086 0.036 0.543 -0.26570.0 60.0 0.222 1.079 0.033 0.540 -0.26875.0 57.5 0.240 1.061 0.026 0.530 -0.27580.0 56.5 0.248 1.053 0.022 0.527 -0.27985.0 56.0 0.252 1.049 0.021 0.525 -0.28090.0 56.0 0.252 1.049 0.021 0.525 -0.28095.0 55.0 0.260 1.041 0.018 0.521 -0.283

100.0 54.0 0.268 1.033 0.014 0.517 -0.287 ∞ 5.0 1.301 0.000

Calculations:

The following sample conversion and calculations is done for any arbitrary pH value (pH = 4.5 at t=20 mins).

T= %T/100 = 81.5/100 = 0.815

AT = -logT = -log(0.815) = 0.0888

A∞ = -logT = -logT = -log[%T/100] = -log[16.5/100] = 0.7825

ACr(III) = A∞ - AT

= 0.7825 – 0.0888 = 0.6937

The following sample calculations also completed using the same conditions (pH = 4.5 at t=20mins) are to display how the points for the curves (logA vs t and logRate vs logA) are determined.

log[ACr(III)] = log0.6937 = -0.1588

RateInstantaneous = y/Δx = ACr(III)/Δx = ACr(III)/2mins = 0.6937/2 = 0.3469 min-1

RateInstantaneous obtained from graph = 0.3859 min-1

logRate = log(0.3469) = -0.4599

Order calculations – Please refer to graph 3.Regarding the order outcome, the partial order with respect to the Cr(III) ion from

the slope of graph 3 is in the first order.

Discussion:

The main objective of the experiment was using the principles of absorbance, transmittance, reaction rates and spectrophotometry to determine the instantaneous rate

on the logRate vs logACr(III) graph and significantly, the partial order with respect to Cr(III) ion. The experiment went accordingly using the procedures from the lab manual, which seemed straightforward and the notion was determined that the data experimentally determined was reproducible. As a result, even though the measurements of the volumes of the EDTA solution and Cr(III) drops may seem adequate and were not the primary emphasis (technique required) for the experiment, volume and temperature measures are important for this experiment. Those two measurements were important because they must be constant for this experiment and in addition, weighing-related measurements are usually where a deviation occurs in the lab (back to data). As well, the concentration of Cr(III) salt will change if volume is not constant.

Next, the spectrophotometer was manually altered to the appropriate standard by the lab demonstrator making all of the spectrometers used the same. If a particular source of error were really observed, it would be the decrease in the temperature of the water bath using tap water throughout the elapsed time of the experiment. The temperature experienced some inconsistency shifting from 22.1°C to around approximately 19.4°C. which effected the rate of reaction causing a decrease in the ACr(III) vs t graph. As well, since the timing for the experiment was not impeccable and the times at when the percent transmittance was recorded were after the spectrophotometer reading, the data’s accuracy for the time (x) values decreased. In addition, another source of error could be when wiping the cuvettes prior to inserting them into the spectrophotometer’s slot because the effectiveness of the Kimwipe’s ability to wipe grease or fingerprints with good durability is questionable. Any oil or dirt could interfere with the light’s passing through the sample that could be a disfavor for the experiment since it could possibly increase the ACr(III) values, following an increase in value for the order of the reaction with respect to Cr(III) and overall rate.

In graph 1, the formula used to calculate the instantaneous rate was y/ Δx, which was approximated instead of simply being Δy/Δx. The approximation that was carried out was acceptable to use because in the end, the approximation is a good aid / (time-efficient) method of the calculation. The partial order of the reaction with respect to Cr(III) ion is determined in the 3rd graph and since dividing the y values by 2 minutes, the time interval (Δx) which is constant and used every time, it maintains the certainty of the rate at which the y values change. Determining the instantaneous rate for any value of y was not necessary.

In addition, there were differences between the 3 samples that affected the values in the lab. The pH values and values of the hydrogen ion concentration varied in the samples. In graph 1 the first two trials were linear and the third trial with a pH of 5.0 was a curved plot. The relationship between both variables noticed explains how the differences in each sample affect the values. The relationship between both variables noticed is how as the pH increases, the rate of the reaction increases and vice-versa applies to the values of ACr(III) and interestingly the H+ concentration (both decrease). As a result, the prediction can be made that the partial order with respect to the hydrogen ion is negative (due to proportionality relationship where [H+] ∝ 1/Reaction rate).

In graph 2, for the two trials of pH = 4.0 and 4.5, the graphs were linear and the slopes for both best fit lines were negative displaying how the reaction is overall pseudo first order since the decrease in the concentration of Cr(III) ions slowed over the elapsed time.

In graph 3, the graph plotted helped in confirming the partial order of the reaction with respect to Cr(III) ion by determining the slope of the graph (since it is equal to the partial order). The slope was equal to around 0.992 and 0.921 respectively for trials 1 and 2.

Rate = k [Cr(III)a[H+] b[EDTA]c = k’[Cr(III)]a

and logRate = logK’+ a[logACr(III)]

y = b + m [x] , where a is slope which is partial order with respect to Cr(III) ion.

Depicting the graph tells how the reaction is first-order. Also, literature information was obtained online which found the reaction to be first-order (Abdel-Messih).

Also, when the reaction was forced at the end of the experiment, it was really evident how after ten minutes at a higher temperature, the boiling hot water bath rapidly made a significant qualitative change in color (increase in dark-purple tone).

Conclusion:

In conclusion, the partial order of the reaction with respect to Cr(III) ion was found to be pseudo first order and the slope measured it to be 0.992 and 0.921 respectively, from the solutions with pH = 4.0 and 4.5. Yet, the slopes that should have been gotten were a value of 1, resulting in percent errors of 7.9 and 0.83 for the 2 trials. In addition, an increase in the following factors; EDTA concentration, temperature and pH result in a more accelerated reaction rate. Moreover, the measure of the concentration of the Cr(III) ion which is also known as the absorbance or optical density, for all values of pH, decreases as a function of elapsed time.

Reference:

Clark, Jim. "The Effect of Temperature on Rates of Reaction." The Effect of Temperature on Rates of Reaction. ChemGuide, 1 Oct. 2013. Web. 27 Oct. 2014. <http://www.chemguide.co.uk/physical/basicrates/temperature.html>.

If it Were Done… Then ‘Twere Well it Were Done Quickly, Dr. Rashmi Ventateswaran, 2013, Exp. 4, p. 52-54.

Messih, M.F. Abdel. "Kinetics and Mechanism of Interaction between Chromium(III) and Ethylenediaminetetra-3-Propinate in Aqueous Acidic Media." Advances in Chemical Engineering and Science 2013.98-104 (2012): 99,103. ScientificResearch Publishing. SCIRP. Web. 26 Oct. 2014. <http://dx.doi.org/10.4236/aces.2013.31012>.

Silberberg, Martin, Sophie Lavieri, and Rashmi Venkateswaran. Chemistry: The Molecular Nature of Matter and Change. 1st ed. McGraw-Hill Ryerson, 2013. Chapter 14. Print.