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Physical Chemistry Sixth Form Practicals - 2016 Porter Laboratory INTRODUCTION Physical chemistry is a quantitative science. Skill in practical work is as important as a knowledge of theory. Many important discoveries have resulted from observations of small inconsistencies in repeated measurements or minor discrepancies between theory and experiment. Well known examples are the discovery of the noble gases from the precise measurement of relative molar masses; the development of the idea of electron and nuclear spin from observations on the fine splitting of spectral lines; the discovery radioactivity from the fogging of photographic plates left in the proximity of uranium salts. These developments would not have taken place without the acute observation of the researchers and an appreciation of the reliability and significance of their measurements. The main objective of physical chemistry laboratory work is to provide training and practice in the collection and critical evaluation of experimental data and in the preparation of reports. The emphasis in the practical work is in making measurements and assessing the errors in the measurements and final results. There is also the opportunity to use a computer for tabulating data, calculating results and plotting graphs. Two programs are available: Microsoft Excel – most students will have used this package previously. OriginPro - A graph drawing package with spreadsheet facilities. It will plot straight line graphs and calculate the gradient and intercept with error limits. Very easy to use! Each student will be able to perform two experiments. 1. The Ionisation Energy of the Hydrogen Atom 2. Kinetics of a first order reaction (hydrolysis of t-butyl chloride) by measurements of conductivity. EXPERIMENT 1 The Ionisation Energy of the Hydrogen Atom The OBJECTIVES of this experiment are: 1. To measure the wavelengths of the first three lines of the Balmer series in the emission spectrum of the H atom using a spectrometer. 2. To calculate the Rydberg constant and the ionisation energy of the H atom. BACKGROUND Spectra refer to patterns of emission and absorption of light from atoms. The observation of spectra was a important step in the development of atomic theory and led to the Bohr model of atoms. In this model, electrons orbiting the nucleus can exist only in discrete orbits and at specific energies. Absorption spectrum - Shows atoms changing states on absorption of electromagnectic radiation. Atomic states are defined by the arrangement of electrons in atomic orbitals. An electron in one orbital i.e. the ground state, may be excited to a more energetic orbital by absorbing one photon of energy. Absorption spectra can be used to identify elements present in liquids and gases. Emission spectrum - a molecule undergoes a transition from higher energy level to a lower energy level, usually the ground state. It gives out energy of a particular wavelength showing the discrete lines of an emission spectrum. The spectra can be used to determine the Energy composition of a material, i.e. composition of stars. Absorption Emission E2 E1 Frequency, wavelength, wavenumber and energy Electromagnetic radiation is characterised by its frequency and its wavelength . These are related to the speed of propagation c by the equation c = . The energy possessed by one quantum of radiation (a photon) of frequency is given by the Planck equation = h , where h is Planck’s constant and has the value 6.62607 10-34 J s. The frequency of a photon is expressed in the SI unit reciprocal seconds (s1). The energy of one mole of photons is given by E = NAh, where NA is the Avogadro’s constant and has the value 6.02214 1023 mol1. This equation yields energy in J mol1. Spectroscopists usually characterise radiation by its wavenumber, 1/ . In SI units the wavenumber would be m1 but invariably the unit used is cm1 (1 cm1 = 100 m1). Hydrogen Spectrum This figure illustrates the energy levels of the hydrogen atom and the possible transitions occurring in the emission spectrum. To the far left is the Paschen series which was discovered by Friedrich Paschen in 1908 and is in the Infra-red region of the electromagnetic spectrum. The middle series was discovered by Theodore Lyman in 1906 and is in the far Ultraviolet region. On the right is the Balmer series and the part of most interest for this experiment. In 1885, the Swiss Physicist Johann Balmer, observed the emission spectrum of hydrogen in the visible region of the electromagnetic spectrum. He deduced that the frequency of each line was given by a formula. This formula related the energy levels that the electron in question left, (n2) and decayed to, (n1). and included a constant. The formula was later refined by Johannes Ryberg, for whom the constant was named. 1 1 1 RH 2 2 n1 n2 (1) RH is the Rydberg constant for the H atom, is wavenumber and n1 and n2 are positive integers (n1 < n2) In this experiment, the different energy levels accessible to the electron in a hydrogen atom are examined using a spectrometer. The wavelengths of the emission lines from a hydrogen discharge lamp will be measured. From these, the values of the electronic energy levels can be calculated, and by extrapolation, the ionisation energy of the hydrogen atom can be determined. Modern spectrometers are made up of a fibre optic cable into a box with the output to a computer. Experimental The spectroscopic method involved in this experiment involves exciting electrons within the hydrogen atoms by means of an electrical discharge. Electrons are promoted to excited states and then emit a photon as they fall back to lower states. When large numbers of atoms undergo such transitions, the emission is of sufficient intensity for spectral lines to be observed by eye. The discharge method is not very discriminating and so a large number of different excited states are produced in the gas which gives rise to several series of lines. The wavelengths of the spectral lines are measured using a spectrometer. Calibration of the spectrometer The first stage in a spectroscopic investigation typically involves an accurate calibration of the spectrophotometer. Commercial instruments have a wavelength scale marked on them, but it may not be sufficiently accurate for our purpose. The calibration is obtained by comparing the measured wavelength of a set of emission lines for which the wavelength is already precisely known, see table on results page. The calibration for each instrument has previously been carried and you will be provided with a value, , which describes the extent to which the spectrometer is inaccurate. This has been calculated as the average of the difference between the observed wavelength and true wavelength ( (true ) (obs ) ) of lines in the Cadmium and Krypton sprecta. To learn how to use the spectrometer and to check the calibration, measure the red line at 643.8 nm from the cadmium lamp - See instructions. Remember that each spectrometer will have a different value of . You will need to use the value of for your spectrometer to correct the readings that you take in the experiment. Emission lines from the H atom (Balmer series) Set up the hydrogen discharge tube with its capillary section horizontal and just in front of the spectrometer slit, see picture below. Switch it on. Set the wavelength drum to 650 nm and adjust the vertical position of the spectrometer until brightest image is obtained. The first and second Balmer lines are red and green; they are easily seen. The violet third line is fainter and will be found at about 430 nm. Open the slit slightly if you have difficulty in seeing the third line. Your eyes may need to be dark adapted for a few minutes. Take two or three independent readings of the lines. You will not be able to see the fourth line, which is at 410.2 nm. Turn the hydrogen lamp off when finished. Results - Write your results on the results page in this script. Use your correction value to obtain the true wavelengths from your measured values and then convert these to the corresponding wavenumbers. Remember that wavelegth is in nanometers and wavenumber is in cm-1 / cm-1 1 / 1 nm = 1 10-9 m Identify the transitions. In each case, we know that the lower energy level has a principal quantum number n1 = 2. The lines must therefore correspond to transitions from higher levels, with n2 = 3, 4 etc. Look back at the diagram of the hydrogen spectrum. To help with the assignment, consider the following questions: which transition in the Balmer series has the lowest energy change? which of the observed lines corresponds to the lowest energy? In this way, assign the principal quantum number n2 of the excited state to each of the observed lines and enter the value of 1/ n22 in the final column in each case. Plot a graph of against 1/ n22 using the computer and obtain the gradient and intercept Gradient = ± Intercept = ± Equation 1 can be written in a straight line form; 1 1 1 RH 2 2 multiplying out gives n1 n2 RH 1 1 RH 2 2 n1 n2 y= c m x RH = ± cm-1 from the intercept: RH = ± cm-1 Mean value: ± cm-1 from the gradient: RH = Compare your result with the literature value: RH = 1.09677 105 cm-1 The Ionisation energy for a hydrogen atom is the energy required to remove the electron from the ground state where n1 = 1 to the state corresponding to complete removal of the electron, i.e. n = Using your value of RH estimate the ionisation energy for the hydrogen atom from the equation E = RH c h N A Speed of light = 2.998 108 m s-1 h = Planck’s constant = 6.62607 10-34 J s NA = Avogadro’s constant = 6.02214 1023 mol1 where c = Ionisation energy of the H atom = Compare your result with the literature value: ± E = 1312 kJ mol-1 kJ mol1 RESULTS SHEET CALIBRATION The true wavelengths for the calibration lines are given in the table: /nm Cadmium /nm Krypton red 643.8 yellow 587.0 green 508.6 green 557.0 blue 480.0 blue 467.8 violet 441.5 Average correction factor: = nm HYDROGEN ATOM (Balmer series) Colour (observed) /nm Mean (observed) /nm RED GREEN/BLUE VIOLET (true) /nm RED GREEN/BLUE VIOLET VIOLET 410.2 / cm -1 n2 1 n 22 EXPERIMENT 2 Kinetics Of Hydrolysis Of Halogenoalkanes The OBJECTIVES of this experiment are: 1. To follow the rate of hydrolysis of t-butyl chloride (2-chloro-2-methylpropane) using conductivity measurements. 2. To determine the value of the rate constant for this reaction. 3. To determine the activation energy EA for this reaction. BACKGROUND Determination of the rates of reactions provides vital clues as to how a process is taking place on molecular scale i.e. the reaction mechanism. A classic illustration of how kinetics can provide evidence for a reaction mechanism is given by the work of Sir Christopher Ingold, a Professor of Organic Chemistry at Leeds between 1924 –1930. He suggested that there were two possible mechanisms of nucleophilic substitution. So, for example, primary haloalkanes react directly with the nucleophile Y¯ (an SN2 process): CH3CH2CH2X + Y¯ CH3CH2CH2Y + X¯ whereas tertiary haloalkanes form water-stabilised carbocations in a rate-determining step (an SN1 process): slow (CH3)3CX (CH3)3C+ + Y¯ (CH3)3C+ + X¯ (CH3)3CY Hence the rate of an SN1 reaction is independent of the nucleophile concentration. In this experiment, you will follow the rate of hydrolysis of tertiary butyl chloride (t-BuCl) to give an alcohol and hydrochloric acid: CH3 3 CCl 2H2O CH3 3 COH H3 O Cl As water plays the role of both nucleophile and solvent in this reaction, it is not possible to distinguish between an SN1 and SN2 mechanism from changes in the nucleophile concentration. However other evidence suggests that the reaction proceeds via two processes: slow CH3 3 C Cl CH3 3 CCl (2) fast CH3 3 COH H3O CH3 3 C 2H2O (3) The reaction rate equation can be written as; d [ t BuCl] k [ t BuCl] dt (4) Integration of equation (4) to obtain the concentration [t-BuCl]t at any time t in terms of the initial concentration [t-BuCl]0 and the rate coefficient k gives; ln[t-BuCl]t = ln[t-BuCl]0 − kt (5) The reaction will be monitored by measuring the change in conductivity G (in S m-1), which is proportional to the concentration of the ions H+ and Cl−, as the hydrolysis proceeds. The concentration of t-BuCl in time is given by: t BuCl G Gt (5) G G where G∞ is the final conductivity. Thus a graph of ln 1t versus time will give a straight S m line if the reaction is first order and the gradient will be -k. The units of conductivity are included to make the log dimensionless. Experimental The reaction is carried out in a jacketed reaction vessel. The temperature is maintained by water pumped through the jacket from a thermostatted water bath. The conductivity cell is a pair of platinum black electrodes with electrical connections and an integrated thermometer. Instructions for the use of the conductivity meters and computer data acquisition units are provided with the apparatus. Each pair of students will follow the variation of conductivity with time at two different temperatures (20C or 30C and 35C or 40C): The rate constant values from the other temperatures can be obtained from another group of students. Run Number 1 Target Temperature/°C 20 2 Time of Run / mins Frequency of readings / s 20 20 30 10 10 3 35 5 1 4 40 5 1 If t-BuCl is added to water at room temperature, the reaction is too rapid to be followed by the techniques available to us in this experiment. The reaction rate can be reduced by diluting the water with a suitable organic solvent, 80/20 (v/v) water/acetone mixture is used in this experiment. Procedure Read the additional instructions with each set of apparatus before starting the run. Each run can be performed in any order. Measure 100 cm3 of the 80/20 water / acetone reaction solvent and pour this into the reaction vessel. Make sure the magnetic stirrer bar is rotating. Note the temperature of the mixture. You should not begin your run until you are satisfied that the temperature of the solvent has settled to a constant value. Record the actual temperature to 0.1°C of your solvent at least 3 times during the run. For runs 1 and 2, you will be using the data logger within the conductivity meter to record the results. For runs 3 and 4, a network connection will allow you to save all your work in a directory (Z:) which will be accessible on any networked PC. Get the computer ready. The reaction is started by introducing 1 cm3 of t-BuCl solution via the metered pipette into the water/acetone solvent. Immediately start the data logger or acquisition unit. The conductivity of the reaction mixture will increase with time. For run 1, readings of conductivity will be logged every 20 s. For run 2, readings of conductivity will be logged every 10 s. For runs 3 and 4, the conductivity will be recorded at 1 second intervals and displayed via the computer data acquisition unit. When you have finished each run, raise the cell out of the vessel by pressing the clamp and lifting. Wash the cell with deionised water. Carefully remove the reaction vessel from the clamp and empty the waste into a plastic bowl. Rinse the vessel and stirrer bar with water, clamp the reaction vessel in place so that it is clean and ready for the next user. Dispose of the solvent into the waste solvent container under the fume cupboard. RESULTS Run __1__ Time /s 0 Target temperature = 20°C Conductivity / S m-1 Time /s 240 Conductivity / S m-1 Actual temperature /°C = Time /s 480 Conductivity / S m-1 Time /s 720 20 260 500 740 40 280 520 760 60 300 540 780 80 320 560 800 100 340 580 820 120 360 600 840 140 380 620 860 160 400 640 880 180 420 660 900 200 440 680 220 460 700 Run __2__ Time /s 0 Target temperature = 30°C Conductivity / S m-1 Time /s 130 Conductivity / S m-1 G Actual temperature /°C = Time /s 260 Conductivity / S m-1 Time /s 390 10 140 270 400 20 150 280 410 30 160 290 420 40 170 300 430 50 180 310 440 60 190 320 450 70 200 330 460 80 210 340 470 90 220 350 480 100 230 360 490 110 240 370 500 120 250 380 G Run __3__ Filename Run __4__ Filename Target temperature = 35°C Actual temperature /°C = _______________________________________ Target temperature = 40°C Conductivity / S m-1 Actual temperature /°C = _______________________________________ Conductivity / S m-1 If you plot the raw data, i.e. conductivity against time, you should get graph 1. Unfortunatly this does not give the rate of reaction so we need to do a little bit of maths on the data. Conductivity values at time t = Gt. Conductance at the end of the run = G. Take the Gt values away from the G value and then take the natural logarithm of these values. This gives ln(G- Gt) for all the values of time. Only process the results where the conductance is changing significantly, i.e. before it starts to level off. In graph 1 this is ~150 seconds. For each of your runs, plot a graph of ln(G - Gt) versus time, see graph 2. This should give a straight line if the reaction is first order and for which the gradient will be – k. Graph 1 Graph 2 G value Plot of ln(G - Gt) against Time/s 0 0.5 for run 2 at 30.1°C -1 -1 Conductivity / mS m-1 Conductance / 0.6 0.4 ln(G - G t) -2 0.3 Gt values 0.2 0.1 Do not include these points when calculating gradient -3 -4 Gradient = rate constant = -k / s -1 0.0 0 100 200 300 400 500 600 700 800 900 1000 -5 0 Time / seconds Time /s 50 100 150 200 250 Time / seconds If your plots show any scatter at long times, see graph 2, replot your data using only the points showing a linear relationship. This may give a slightly different result for the gradient and, hence, the rate constant in each case. Run Actual Temperature/C T/K k/s-1 1 or 2 3 or 4 You should get to this point. We can now show by looking at the values of k for the whole group that as the temperature increases, the rate of reaction also increases. The results can then be used in the next part to determine the activation energy of the reaction. Your School can do this bit with you at a later date. Activation Energy The final part of the experiment involves determining the activation energy from the rate constants. The activation energy, Ea - is the minimum kinetic energy required for a collision to result in reaction. The Arrhenius equation expresses how rates of chemical reaction vary with temperature. k = A exp (-Ea/RT) where Ea is the activation energy, A is the pre-exponential factor R is the gas constant, T is temperature. Transformation of the Arrhenius equation into a form that can be used to obtain Ea and A from the gradient and intercept of a straight-line plot gives; ln k = ln A - Ea / RT Ea 1 R T m x which is the same as ln k = ln A y= c You have obtained values of the rate constant at two temperatures and should obtain values at the other temperatures from another group of students. A graph of ln k versus 1/T (where T is in Kelvin) should be a straight line with gradient = -Ea/R and intercept= ln A. Complete the following table: Run T/K k / s-1 T-1/K-1 From the plot, calculate the activation energy Ea. where R = Gas Constant = 8.314 J K-1 mol-1 Ea / kJ mol-1 Compare your result with the literature value: Ea = ≈ 80 kJ mol-1 ln(k / s-1)