Chemistry (Physial hemistry) Leture 0. EPM, semester II by Wojieh Chrzanowsi, PhD, DS Wyłady współfinansowane ze środów Unii Europejsiej w ramah EFS, UDA-POKL 04.0.02.-00-37/-00 Absolwent Wydziału Chemiznego Politehnii Gdańsiej inŝynier z przyszłośią. Physial Chemistry EPM/0 A quote of the wee (or amel of the wee): Apply yourself. Get all the eduation you an, but then... do something. Don't just stand there, mae it happen. Lee Iaoa Physial Chemistry EPM/0 2 reation order Reation order is a purely formal quantity, hene, its may be determined only experimentally. In the ase of elementary reations their order is equal to their moleularity (more later). The subjet of the onsiderations to follow may be summarized as: How to find the reation order on the basis of experimental data? It s worthy to notie that the methods presented in next slides are of historial importane rather, beause nowadays at the age of omputerized instrumentation (measuring and analytial devies) it is rather easy to aquire large data sets =f(t), whih subsequently may be fitted to ineti equations of different orders using omputerized regression tehniques. Physial Chemistry EPM/0 3
reation order (2) Those regression tehniques, however, are based stritly on the theory presented earlier and the methods presented below. These methods have their origins in times where data olletion was not so easy and omputation methods were more tedious. Therefore, planning of experiments required muh more sophistiated approah. These old methods are also very useful for analysis of ineti data (small data sets) in text problem solving exerises. Hene, their appliation is essential for hemists. It is always useful to inspet the data arefully if any regularities disussed in next setions may be observed. Quite frequently, espeially if the experiment was designed in a way favoring suh observations, one an notie, for example, independene of half-life time of onentration. Suh observations are still important even at the age of omputers, when they may suggest whih model (order) should be tested first. Physial Chemistry EPM/0 4 Equation testing method reation order (3) This is the simplest (most primitive), though most effetive approah (esp. if no regularities might be observed). In this method we use the data in integrated rate laws of several orders and he, whih one yields invariable rate onstant (independent of varying onentrations of reagents). Graphial method In this method, we plot the data in linearized systems of oordinates (suitable for different reation orders) and loo, whih system yields a straight line plot. Its slope is the rate onstant. One an notie that the regression method is a generalization of the both above mentioned methods. Physial Chemistry EPM/0 5 Half-reation time method reation order (4) We saw before that half-reation time id diretly proportional to the initial onentration for 0 th order, independent of the initial onentration for st order, and is inversely proportional for the 2 nd order. This may be generalized by formula: τ n / 2 0 After finding the half life-time for several initial onentrations, proportionality may be tested using this formula for different orders n. Integral method by Ostwald-Zawidzi-Noyes This is a variant of the former method, in whih half life-time (or redued time, i.e. time of the same fration of reatants transformed) must be determined for two different initial onentrations. Subsequently, reation order n may be found from the formulae: n t ln t 02 ln t2 = or n = + t2 0 ln 02 ln 0 Physial Chemistry EPM/0 6
reation order (5) Differential method by van t Hoffa In this method one utilizes no onentrations at given time but rates of reations at given time. It may be employed when reations are not very fast. Most frequently it is utilized for initial rates, when the following formula is valid: ln v n = ln Isolation method (initial rates) 0 0 ln v ln In this method initial rates are measured in several experiments planned in a way permitting elimination of indluene of one or more reatants on the rate observed. An example is shown in the next slides. The method is important beause it permits to find the partial orders versus eah of the reatants!!! 02 02 Physial Chemistry EPM/0 7 Example: reation order (6) X 2 + Y XY + X # Initial onentration mmol/dm 3 X 2 Y Initial rate mmol/(dm 3 min) 450 270 0,8 2 50 270,2 3 450 90 3,6 Physial Chemistry EPM/0 8 reation order (7) When we write rate laws for experiments # and #3 we an eliminate influene of reatant X 2, whose initial onentrations are the same in these experiments, by dividing both sides of the rate laws: m n m n m m v0 = X 0 2 Y0 v03 = X 03 2 Y03 X 0 = 2 X 2 03 n n v 0 Y0 Y0 ln v = = n v 0 ln v03 n = 03 Y03 Y03 ln Y0 ln Y03 Even without taing the logarithms, one an see that onentration of Y is 3 times smaller in #3 than in # and the initial rate is 3 times smaller, too. Thus, the reation order vs. Y is. Treating experiments # and #2 in an analogous manner, eliminating influene of reatant Y, we see that onentration of X 2 is 3 times smaller in #2 than in #, whereas the initial rate is 9 times smaller, meaning 2 nd order vs. X 2. Physial Chemistry EPM/0 9
reation order (8) Experimental measurements of onentrations in time may be diffiult. If we measure during the ourse of reation any additive quantityx(e.g. pressure, volume, eletri ondutivity, density, absorption of light), we an alulate onentration after timet using the formula: t X = X 0 X 0 where subsript means measurement after time, when the additive quantity in question does not hange anymore (within the unertainty limits of the used measuring or analytial tehnique). X t Physial Chemistry EPM/0 0 Elementary reations & omplex reations Chemial reations usually do not our as they are written in hemial equations, whih represent their summarial stoihiometry only. Majority of reations are from the point of view of their inetis omplex reations. It means that their our is several steps (stages), eah of the latter being an elementary reation. All elementary reations onstituting given omplex reation show its mehanism. Elementary (simple) reations do our as indiated by their equations. Therefore, their order may be inferred on the basis of their moleularity, i.e., the number of moleules whih must meet (ollide) to result in the hemial reation. For elementary reations order = number of moleules of the reatants. Physial Chemistry EPM/0 Reation rates dependene on temperature Rate of majority of hemial reations (and all elementary reations) inreases with temperature. A useful approximate rule (van t Hoff s) is assumtion that reation rate inreases twie when temperature is raised by 0 o C (K). Dependene of reation rate on temperature means atually dependene of its rate onstant on temperature. T +0 = 2 T More exat relation between temperature and reation rate onstant is given by Arrhenius equation: = A e Physial Chemistry EPM/0 2
Arrhenius equation E A ativation energy A preexponential fator (frequeny fator) = A e Ea ln = ln A a tanα= Physial Chemistry EPM/0 3 Results of measurements ofas a funtion oft, plotted in a linearized system of oordinates ln=f(/t), permit determination of the parameters of Arrhenius equation. Slope: E R Arrhenius equation (2) E A ativation energy is the lowest energy that the reatants must have to get transformed to produts. It may also be interpreted as the fration of ollisions between moleules of suffiient ineti energy to exeed. This is given by Boltzmann distribution. A preexponential fator is requently nown as the frequeny fator reflets the frequeny of ollisions regardless their energy. The produt of both represents the number of suessful ollisions in time. = A e e Physial Chemistry EPM/0 4 Kinetis of reversible reations So far we have treated all reation as running to ompletion (in stoihiometri sense), though sometimes ompletion was ahieved after time t=. In reality, reations run to the point of equilibrium rather and we must find a suitable desription of suh situations. Equilibrium is not a stati state (altough observation may suggest that the reation does not our at this state nothing happens ). Atually, a dynami equilibrium exists, when two reations our: left to right and right to left, but their rates are the same. A - B = v A B = A = v = B v = v A = K B K is reation (onentration)equilibrium onstant. Physial Chemistry EPM/0 5
Kinetis of reversible reations (2) da Rate law (differential) may be expressed as: = A dt A0 B0 whih, after integration, assumes ln = ( + )t the following form: A B If the equilibrium omposition (onentrations) is nown, one an write: A0 A ln = ( + )t A A The ase with two seond order reations is more omplex, beoming very omplex when reations ba and forth are of different orders. B Physial Chemistry EPM/0 6 Parallel reations If, at given onditions, one reatant yields more than one produt, whih may be represented by the sheme: then, assuming that all three reations are st order reations, one an write: da = A + 2A + 3A dt 0A obtaining after integration: ln = ( + 2 + 3 )t Suh situations an be met in organi hemistry, when three isomers may be obtained (e.g. o-, m-, and p-). A Chem. Fiz. TCH II/8 7 Catalysis Catalysis is a proess of hanging the reation rate by ertain substanes nown as atalysts. Usually, the hange means inrease in the reation rate (aeleration). Sometimes, however, the desired effet is slowing the reation down. Suh a proess is nown as inhibition and the negative atalysts as inhibitors. Inhibitors are frequently used in fighting orrosion (if unavoidable then at least slow it down) and in osmetis industry. Catalyst is a substane that hanges the rate of reation without being onsumed in the reation, hene it is not shown in the stoihiometri equation. Catalysts atually reat (tae part in reations), hging their mehanisms (othwerwise, how an they influene the reation rate?). Physial Chemistry EPM/0 8
Catalysis (2) There are two basi types of atalysis: homogenous when atalyst is present in the same phase as the reatants (pratially it means atalysis in solutions) heterogenous when atalyst is present in the different phase from the reatants (pratially a solid atalyst ating on reatants in solution or in a gas phase). In reation mehanisms of omplex reation, there is usually one step, whih is slow and determines the rate of the whole omplex reation. It ats very muh lie a part of a three-lane highway, where repairs are being made and only one lane is open, thus limiting the traffi speed along the highway. This step is nown as the rate limiting step. Catalysts usually target this step. Physial Chemistry EPM/0 9 Howgh!!!