Kinetics III
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Reactions Rates and Temperature • Reactions happen when reactants collide…with enough energy and in the right orientation. • The more reactants colliding (the higher the concentration), the faster the reaction. • As a result of the collision, new bonds form and old bonds break. Cl + NOCl ClClNO‡ transition state Cl2 NO Transition State Theory Energy is needed to form a transition state (with reactants in the correct orientation). The transition state can then either form products or return to reactants. ClClNO‡ EA, the activation energy Cl + NOCl ClClNO‡ transition state Cl2 NO Activation Energy The activation energy EA is the minimum energy needed to initiate the chemical reaction. This energy is different than the overall energy change for the reaction. The value of the activation energy depends on the mechanism for the reaction. ClClNO‡ EA, the activation energy ΔE, the energy change for the reaction Reactions Rates and Temperature • The kinetic theory of gases says that the average kinetic energy of a gas depends on its temperature. It also says that the kinetic energies of the gas molecules themselves are not all the same but follow a distribution like the one below. average kinetic energy fraction of molecules Reactions Rates and Temperature • If the activation energy for a reaction is EA then, for a given temperature, only a fraction of the molecules will have kinetic energies ≥ EA. • At a higher temperature, more reactant molecules will have kinetic energies ≥ EA. Activation energy EA Reactions Rates and Temperature • The reaction rate increases with increasing temperature. • Where in the rate equation does this dependence on T occur? In the rate constant k. k is a function of temperature. For the reaction shown below, rate = k(T) [Cl] [NOCl] Cl + NOCl ClClNO‡ transition state Cl2 NO The Arrhenius Equation • The dependence of the rate constant k on temperature was found by Arrhenius to have following form for a large number of đ = đ¨đ reactions. −đŦđ¨ đšđģ Arrhenius equation This equation is based on experimental results. A is a constant. R is the gas constant = 8.3145 T is the temperature in kelvin. đą đđđ đ˛ . The Arrhenius Equation How does the rate constant k vary with T? đ= −đŦđ¨ đ¨đ đšđģ or đŦđ¨ đĨđ§ đ = − + đđ đ¨ đšđģ đŦđ¨ đšđģ As T increases, decreases, and k increases. When k increases, the rate increases. The Arrhenius Equation How does the rate constant k vary with EA? đ= −đŦđ¨ đ¨đ đšđģ or đŦđ¨ đĨđ§ đ = − + đđ đ¨ đšđģ đŦđ¨ đšđģ As EA increases, increases, and k decreases. When k decreases, the rate decreases. Plots of the Arrhenius Equation Plots of the Arrhenius Equation closely resemble those for 1st order reactions: đ = đ¨đ −đŦđ¨ đšđģ đĨđ§ đ = − đŦđ¨ đšđģ + đđ đ¨ Getting EA from Rate Constant Data The following table shows the rate constants for the rearrangement of methyl isonitrile at various temperatures. Temperature (°C) k (s-1) 189.7 2.52 x 10-5 198.9 5.25 x 10-5 230.3 6.30 x 10-4 251.2 3.16 x 10-3 1. What is the activation energy for the reaction? 2. What is the value of the rate constant at 430.0 K? Getting EA from Rate Constant Data 1. What is the activation energy for the reaction? đĨđ§ đ = − A plot of ln k vs đ đģ đŦđ¨ đšđģ + đđ đ¨ will have a slope of đŦđ¨ − đš . So, we change T to kelvin and invert, and change k to ln k: T (°C) T (K) 1/T (K-1) k (s-1) ln k 189.7 462.8 2.160 x 10-3 2.52 x 10-5 -10.589 198.9 472.0 2.118 x 10-3 5.25 x 10-5 -9.855 230.3 503.4 1.986 x 10-3 6.30 x 10-4 -7.370 251.2 524.4 1.907 x 10-3 3.16 x 10-3 -5.757 Getting EA from Rate Constant Data ln k 1/T 0 (K-1) -2 -10.589 2.160 x 10-3 2.118 x 10-3 -7.370 1.986 x 10-3 -8 -5.757 1.907 x 10-3 -1 0 ln k -9.855 đŦđ¨ đđ đ = − + đđ đ¨ đšđģ slope = -EA/R -4 -6 -1 2 1 .8 0 E -0 3 1 .9 0 E -0 3 2 .0 0 E -0 3 2 .1 0 E -0 3 2 .2 0 E -0 3 1 /T The slope (and therefore EA) can be found from any two pairs of data points, either from the plot or from a calculation. Getting EA from Rate Constant Data EA from a pair of data points: đŦđ¨ đđ đđ = − + đđ đ¨ đšđģđ đŦđ¨ đđ đđ = − + đđ đ¨ đšđģđ Subtracting the second equation from the first gives đđ đđ − đđ đđ = − đŦđ¨ đšđģđ + đŦđ¨ đšđģđ đđ đŦđ¨ đ đ đđ ( ) = − ( − ) đđ đš đģđ đģđ This equation is helpful for comparing rates at different temperatures. It only applies to systems with the same activation energy. Getting EA from Rate Constant Data Now, any two pairs of k and T will allow EA to be calculated. Temperature (°C) k (s-1) 189.7 2.52 x 10-5 198.9 = 472.0 K 5.25 x 10-5 230.3 = 503.4 K 6.30 x 10-4 251.2 3.16 x 10-3 đ. đđđđđ−đ đŦđ¨ đ đ đđ = − − đš đđđ. đ đđđ. đ đ. đđđđđ−đ đŦđ¨ đđ đđ. đ = − (−đ. đđđđđđđ−đ ) đš đ. đđđđ đš đŦđ¨ = = đđđđđđ đą = đđđ đđą đ. đđđđđđđ−đ đ˛ Getting a Rate Constant at a New Temperature 2. What is the value of the rate constant at 430.0 K? We can again use: Temperature (°C) k (s-1) 189.7 2.52 x 10-5 198.9 5.25 x 10-5 230.3 = 503.4 K 251.2 6.30 x 10-4 3.16 x 10-3 Since we know the activation energy: EA = 156343 J, we can use any value of T and k already known: T1 = 503.4 K k1 = 6.30 x 10-4 s-1 Getting a Rate Constant at a New Temperature 2. What is the value of the rate constant at 430.0 K? Temperature (°C) k (s-1) 189.7 2.52 x 10-5 198.9 5.25 x 10-5 EA = 156343 J 230.3 = 503.4 K 6.30 x 10-4 251.2 3.16 x 10-3 T1 = 503.4 K đđ đđđđđđ đ đ đđ =− − = −đ. đđđ đđ đš đđđ. đ đđđ. đ đđ = đ−đ.đđđ = đ. đđđđđđ đđ đđ = đ. đđđđđ−đ đ. đđđđđđ = đ. đđđđđ−đ đ−đ k1 = 6.30 x 10-4 s-1 T2 = 430.0 K The Arrhenius Equation For the reaction C+Bī Z If the rate is found by experiment to be second order, then the rate equation would be rate = ΔZ = k[C][B] Δt Substituting the Arrhenius equation for k shows the T and EA dependence of the reaction rate: đđđđ = đ¨đ đŦ đ¨ −đšđģ đĒ [đŠ] Catalysts and Rates Catalysts change the rate of a reaction by providing an alternate mechanism that has a lower activation energy. Potential Original reaction catalyzed reaction đŦ đ¨ −đšđģ This means the rate constant (đ = đ¨đ ) for the catalyzed reaction will be larger, and the rate for the catalyzed reaction will be faster than the uncatalyzed rate. How the Rate Constant Changes with Activation Energy Fumarase lowers the activation energy of the fumarate to malate reaction from 156 kJ to 25 kJ. Calculate the factor by which the enzyme increases the reaction rate at body temperature. đŦđ¨đ đđ đđ = − + đđ đ¨ đšđģ đŦđ¨đ đđ đđ = − + đđ đ¨ đšđģ đđ đ đđ ( ) = − (đŦđ¨đ − đŦđ¨đ ) đđ đšđģ How the Rate Constant Changes with Activation Energy Fumarase lowers the activation energy of the fumarate to malate reaction from 156 kJ to 25 kJ. Calculate the factor by which the enzyme increases the reaction rate at body temperature. đđ đ đđ ( ) = − (đŦđ¨đ − đŦđ¨đ ) đđ đšđģ đđ đ đđ ( ) = − (đđđđđ − đđđđđđ) đđ đš đđđ. đđđ˛ đđ đđ ( ) = đđ. đđ đđ How the Rate Constant Changes with Activation Energy Fumarase lowers the activation energy of the fumarate to malate reaction from 156 kJ to 25 kJ. Calculate the factor by which the enzyme increases the reaction rate at body temperature. ln( k2 k1 ) īŊ 50 . 82 k2 k1 īŊ e 50 . 82 k2 īŊ 1 . 2 x10 22 k1 The presence of fumarase increases the reaction rate by a factor of 1.2x1022. In effect, the reaction does not happen unless catalyzed by fumarase. Reaction Profile for a Reaction with a Multistep Mechanism Potential The reaction profiles you have seen so far are those for elementary reactions. Elementary reactions are reactions that occur in a single collision step. Reaction Profile for a Reaction with a Multistep Mechanism Many reactions occur by mechanisms that involve more than one elementary step. Each step has its own activation energy and rate constant. Reaction Profile for a Reaction with a Multistep Mechanism Step 1 has the larger EA, so it is slower than step 2. Step 1 is called the rate-determining step.
