W2–Kinetics I.pptx

PY4040: Introduction to Physical Chemistry for Pharmacy TW2 ep1: Kinetics… rates of reaction Dr Gemma Shearman Learning Outcomes • Understand the importance of ‘kinetics’ to Pharmacy • Define the terms: rate and order of reaction • Understand the relevance of stoichiometry to the rate of rea...

PY4040: Introduction to Physical Chemistry for Pharmacy TW2 ep1: Kinetics… rates of reaction Dr Gemma Shearman Learning Outcomes • Understand the importance of ‘kinetics’ to Pharmacy • Define the terms: rate and order of reaction • Understand the relevance of stoichiometry to the rate of reaction with respect to a particular reactant / product. • Explain what information rate laws and integrated rate laws provide. • State the rate law for each of: 0th, 1st and 2nd order reactions. • Manipulate and apply the rate laws and the integrated rate laws. • State the integrated rate law for each of: 0th, 1st and 2nd order reactions AND be able to sketch / plot linear graphs for each, recognising the relevance of the values obtained for each slope and y-intercept. Useful for pharmacy? Knowledge of rates of reaction is important in a number of areas of pharmacy and pharmaceutical sciences: • Stability / shelf life of medicines… decomposition of drugs • Dissolution rate of drugs (from their formulation state e.g. tablet) • Metabolism of drugs in the body (affects duration of action and toxicity) • Manufacture of drugs • Activation of pro-drugs etc. What is Kinetics? Kinetics tells you ‘how fast’ a process occurs. (whether that process is a reaction between substances, a dissolution or the rate at which a drug is released from its formulation) Thermodynamics tells you whether it will ever happen and ‘how much’. What is Kinetics? Dissolution rate: Here (in Cooley, Ireland), the limestone rocks are being dissolved very slowly… Solubility: The solubility of limestone in acid is the maximum amount (concentration) dissolved at equilibrium… ! Both are important for formulations!! What is Kinetics? Q. What would happen to a patient if a drug dissolved very slowly? Q. What would happen to a patient if the solubility of a drug was very low? A. Intermolecular forces NB not to be confused with intramolecular forces (such as the covalent bonds themselves) that hold the molecule together. Definition of RATE Given the generic chemical reaction (reactants (R) forming products (P): R P The rate (denoted as ) at which the reaction proceeds can be described in a number of different ways: change in concentration of R R is disappearing Rate will have units of mol L-1 s-1 change in time Definition of RATE Also… P is appearing … in terms of formation of P. So: Rate of reaction R → P This can be shown graphically for both R and P: Note: The (instantaneous) rate can be determined by fitting a tangent (blue dotted line) to the curve in the plot [ ] vs. t. Rate of reaction R → P This can be shown graphically for both R and P: Note: The (instantaneous) rate can be determined by fitting a tangent (blue dotted line) to the curve in the plot [ ] vs. t. Stoichiometry However, stoichiometry MUST be preserved, hence for the reaction: During the reaction we obtain two NO molecules but only one O2 molecule for the loss of two NO2 molecules! i.e. NO2 is disappearing at the same rate as NO is appearing Stoichiometry So rate of reaction can be defined as: Q. Which ONE of the following is not a definition of the rate of reaction of ? A. B. C. D. Reaction orders It is observed for many (not all!) reactions, that the rate of reaction, n, is proportional to the molar concentrations of the reactants raised to a power: where the power to which each reactant is raised (here given by , ) is known as the ORDER of the reaction w.r.t. that species and may have the values 0, 1, 2 etc. or fractional. Reaction orders So… if for a reaction A P: then the reaction would be first order. If: then the reaction would be second order. If: then the reaction would be zeroth order. … and so on! Q. What is the order of reaction when Reaction orders Units are variable and depend on the rate equation Rather than saying ‘proportional to’, we can use a constant instead. So… for a reaction: A + B P, would then be able to say: where k is the rate constant for the reaction (and is independent of the concentrations but dependent on temperature). This expression is known as a RATE LAW and can only be determined experimentally. Overall orders of reaction for a given rate law of e.g. ... We would say that the reaction is first-order w.r.t. A and second-order w.r.t. B. The overall order of a reaction is the sum of each individual order, hence for: The overall order is 1 + 2 = 3 i.e. third-order An example… Q. For the reaction A + 2B C: (a) If the rate of consumption of A is 5.0 mmol L-1 s-1, state the rates of consumption of A and the rate of formation of C. A. Since , and = 5.0 mmol L-1 s-1, we can say that: So: = 10.0 mmol L-1 s-1 and = 5.0 mmol L-1 s-1. An example… Q. For the reaction A + 2B C: (b) A. Given , determine: (i) the order of reaction with respect to each species (ii) the overall order (iii) units for the rate constant (i) 1 (ii) 1 (iii) Write down units for everything you do know… then cancel to get units for k! Here… s-1. Your turn… Q. For the reaction 2A + B C + 2D + 3E: (a) (b) If the rate of formation of D is 2.0 mol L-1 s-1, state the rates of consumption of both reactants and the rate of formation of C and E. Given , determine: (i) the order of reaction with respect to each species (ii) the overall order (iii) units for the rate constant A quick recap So: for a zero order reaction, for a 1st order reaction, and for a 2nd order reaction etc. Determining n (the order) Rate law is: rate = k [A]n taking logs: log rate = n log [A] + log k This will give a straight line graph (y = mx + c) so plotting the experimentally derived data: Integrated rate laws The rate laws are all differential equations (as they simply tell you how the rate of change of concentration varies with time). If you were interested in knowing the exact concentration at a particular point in time, , you would need to integrate! Integrated rate laws link concentrations of reactants or products DIRECTLY. However, you do also need to know the initial concentration! Integrated rate laws For a general reaction , we can define: • The concentration of reactant A at time is [A] • The initial concentration (at time ) is given by [A]0 Integrated rate laws Q. Given the data shown in the graph, what is [A]0? Estimate [A] after 30 seconds. First order rate equation A P For a 1st order reaction, we can state that the rate of reaction aka the rate law is given by: NB we assume for simplicity here that all stoichiometries are equal to 1. The integrated rate law (i.e. the solution to this) is: How? Graphical determination of a first order reaction Since the integrated rate law of a 1st order reaction is: Therefore, a plot of ln[A] vs. time should give a straight line with : •Slope: –k •y-intercept: ln[A]0 Slope = -k y-intercept = ln[A]0 First order reaction: exponential! Since the integrated rate law of a 1st order reaction is: This can be rearranged, to form another way of expressing the solution: which is an exponential decay! For all first-order processes, the concentration of reactant decays exponentially with time. The greater the rate constant, the more rapid the decay... y-intercept = [A]0 Zeroth order rate equation A P For a 0th order reaction, we can state that the rate of reaction aka the rate law is given by: The integrated rate law (i.e. the solution to this) is: Therefore, a plot of [A] vs. time should give a straight line with slope –k and y-intercept [A]0. Slope = -k Second order rate equation A P For a 2nd order reaction, we can state that the rate of reaction aka the rate law is given by: The integrated rate law (i.e. the solution to this) is: Q. A plot of vs. time should give what? Reading list • ‘Aulton’s Pharmaceutics’ ed. by M.E. Aulton and K.M.G. Taylor, 5th Ed. Part 1 Chapter 7 (Kinetics) pp. 114-127 Accessible online through iCat Further reading (for context): • ‘Physicochemical Principles of Pharmacy’ by A.T. Florence and D. Attwood, 6th Ed. Chapter 3: Drug stability Accessible online through iCat 3