I Chapter 14 Chemical Kinetics Reaction rate the speed at which a chemical reaction occurs Reaction mechanism a step by step molecular level view of the pathway from reactants to products Chemical kinetics the area of chemistry concerned with the speed or rates or reactions A Four factors allow us to change the rate at which any particular reaction occurs 14 1 Factors that Affect Reaction Rates o Physical state of reactants Heterogeneous reactions that involve solids tend to proceed faster if the surface area of the solid is increased o Reactant concentrations Chemical reactions tend to proceed faster if the concentration of one or more reactants in increased o Reaction temperature Reaction rates generally increase as temperature is increased Increasing the kinetic energy of molecules allows more collisions to occur more frequently because the molecules move more rapidly o The presence of a catalyst Catalysts are agents that increase reaction rates without being used up They affect the kinds of collisions that lead to reaction 14 2 Reaction Rates B The speed of an event is defined as the change that occurs in a given time interval Reaction rate is the change in concentration of reactants or products per unit of time If A is a reactant and B is product the average rate of appearance of B over a particular period of time if given by change concentration of B B at t 2 B at t1 change time t 2 t 1 B t Brackets indicate molarity To describe the rate of disappearance of A average disappearance of A is given by change concentration of A change time A t Rates are always expressed as positive quantities The minus sign we put in the equation converts the negative A to a positive rate of disappearance Because one molecule A is consumed for every molecule of B that forms the average rate of disappearance of A equals the average rate of appearance of B 1 Change of Rate with Time It is typical for rates to decrease as a reaction proceeds because the concentration of reactants decreases 2 Instantaneous Rate Instantaneous rate of reaction the rate at a particular instant during the reaction The instantaneous rate is determined by the slope of the curve at a particular point The slope of the tangent line is the ratio of the height of the vertical side to the length of the horizontal side Initial rate of reaction the rate at t 0 3 Reaction Rates and Stoichiometry 1 c 1 d B t A t 1 b D t If stoichiometric relationships are not 1 to 1 in general for the reaction aA bB cC dDthe rate is given by C Rate 1 a t C 14 3 Concentration and Rate Laws Rate law an equation that shows how the rate depends on reactant concentrations In general for the reaction aA bB cC dDThe rate law has the general form Rate k A m B n The constant k is called the rate constant which changes with temperature and there determines how temperature affects rates The exponents n and m are typically whole numbers 1 Reaction Orders The Exponents in the Rate Law The rate law for most reactions has the form Rate k reactant 1 m reactant 2 n The exponents n and m are called reaction orders The overall reaction order is the sum of the orders with respect to each reactant represented in the rate law For any reaction the rate law must be determined experimentally 2 Magnitudes and Units of Rate Constants A good general rule a large vale of k around 109 or higher means a fast reaction and a small value of k 10 or lower means a slow reaction The unit of the rate constant depend on the overall reaction order of the rate law In our usual units of molarity for concentration and seconds for time we have Units of rate constant units of rate M 1 s 1 units of concentration 2 M s M 3 Using Initial Rates to Determine Rate Laws In order to determine the rate law one has to determine reaction orders m and an In most reactions the reaction orders are 0 1 or 2 If a reaction is zero order in a particular reactant changing the concentration of that reactant has no effect on rater as long as some of the reactant is present because any concentration raised to the zero power equals 1 When a reaction is first order in a reactant changes in the concentration of that reactant produce proportional changes in the rate When a rate law is second order in a particular reactant doubling its concentration increases the rate by a factor of 4 tripling it increases rate by a factor of nine and so on The rate of a reaction depends on the concentration but the rate constant does not The rate constant and hence the reaction rate are affected by temperature and by the presence of a catalyst D 14 4 The Change of Concentration with Time 1 First Order Reactions First order reaction a reaction whose rate depends on the concentration of a sing reactant raised to the first power For a reaction of the type A products the rate law may be first order Rate A t k A This form of a rate law which expresses how rate depends on concentration is call the differential rate law Using integration this can turned into an equation that relates the initial concentration of A A 0 to its concentration at any other time t A t 14 12 ln A t ln A 0 ktor 14 12 ln kt A t A 0 This form of the rate law is called the integrated rate law Another form of this equation that is just rearranged 14 13 ln A t kt A 0 14 12 And 14 13 can be used with any concentration units as long as the units are the same for both A t and A 0 For a first order reaction equations 14 12 and 14 13 given any three of the following quantities we can solve for the fourth k t A 0 and A t 14 12 and 14 13 can be used to determine The time interval required for a given fraction of a The concentration of a reactant remaining at any 1 time after the reaction has started 2 sample to react 3 concentration to fall to a certain level The time interval required for a reactant Equation 14 13 can be used to verify whether a reaction is first order and to determine its rate constant Equation 14 13 has the form of the general equation for a straight line y mx b in which m is the slope and b is the y intercept A graph of ln A t versus time gives a straight line with a slope of k and a y intercept of ln A 0 A reaction that is not first order will not yield a straight line 2 Second Order Reactions Second order reaction a reaction whose rate depends on either a reactant concentration …