CHEM 1212 1nd Edition Lecture 7 Outline of Last Lecture I Rates of Chemical Reactions II Reaction Conditions and Rate III Effects of Concentration on Reaction Rates IV Rate Equations V The Order of a Reaction VI The Rate Constant k VII Determining a Rate Equation Outline of Current Lecture I Concentration II Collision Theory III The Arrhenius Equation IV Effects of Catalysts on Reaction Rates Current Lecture I Concentration Time Relationships Integrated Rate Laws a Equations used to calculate the concentrations of reactions and products after an elapsed period of time b First order reactions i Integrated rate equation ln R 2 kt R 0 ii The R s in this equation are the concentrations of the reactants at time t 0 and at a later time iii Calculations where this would be used These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute 1 If R 2 R 0 is measured in the laboratory after some amount of time has elapsed then k can be calculated 2 If R 0 and k are known then the concentration of material remaining after a given amount of time R t can be calculated 3 If k is known then the time elapsed until a specific fraction R t R 0 remains can be calculated c Second order reactions i Rate equation 1 1 kt R t R 0 d Zero order reactions i Rate equation R 0 R t kt ii Units of k are mol L x s e Graphical methods for determining reaction order and the rate constant i Rate equations if rearranged have the form y mx b f Half Life and First Order Reactions i The half life t1 2 of a reaction is the time required for the concentration of a reaction to decrease to one half its initial value ii The longer the half life the slower the reaction iii Usually used when dealing with first order reactions iv The half life is the time when R t R 0 v In order to find the half life we substitute in the as the concentration fraction and replace t with t1 2 vi For first order reaction half life t1 2 0 693 K II Collision Theory Concentration and Reaction Rate a Collision theory of reaction rates i The reacting molecules must collide with one another ii The reacting molecules must collide with sufficient energy to initiate the process of breaking and forming bonds iii The molecules must collide in an orientation that can lead to rearrangement of the atoms and the formation of products b The number of collisions between the two reactant molecules is directly proportional to the concentration of each reactant and the rate of the reaction shows a first order dependence on each reactant c Temperature and Reaction Rate i Higher temperatures allow reactions to occur more rapidly ii Lowering a temperature slows down a reaction iii Molecules gain the energy to react through heat kinetic energy d Activation energy Ea III IV i Defined as the amount of energy a molecule must obtain in order to react a sort of energy barrier to reactions ii If the barrier is low less energy is required for the reaction and vice versa iii Transition state state at which the molecules have obtained sufficient energy e Effect of Molecular Orientation on Reaction Rate i Heat along is not enough to ensure that the reaction will occur ii The reaction also requires that the molecules come together in the correct orientation iii The lower the probability of achieving the proper alignment the smaller the value of k and the slower the reaction The Arrhenius Equation a This is the observation that reaction rates depend on the energy and frequency of collisions between reacting molecules on the temperature and on whether the collisions have the correct geometry b k rate constant Ae Ea RT i A frequency factor specific to each reaction and is temperature dependent ii The superscript of the equation the fraction of molecules having the minimum energy required for reactions value is always less than 1 c This equation allows you to i Calculate Ea from the temperature dependence of the rate constant ii Calculate the rate constant for a given temperature if Ea and A are known d The activation energy can be obtained if k is known at two different temperatures i Ln k1 Ea RT1 ln AND ln k2 Ea RT2 ln A Effects of Catalysts on Reaction Rate a Catalysts are speed up the rate of reactions by lowering the activation energy b Catalysts are not consumed in a chemical reaction c Catalysts allow reactions to occur at lower temperatures than they normally would d Catalysts do not appear in balanced equations but appears in the reaction rate law e If a catalyst is present in the same phase of the reacting substance it is called a homogeneous catalyst f Catalyzed reactions occur much quicker than the un catalyzed reaction i Un catalyzed reactions are a 1 step process ii Catalyzed reactions have multiple steps