AP Chemistry : kinetics and rate

The rate of a reaction is its speed , and its slope in a graph. It is in units of concentration (usually molarity )   over time (usually seconds )  M/s. The rate law is in the form : rate=k[A]^m[B]^n

Where k is the rate constant ( which is variable with temperature and a few over things ) A and B are the reactants and the [ ] around them mean Molarity which is a unit of concentration. The m and n are orders of the reaction and they can be many numbers but the most common ones are 0 , 1 and 2. The Rate or speed of a reaction changes with changes in temperature, surface area, concentration, orientation and the presence of a catalyst. Increased temperature increases the reaction rate because of the equation k=Ae^-Ea/RT ( k increases with increased temperature , since T is on the denominator of a negative exponent on a directly proportional figure to k ), and because increased temperature increases the speed of the reactants so they collide and react more often. Increased surface area increases the rate of reaction because there are more reactants that you can collide with and react. Increased concentration increases the rate of the reaction because there are extra reactants and the likely-hood of a collision and reaction is increased ( also because of the rate law , at least mathematically ). Molecules need the correct orientation to have a reaction when they collide  ( they also need the required amount of energy , supplied to them by temperature ), And finally the catalyst increases the reaction rate by (" splitting" the Ea, activation energy ) and lowering the Ea. The activation energy is the minimum energy required for a reaction to happen. If the reaction is 0th order , then its graph ( of M/time , M on the y axis and time on the x axis ) is a straight slope, if its 1st then the graph is curved and if its 2nd it is also curved ( but differently than the 1st order ). To make the 1st order have a straight slope you graph the natural logarithm of Molarity over time ( lnM/t) . And to make the 2nd order straight , you graph the reciprocal of molarity over time ( 1/M / t ). With 1st order reactions you can do half life problems , the equation is t1/2=.693/k where t1/2 is the half life. To figure out the orders of reactants and thereby the overall order of the reaction you can use either the method of initial rates or mechanisms. To do the method of initial rates you have a data table of  concentrations of reactants in different trials and the initial rate in each trial ( you get this data by experiment). You find where one reactant changes concentration in the trials and all the others stay the same in the same trials . Then you figure out the factor by which the reactant changes. Then you figure out the factor by which the initial rate changes in the same trials. You then figure out what exponent needs to be added to the factor of change by the reactant to equal the factor of change by the initial rate and this is the order. Where mechanisms can be used, you look at the slow step and use the coefficients of the reactants in it for the rate law. A mechanism has several elementary steps that add together to make the overall reaction