--- ## Definition and facts - A rate law equation relates the rate of a reaction to the concentration of the reactants. - The three things that can influence the rate of a reaction is the **concentration of reactants, the temperature of the reactants and any catalysts added to the reaction**. - Increasing the temperature of a reaction **exponentially increases the rate of the reaction --- ## Equations - The value of K in a rate law equation **is the slope of the linearized line** that is formed when data about a reaction is graphed on a concentration vs time plot. - The **integrated rate law** *(2nd image down)* is used to express how the concentration of different reactants changes over time. - The **differential rate law** expresses how the rate of a reaction changes depending on the concentration of reactants. - Which rate law equation you used is entirely dependent on the **order of the reaction**. This is explained further in the next section. >[!quote] >##### Basic rate law equations: >![[Pasted image 20230301125032.png|800]] >![[Files/Rate laws-1.png|800]] #### Writing a rate law equation - After determining the order of each reactant through testing *see the section below for more* you must find the rate constant *k* for the overall reaction. This is done by plugging in the rate and concentration of each reactant into that reaction's rate equation (*shown in this page's first image*). Then re-arrange the equation and solve for k. - To write an **overall rate law equation** where there is a reverse reaction and or intermediaries begin first by writing the rate law of the **rate limiting step**. If this equation contains an intermediary set the rate law *(rate =k(a)(b))* of the forward reaction equal to that of the reverse reaction and solve for the intermediary, **plugging it back into the equation of the rate limiting step.** - In summary the **rate of production always equals the rate of consumption**. Only true by the *steady state approximation, explained below in 'reaction mechanics'.* #### Reaction order - A reactant is **first order** if doubling the concentration of it **doubles the rate of the reaction**. A reactant is second order if doubling its concentration **quadruples the rate of the reaction**. Finally a reactant is **zero order** if changing its concentration has **no effect on the rate of the overall reaction**. - Its important to note that the rate *k* has a different value depending on what the **overall rate of the equation is**. This is found by adding up the rates of all reactants involved. >[!quote] >![[Rate laws 1.png|400]] >[!tip] >##### Finding the order of a reaction >- To experimentally test the order of a reaction you must plot time vs concentration in multiple different ways. A **zero order reaction** is time vs concentration. A **first order reaction** is time vs **the natural log *ln* of concentration** and a second order reaction is time vs **1/concentration**. >- After graphing all three of these relationships it is easy to tell which one produces a **linear relationship**. The equation that does so indicates the order of that specific reactant *(the one you are measuring the concentration of)*. >- The slope of that graph is the **rate** of that reaction. ></br> > >##### Example: > >![[Pasted image 20230227124851.png|800]] --- ## [[Reaction Mechanics|Reaction mechanisms]] - The overall rate of a reaction **is determined by the slowest elementary step**. This step is also known as the **rate determining step** since it has the greatest effect on the rate of a reaction. - Since reaction mechanisms can become very complex rate laws for those reactions can also **be significantly more complicated then outlined on this page.** As a result most chemists assume something called *steady state approximation*. This is the assumption that the concentration of intermediaries remains constant. - The Arrhenius equation *shown below* is an equation that allows one to relate the mechanics of a reaction specifically its activation energy (and heat) to the rate of that reaction, or the other way around. >[!quote] >##### The Arrhenius equation >![[Rate laws arrhen.png|445]] >![[Rate laws arrhenius.png|400]] >##### This re-arranged equation can be used for experimental data measuring the rate of a reaction at two different temperatures: >![[Rate laws 333333.png|420]] >![[Rate laws33111.png|350]] > --- ## Forward vs reverse reaction - Recall that **when a chemical reaction is at equilibrium the rate of the forward reaction is equal to that of the reverse reaction**. *This is an important fact that is used in equations to solve for unknown variables or concentrations/rates by setting both equations equal to each other.* - It is very important to recall that intermediary chemicals get consumed by both the reverse reaction *(where they digress to the previous step)* and the forward reaction to the next step. --- ## Half life - The half life of an element is the time it takes for **half of that element to decay into another element** one number down on the periodic table - However the half life of a reaction is the time it takes for **half of a reactant to react into the product that it is forming**. - Assuming the first half life of a reaction is 20 seconds the second half life of a **zero order reaction would be 10 seconds *(1/2)*, a first order reaction would be 20 seconds and a second order reaction would be 40 seconds *(2)*. >[!quote] >##### Half life equations > >![[Rate laws 342.png|800]] --- #mainpage