Kinetics: Initial Rates and Integrated Rate Laws - YouTube

hey it's professor Dave, let's talk about kinetics

kinetics is the study of reaction rates or how fast a reaction goes. there are a

lot of reasons why one chemical reaction might happen in the snap of a finger and

another might take a whole day so let's learn about what those reasons might be

reaction rates are generally measured as an increase in the concentration of

products per unit time or molarity per second. so for the following reaction we

can discuss the rate as the change in the concentration of each product over

the change in time or the change in concentration of reactant over change in

time, though that one will be negative since we are using up the reactant to

make products. remember the triangle is a capital delta and it means "change in" and

brackets mean concentration. rates of change will obey stoichiometry so for

example if we look at this reaction we have to understand that oxygen appears

at one-fourth the rate of NO2 and at one half the rate at which N2O5

disappears

we can measure rates of reaction in different ways but any method will

involve measuring the changing concentration of a substance. for example

if the product of a reaction is a gas we can measure the changing pressure of the

gas being produced. if a reaction goes from clear to a colored solution we can

monitor the light absorbance using a spectrophotometer. but whatever we do we

can use the data to plot concentration versus time. when looking at this data we

can calculate the instantaneous rate which is the rate at any given moment. we

do this by looking at the slope of the tangent line at a point or the line that

just touches an individual point on the line. this is more precise than taking an

average value over a range of points. the rate will always depend on the

concentration of one or more reactants in some way. the relationship between the

rate and a particular concentration is illustrated by the reaction order with

respect to a particular substance. for example let's say we run a reaction

several times with different initial concentrations to see what it does to

the rate. if we keep everything else the same but we double the concentration of

one reactant and as a result the rate doubles then the reaction is first order

with respect to that reactant. instead if we double the concentration and the rate

quadruples the reaction is second order with respect to the reactant. and if a

change doesn't affect the rate it's zero order. the overall reaction order is just

the sum of the orders from the individual reactants so if a reaction is

first order with respect to each of two reactants it would be second order

overall we can describe the kinetics by using a rate law. let's say we have the

following generic reaction, we would write the rate law by representing the

concentration of each reactant raised to an exponent that reflects the reaction

order. these exponents are not related to the stoichiometric

coefficient from the chemical equation and must be determined experimentally

there is also a rate constant k which is a proportionality constant between rate

and concentration. now that we have the terminology down how do we

experimentally determine the order of a reaction with respect to each given

reactant? we do so by using initial rates data. we can run several trials of a

reaction and vary the initial concentration of one reactant at a time

by doing this we can see the effect that one reactant concentration has on the

rate. let's look at the reaction from before. we can clearly see that doubling

the initial concentration of the reactant makes it disappear twice as

fast so the reaction is first order with respect to N2O5 and therefore first

order overall. we can determine the reaction order for each reactant this

way. if we double our concentration the impact on the rate tells us the order

with respect to that substance. if the rate doesn't change its zero order. if it

doubles its first order. quadruples, second order and if it's cut in half

that it's an order of negative one. so let's look at some sample data and try

to decipher the reaction order for each substance. for this reaction let's

perform trials where one substance's concentration stays the same but the

other one changes. we can see for the first two trials O2 concentration stays

the same but NO doubles. as a result the rate quadruples so the reaction must

be second order with respect to NO. if we compare trials 1 and 3, NO stays the

same but 02 doubles. the rate doubles so the reaction must be first

order with respect to O2. this must be the rate law. the reaction orders

happen to match the stoichiometric coefficients but this is a coincidence

it will not always be the case. also from the rate data we can calculate the rate

constant

just plug in the rate and concentrations from any one of the trials and solve for

k

while we're discussing the rate constant we should understand that the units on

it will be specific to the overall reaction order. this is because they must

cancel out the concentration units to give molarity per second which are units

that make sense for the rate. so for zero order they will be molarity per second since a

zero-order reaction doesn't depend on concentration. for first order it's

inverse seconds so that when combined with molarity we get molarity per second

for second order it's one over molarity times seconds so that when combined with

molar squared we get molarity per second

looking at the previous reaction the units on k

must be one over molar squared times seconds since there will be molar

cubed in the numerator. likewise this means that if you know the rate constant

you know the overall reaction order, just see how many powers of molarity have to

be in the numerator to result in a rate of molarity per second. if we want to

discern the concentration at any given time we can use the integrated rate law

we will use different integrated rate laws depending on the overall reaction

order. here are the different rate laws and resulting integrated rate laws that

correspond to each reaction order. the great thing about these integrated

rate laws is that they can be plotted in y = mx + b format to give us

a linear plot see how in each case there is a distinct y, m, x, and b, and x

is always time. we can see that for a zero-order reaction concentration versus

time gives us a straight line. for a first order reaction natural log of

concentration versus time gives us a straight line. and for a second-order

reaction the inverse of concentration versus time gives us a straight line

so when we record kinetic data we can try to plot according to these

different relationships and the one that gives us a straight line will tell us

the overall reaction order simply by graphical analysis

let's check comprehension

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