Kinetics: Initial Rates and Integrated Rate Laws
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Kinetics: Initial Rates and Integrated Rate Laws

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 thanks for watching, subscribe to my
channel for more tutorials and as always feel free to email me


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