Chemical kinetics is all about how fast reactions happen. Differential rate laws are the key to understanding reaction speeds. They show how concentrations of reactants affect the rate, using a and reaction orders.
These laws help us predict how quickly chemicals will react or form. By integrating them, we can figure out concentrations at any time and calculate half-lives for first-order reactions. It's like having a crystal ball for chemical reactions!
Differential Rate Laws
Differential rate law derivation
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Top images from around the web for Differential rate law derivation
Chemical Reaction Rates – Atoms First / OpenStax View original
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The Rate Law: Concentration and Time | Boundless Chemistry View original
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Chemical Reaction Rates | Chemistry: Atoms First View original
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The Rate Law: Concentration and Time | Boundless Chemistry View original
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Expresses reaction rate in terms of reactant concentrations and rate constant
General reaction: aA+bB→cC+dD
: Rate=k[A]m[B]n
k: rate constant, specific to reaction at given temperature
m, n: reaction orders for reactants A and B
for each reactant determined experimentally, not from balanced equation
Overall reaction order: sum of individual reaction orders m+n
Examples:
with respect to A: Rate=k[A]
with respect to B: Rate=k[B]2
Rate expression from concentration changes
Rate expressed as change in reactant or product concentration over time
For reactant: Rate=−a1dtd[A]=−b1dtd[B]
For product: Rate=c1dtd[C]=d1dtd[D]
Negative sign for reactants: concentrations decrease over time
Coefficients a, b, c, d: normalize rate expression based on balanced equation
Examples:
Reactant A disappearing at 0.5 M/s: Rate=−dtd[A]=0.5 M/s
Product C forming at 0.2 M/min: Rate=dtd[C]=0.2 M/min
Rate law components and relationships
Differential rate law combines reaction orders and rate constant
Reaction order for each reactant: exponent of its concentration term
First-order with respect to A: m=1, Rate=k[A]
Second-order with respect to A: m=2, Rate=k[A]2
Rate constant k: specific to reaction and temperature
Represents intrinsic reactivity of reactants, determined experimentally
Units of k depend on overall reaction order, ensure rate has units of concentration/time
Examples:
First-order reaction: Rate=k[A], k has units of s−1
Second-order reaction: Rate=k[A][B], k has units of M−1s−1
Integrated rate law for first-order reactions
Obtained by integrating differential rate law
Allows determination of reactant or product concentrations at any time
For first-order reaction, differential rate law: Rate=k[A]
Rearrange and integrate with respect to time: ∫[A]0[A]t[A]d[A]=−k∫0tdt
Integrated rate law: ln[A]0[A]t=−kt
[A]0: initial concentration of reactant A
[A]t: concentration at time t
Uses of integrated rate law:
Determine at any time t
Calculate half-life of first-order reaction, independent of initial concentration: t1/2=kln2
Examples:
Reactant A with initial concentration 1.0 M, rate constant 0.1 s−1, concentration after 10 s: [A]10=[A]0e−kt=1.0 M×e−(0.1 s−1)(10 s)=0.37 M
Half-life of first-order reaction with rate constant 0.05 min−1: t1/2=0.05 min−1ln2=13.9 min