## Deriving the integrated rate laws [ENDORSED]

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Michael Lonsway 3O
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### Deriving the integrated rate laws

How can we derive the integrated rate laws for zero, first, and second order reactions? In the 2014 final exam question 4 asked to derive a second order reaction with A as a reactant so how could we derive this?

Chem_Mod
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### Re: Deriving the integrated rate laws  [ENDORSED]

Remember that Rate of consumption is $\frac{d[A]}{dt}$, and you would want to integrate to get [A].

See your lecture notes, in the course reader it is pages: 62 to 67

It is also covered in the 15 page PDF on my class website:
https://lavelle.chem.ucla.edu/wp-content/supporting-files/Chem14B/Kinetics_Integrated_Rate_Laws_Examples.pdf

Examples can be seen in the textbook, 6th ed.
First order: pg. 623-624
Second order: pg. 630

Summary: pg. 631