Integrated Rate Law

Integrated Rate Law

​(Textbook: N. Tro)

Ms. Woltschlaeger

​Integrated Rate Law

​So far we have looked at the relationship between rate of reaction and concentration of a reactant.

​

​Often it's interesting or important to know the relationship between concentration of a reactant and time.

​The integrated rate law for a chemical reaction is a relationship between the concentration of the reactants and time.

​

​Consider the simple reaction, A --> Products

​

​The integrated rate law depends on the order of the reaction.

Multiple Choice

For A --> Products, what is the first-order rate law?

• $$Rate\ =\ -\frac{\Delta A}{\Delta t}$$  

• $$Rate\ =\ k\left[A\right]^0$$  

• $$Rate\ =\ k\left[A\right]$$  

• $$Rate\ =\ +\frac{\Delta\Pr oducts}{\Delta t}$$  

​The first order integrated rate law

​ln[A]_t = -kt + ln[A]₀

​

​You don't need to know the calculus behind it, but it's nice to know!

​

​More importantly, however, is that you notice that the integrated rate law has the form of a straight line.

​1^st order integrated rate law

• ​Plot of ln[A]_t vs. time

• ​The slope is equal to -k

• ​The y-intercept is ln[A]₀

Multiple Choice

For A --> Products, what is the second-order rate law?

• $$Rate\ =\ -2\frac{\Delta A}{\Delta t}$$  

• $$Rate\ =\ k\left[A\right]^2$$  

• $$Rate\ =\ k\left[A\right]$$  

• $$Rate\ =\ +\frac{\Delta\Pr oducts}{2\Delta t}$$  

​2^nd order integrated rate law

Multiple Select

For A --> Products, what is the zero-order rate law?

• $$Rate\ =\ -k$$  

• $$Rate\ =\ k$$  

• $$Rate\ =\ k\left[A\right]^0$$  

• There is no rate law since it is zero. Zero implies that there is nothing.

​Zero-order integrated rate law

​[A]_t = -kt + [A]₀

Multiple Choice

What order is a reaction that has a plot of concentration of the reactant vs. time that yields a straight line.

• zero-order

• 1st order

• 2nd order

• none of these

Multiple Choice

If the inverse of the concentration vs. time yields a straight line, what reaction order is this?

• zero-order

• 1st order

• 2nd order

• none of these

Multiple Choice

Consider the reaction A --> Products.

What is the order of the reaction with respect to A?

• zero-order

• first-order

• 2nd-order

• This is not an integrated rate law graph, thus the order cannot be determined.

Fill in the Blanks

Multiple Choice

Consider the reaction A --> Products.

What is the unit (aka. label) for k?

• $$M\cdot s^{-1}$$  

• s^-1

• $$M^{-1}\cdot s^{-1}$$  

• $$M\cdot s$$  

Poll

How are you feeling thus far about kinetics?

• I get it.

• It's okay...

• I'm pretty confused.

• I haven't understood a single thing so far.