first order reactions
DESCRIPTION
Rate Laws Concentration [time]. First Order Reactions Goal: convert rate law into a convenient equation to give concentrations as a function of time. For a first order reaction, the rate doubles as the concentration of a reactant doubles. Rate Laws Concentration [time]. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/1.jpg)
First Order Reactions• Goal: convert rate law into a convenient equation to give
concentrations as a function of time.• For a first order reaction, the rate doubles as the
concentration of a reactant doubles.
Rate Laws Rate Laws Concentration [time]Concentration [time]
kt
kt
kt
t
t
0
0
A
Aln
AlnAln
]A[A][
Rate
![Page 2: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/2.jpg)
First Order Reactions
• A plot of ln[A]t versus t is a straight line with slope -k and intercept ln[A]0.
• In the above we use the natural logarithm, ln, which is log to the base e.
Rate Laws Rate Laws Concentration [time]Concentration [time]
![Page 3: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/3.jpg)
First Order Reactions
Rate Laws Rate Laws Concentration [time]Concentration [time]
0AlnAln ktt
![Page 4: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/4.jpg)
Second Order Reactions• For a second order reaction with just one reactant
• A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0
• For a second order reaction, a plot of ln[A]t vs. t is not linear.
Rate Laws Rate Laws Concentration [time]Concentration [time]
0A1
A1 ktt
![Page 5: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/5.jpg)
Second Order Reactions
Rate Laws Rate Laws Concentration [time]Concentration [time]
0A1
A1 ktt
![Page 6: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/6.jpg)
Half-Life• Half-life is the time taken for the concentration of a
reactant to drop to half its original value.
• For a FIRST ORDER process, half life, t½ is the time taken for [A]0 to reach ½[A]0.
• Mathematically,
Rate Laws Rate Laws Concentration [time]Concentration [time]
kk
t693.0ln
21
21
![Page 7: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/7.jpg)
![Page 8: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/8.jpg)
Half-Life• For a SECOND ORDER half-life depends in the
initial concentration:
Rate Laws Rate Laws Concentration [time]Concentration [time]
0A1
21
kt
![Page 9: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/9.jpg)
First Order Reactions• Goal: convert rate law into a convenient equation to give
concentrations as a function of time.• For a first order reaction, the rate doubles as the
concentration of a reactant doubles.
Rate Laws Rate Laws Concentration [time]Concentration [time]
kt
kt
kt
t
t
0
0
A
Aln
AlnAln
]A[A][
Rate
![Page 10: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/10.jpg)
First Order Reactions
• A plot of ln[A]t versus t is a straight line with slope -k and intercept ln[A]0.
• In the above we use the natural logarithm, ln, which is log to the base e.
Rate Laws Rate Laws Concentration [time]Concentration [time]
![Page 11: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/11.jpg)
First Order Reactions
Rate Laws Rate Laws Concentration [time]Concentration [time]
0AlnAln ktt
![Page 12: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/12.jpg)
Second Order Reactions• For a second order reaction with just one reactant
• A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0
• For a second order reaction, a plot of ln[A]t vs. t is not linear.
Rate Laws Rate Laws Concentration [time]Concentration [time]
0A1
A1 ktt
![Page 13: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/13.jpg)
Second Order Reactions
Rate Laws Rate Laws Concentration [time]Concentration [time]
0A1
A1 ktt
![Page 14: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/14.jpg)
Half-Life• Half-life is the time taken for the concentration of a
reactant to drop to half its original value.
• For a FIRST ORDER process, half life, t½ is the time taken for [A]0 to reach ½[A]0.
• Mathematically,
Rate Laws Rate Laws Concentration [time]Concentration [time]
kk
t693.0ln
21
21
![Page 15: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/15.jpg)
![Page 16: First Order Reactions](https://reader033.vdocuments.mx/reader033/viewer/2022061422/5681473c550346895db47b3d/html5/thumbnails/16.jpg)
Half-Life
• For a SECOND ORDER half-life depends in the initial concentration:
Rate Laws Rate Laws Concentration [time]Concentration [time]
0A1
21
kt