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Determining rate laws…

So, we know how to measure a reaction rate. This doesn’t help much, if Idon’t know the rate law. What then?

1) Look it up.

2) Estimate it.

3) Calculate it.

4) Measure it.

So, how do you determine a rate law in kinetic measurements?

1 j

j

dCr

dtν=

(constant density BR) 0

A

A

CA

AC

dCtrν

=⋅∫

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Experimental Rate MeasurementsHow do we set up an experiment to measure a reaction rate?How do we set up an experiment to measure a reaction rate?For a kinetic experiment, we need to follow concentrations vs time. Hence, we need to measure reactant concentrations. The appropriate way to do this depends on the individual reaction system (and the equipment available in your lab).

ExEx--situ:situ: a sample is taken out of the reactor and analyzed. Pro: Con:

InIn--situ:situ: the measurement is taken inside the reactor as the reaction proceeds.Pro:Con:

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Experimental TechniquesSome Common Methods:Some Common Methods:

Chromatography: Gas-Chromatography or Liquid-Chromatography. Probably the most commonly used methods. Rely on affinity of species to an absorbing or adsorbing phase. Relatively slow, but reliable. Able to detect almost any species.

The “workhorse” in almost all lab and industrial environments!

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Gas ChromatographyTypical GC setTypical GC set--upup

Photo of GCPhoto of GC typical GC columntypical GC column

Thermal conductivity detector(TCD)

sample

reference

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Experimental TechniquesSome Common Methods:Some Common Methods:

Chromatography: Gas-Chromatography or Liquid-Chromatography. Probably the most commonly used methods. Rely on affinity of species to an absorbing or adsorbing phase. Relatively slow, but reliable. Able to detect almost any species.

Optical spectroscopy (IR, visible, UV):

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UV-Vis Spectroscopy

Since L is only a function of the optical cell used (= constant) and ε is a physical property of the substance to be detected (=constant), the absorbance A is a direct measure of the concentration C.

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IR Spectroscopy

photo of an IR spectrometerphoto of an IR spectrometer

Principle of (dispersive) IR spectroscopyPrinciple of (dispersive) IR spectroscopy

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IR-Spectroscopy

Let’s check out some more examples: http://www.colby.edu/chemistry/JCAMP/IRHelper.html

Let’s check out some more examples: Let’s check out some more examples: http://http://www.colby.edu/chemistry/JCAMP/IRHelper.htmlwww.colby.edu/chemistry/JCAMP/IRHelper.html

Let’s see an example: http://webbook.nist.gov/Let’s see an example: Let’s see an example: http://http://webbook.nist.govwebbook.nist.gov//

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Experimental TechniquesSome Common Methods:Some Common Methods:

Chromatography: Gas-Chromatography or Liquid-Chromatography.

Optical spectroscopy (IR, visible, UV):

Mass spectrometry:

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Mass Spectrometry

photo of a mass specphoto of a mass spec

principle of mass principle of mass spectrometryspectrometry

““QuadrupolQuadrupol--MS”MS”

MS needs ultra-high vacuum(UHV) conditions. Why?

MS needs ultra-high vacuum(UHV) conditions. Why?

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MS: Samplemethyl – 2 methyl benzoate

Problems:--

Problems:Problems:--

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Experimental TechniquesSome Common Methods:Some Common Methods:

Chromatography: Gas-Chromatography or Liquid-Chromatography. Probably the most commonly used methods. Rely on affinity of species to an absorbing or adsorbing phase. Relatively slow, but reliable. Able to detect almost any species.

Optical spectroscopy (IR, visible, UV): measures absorption of light with a specified wavelength by some reactant/product. Sensitive, specific, and widely available. Can typically detect only certain species, though.

Mass spectrometry: Detection based on mass of molecule (or fractions after ionisation). Versatile but difficult. Often not specific enough.

Titration: limited in applicability and only ex-situ. Mostly historically relevant.

Change in physical property: often, a reaction is accompanied by a change in some physical quantity (pressure, electric conductivity, refractive index etc). This is typically easy to measure, but completely unspecific.

Any measurement is only as good as the calibration done before startingthe measurement! Calibrations need to be done at the conditions of the experiment!

Any measurement is only as good as the calibration done before startingthe measurement! Calibrations need to be done at the conditions of the experiment!

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Determining k: Integral MethodLet’s have a look again at some integrated rate expression for the BR:

Order integrated rate law linear plot for0

1

2

0A AC C kt= −

0kt

A AC C e−=

0

1 1

A A

ktC C

= +

measuring CA vs t at one fixed temperature (isothermal!)at one fixed temperature (isothermal!) yields k(Ti) as the slope of the linearized expression!

Why isothermal? k(T) is a function of temperature. Therefore, it is crucial to keep the reactor temperature constant during a kinetic experiment. This sounds easy, but can in practice be very difficult to achieve!

k(T) is a function of temperature. Therefore, it is crucial to keep the reactor temperature constant during a kinetic experiment. This sounds easy, but can in practice be very difficult to achieve!

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Assumptions:1. I2. P3. C

4. T

Determining k: Differential Method

You can “measure” the rate of a reaction by using differential-reactor data

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Determining k: Differential Method

Plot ln(-ΔCA/Δt) vs. ln(CA) to find the order of the reaction