Collection and Analysis of Rate Data
Determining the Rate Law Example: Reaction of triphenyl methyl chloride (trityl) (A) and methanol (B) A + B C + D was carried out in a solution of bezene and pyridine at 25OC. Pyridine reacts with HCl that then precipitates as pyridine hydrochloride thereby making the reaction irreversible. The concentration-time data in Table was obtained as in a batch reactor At t=0, CA = 0.05M) Time (min 50 100 150 200 250 300 Concentration of A (mole/dm3) X 38 30.6 25.6 22.2 19.5 17.4
The initial concentration of methanol was 0.5 mole/dm3 Part (1): Determine the reaction with respect to triphenyll methyl chloride. Part (2): In a separate set of reaction the reaction order wrt methanol was found to be first order. Determine the specific reaction constant
Solution Part (1) Find the reaction order wrt trityl. Step 1 Postulate rate law Step 2 Process your data in terms of the measured variables, which in this case is CA Step 3 Look for simplification. Concentration of methanol is 10 times the initial concentration of triphenyl methyl chloride, its concentration is essentially constant. CB = CB0
Substituting CB in equation Where Step 4 Apply the CRE algorithm Mole balance Rate Law
V = V0 Stoichiometry: Liquid Combine: mole balance, rate law and stoichiometry Taking the natural log on both sides of equation
Slope of vs will yield reaction order a Slope of vs will yield reaction order a with respect to triphenyl methyl chloride (A). Step 5 Find as a function of CA from the concentration-time data.
could be find in three ways Graphical Method Finite Differential Method Polynomial Method
Graphical Method t (min) CAx103 (mol/dm3) (mol/dm3 - min) 50 3.0 2.40 50 3.0 2.40 38 1.86 1.48 100 30.6 1.20 1.00 150 25.6 0.80 0.68 200 22.2 0.50 0.54 250 19.5 0.47 0.42 300 17.4
Graphical Method The derivative –dCA/dt is determined by calculating and plotting (-DCA/Dt) as a function of time, t, and using differential technique (Appendix A.2) to determine (-dCA/dt) as a function of CA.
Graphical Method First calculate the ratio (-DCA/Dt) from the first two columns of the Table. The result is written the third column Next plot the third column as a function of first column. i.e., (-DCA/Dt) versus t. Using the equal-area differentiation, the value of (-dCA/dt) is read off the figure. The value is put in the fourth column of the Table.
Graphical Method
Graphical Method
Finite Difference Method
Summary Table Graphical Finite Difference t (min) (mol/dm3-min) (mol/dm3) 3.0 2.86 50 1.86 1.94 38 100 1.20 1.24 30.6 150 0.80 0.84 25.6 200 0.68 0.61 22.2 250 0.54 0.48 19.5 300 0.42 0.36 17.4
Plot column 2 and 3 ( ) as a function of column 4 (CA X 1,000) on log scale. We could substitute parameter values into Excel to find and k’.
To evaluate k’ we can derivative and CAP=0.5X10-3 mol/dm3, which is Then
Excel Plot
Excel Plot Graphical method Slope = 2.05 Finite Difference Method The reaction is consider as Second order