CHM ENG 140 Study Guide - Midterm Guide: Continuous Stirred-Tank Reactor, Volumetric Flow Rate, Chemical Engineering
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You are part of a team working on the development of a process in which a mineral species (labeled A for proprietary reasons) undergoes a reaction to form a new pigment to be used in house paints. In a series of experiments in a large well-mixed stirred tank reactor, you fill a tank with a known quantity of an inert liquid, bring the liquid up to a specified temperature, add a known quantity of A, and measure the concentration of A in the tank as a function of time. The reaction gives off heat as it progresses, but cooling water circulating in a jacket around the reactor keeps the temperature of the reacting mixture constant. The following data are recorded.
Concentration of A, CA(mol A/L) | ||||
---|---|---|---|---|
t(min) | T = 94°C | T = 110°C | T = 127°C | T = 142°C |
10 | 9.30Ã10â2 | 5.19Ã10â2 | 2.10Ã10â2 | 9.87Ã10â3 |
20 | 6.17Ã10â2 | 2.35Ã10â2 | 1.33Ã10â2 | 5.55Ã10â3 |
30 | 4.41Ã10â2 | 1.91Ã10â2 | 8.15Ã10â3 | 3.97Ã10â3 |
40 | 3.12Ã10â2 | 1.45Ã10â2 | 5.92Ã10â3 | 2.45Ã10â3 |
50 | 2.58Ã10â2 | 1.01Ã10â2 | 4.48Ã10â3 | 2.27Ã10â3 |
60 | 9.30Ã10â2 | 9.50Ã10â3 | 4.36Ã10â3 | 1.83Ã10â3 |
A research article indicates that concentration of A should vary with time according to the following expression:
CA(t)=11CA0+kt
(1)
where CA0 (mol/L) is the initial concentration of A in the reactor [CA(t=0)] and k is called the reaction rate constant. Despite being called a constant, k is a strong function of the absolute temperature in the reactor:
k(T)=k0 expâEaRT(K)
(2)
In this equation (known as the Arrhenius equation after the Swedish chemist who proposed it), k0 is a constant, Ea(J/mol) is the reaction activation energy, and R=8.314 J/(mol·K) is the universal gas constant. Your task will be to verify that the expressions for CA(t) and k(T) fit the data, and if they do, to determine the parameters CA0 and k at each temperature and then the constants k0 and Ea.
(a)
What are the units of k, k0, and Ea if CA is in mol/L and t is in min?
(b)
Transform Equation 1 into an equation of the form y=at+b, so that if Equation 1 is valid, a plot of yvs. t would be a straight line. How would you determine CA0 and k from the slope and intercept of the line?
(c)
Create an Excel spreadsheet with the structure shown as Rows 1-10 in the figure at the end of this problem statement, and fill in the data table in Columns A-I. Then create the four scatterplots shown in Rows 15-21. In the âTrendlineâ options of each plot, check the boxes for âDisplay equation on chartâ and âDisplay R-squared value on chartâ but not the one for âSet intercept.â R2 is the coefficient of determination (it has several other names as well), and provides a measure of how well a straight line fits a set of data: the closer it is to 1, the better the fit. What can you conclude about Equation 1 from the four plots?
(d)
From the four trendline equations, calculate the values of k and CA0 for each of the four experimental temperatures and fill in Columns B-I in Rows 12 and 13 of the spreadsheet.
(e)
Enough A was initially added to the tank to make the initial concentration CA0=0.25 mol/L, yet you calculated four different values of CA0 in Part d. How do you explain this result?