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CHM ENG 142 Study Guide - Midterm Guide: Uncompetitive Inhibitor, Enzyme Kinetics, Competitive Inhibition

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redcockroach875
9 May 2020
School
Berkeley
Department
Chemical and Biomolecular Engineering
Course
CHM ENG 142
Professor
All

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Document Summary

Due: wednesday, march 4, 2020: enzyme kinetics, the rate of this reaction is r = a[s] / (b + [s]) for constants a and b. Use pssh to solve for a and b as a function of rate constants and the total enzyme concentration [e] t . Pssh on e s: k 1 [e][s] = (k -1 + k 2 )[e s] [e s] = k 1 /(k -1 + k 2 ) [e][s] Site balance: [e] t = [e] + [e s] = [e] (1 + k 1 /(k -1 + k 2 ) [s]) Therefore [e] = [e] t (k -1 + k 2 )/(k -1 + k 2 + k 1 [s]) Rate = k 2 [e s] = k 1 k 2 /(k -1 + k 2 ) [e][s] = k 1 k 2 [e] t [s] / (k -1 + k 2 + k 1 [s])

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Related Questions


A 5 00μl reaction co ntaining 0.5 pmol of an enzyme following Michaelis – Menten kinetics with saturating substrate concentration is studied . For this enzyme k1 = 1 x 10 9 M - 1 s - 1 , k - 1 = 2 x 10 3 s - 1 , and k2 = 1 x 10 5 s - 1 .

a . What is the Vmax for the enzyme considering that it has only one substrate binding site ? b. What are the values of Km and Ks? Is this a rapid equilibrium enzyme or does it follow steady state kinetics? Explain why .

c . What is the substrate concentration needed to achieve half maximal velocity? Explain the basis for your answer.

d . If the substrate concentration in part c is doubled , how many fold will the initial velocity increase?

e . What is the Km i f the concentration of the enzyme is doubled? f . What is the efficiency of this enzyme?

g. Would this enzyme be considered a perfect enzyme? Explain.

h . If 0.25 pmol of an irreversible or classic non - competitive inhibitor is added before starting the reaction. What is the resulting Km for the enzyme?

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

9.30×10−2

5.19×10−2

2.10×10−2

9.87×10−3

20

6.17×10−2

2.35×10−2

1.33×10−2

5.55×10−3

30

4.41×10−2

1.91×10−2

8.15×10−3

3.97×10−3

40

3.12×10−2

1.45×10−2

5.92×10−3

2.45×10−3

50

2.58×10−2

1.01×10−2

4.48×10−3

2.27×10−3

60

9.30×10−2

9.50×10−3

4.36×10−3

1.83×10−3

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 exp−EaRT(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 “Trendline” options of each plot, check the boxes for “Display equation on chart” and “Display R-squared value on chart” but not the one for “Set intercept.” 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?