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Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

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BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

The enzyme lipase catalyzes the hydrolysis of esters of fatty acids. The hydrolysis of p-nitrophenyloctanoate was followed by measuring the appearance of p-nitrophenol in the reaction mixture:

images

This reaction obeys Michaelis-Menten kinetics (Section 14.6). Determine the value of Ratemax for this reaction using the method described in Study Question 14.45.

Interpretation Introduction

Interpretation:

The value of Ratemax for the given reaction has to be determined.

Concept introduction:

For enzymatic reaction, the common equation is given below,

  E+SESE+P

Here,

E is the enzyme.

S is the substrate.

ES is the enzyme substrate complex.

P is the product.

The general equation for Michaelis-Menten is dervied from above equation,

  v°=Vmax([S][S]+Km)                                                                                      (1)

Here,

v° is the initial rate of the reaction.

Vmax is the rate maximum of the reaction.

S is the substrate concentration.

Km is the Michaelis-Menten constant which is half of the maximum velocity of the reaction.

Take the Reciprocal of both the sides in equation (1),

  1v°=(KmVmax)(1[S])+1Vmax (2)

This equation is called as Lineweaver-Burk equation. By using this equation the value of Ratemax is calculated for the given reaction.

Explanation

The Ratemax for the given reaction is calculated below,

Given:

The substare concentration and reaction rate are given.

By using the equation,

  1v°=(KmVmax)(1[S])+1Vmax

Calculate the value of 1v° and 1[S],

The graph between 1v° and 1[S] is plotted by taking the values from table (1).

The equation for the straight line obtained from the graph is y=0.148x+0.0092.

1v°×106=0.148×105x+1Vmax

Rearrange the equation, in form of y = mx + c.

y=1

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