   Chapter 12, Problem 89AE

Chapter
Section
Textbook Problem

# Cobra venom helps the snake secure food by binding to acetylcholine receptors on the diaphragm of a bite victim, leading to the loss of function of the diaphragm muscle tissue and eventually death. In order to develop more potent antivenins, scientists have studied what happens to the toxin once it has bound the acetylcholine receptors. They have found that the toxin is released from the receptor in a process that can be described by the rate lawRate = k [acetylcholine receptor−toxin complex]If the activation energy of this reaction at 37.0°C is 26.2 kJ/mol and A = 0.850 s−1. what is the rate of reaction if you have a 0.200−M solution of receptor-toxin complex at 37.0°C?

Interpretation Introduction

Interpretation: The rate law of toxin released from the receptor, the activation energy of this reaction and frequency factor is given. The rate of reaction for the given concentration of solution at 37°C is to be calculated.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The relationship between the rate constant and temperature is given by the Arrhenius equation, k=AeEaRT .

To determine: The rate of reaction for 0.200M solution of receptor-toxin at 37°C .

Explanation

Given

The frequency factor is 0.850s1 .

The given temperature is 37°C .

The concentration of toxin is 0.200M .

The activation energy is 26.2kJ/mol .

The conversion of kilo-joule (kJ) into joule (J) is done as,

1kJ=103J

Hence,

The conversion of 26.2kJ into joule is,

26.2kJ=(26.2×103)J=26.2×103J

The conversion of degree Celsius (°C) into Kelvin (K) is done as,

T(K)=T(°C)+273

Hence,

The conversion of 37°C into Kelvin is,

T(K)=T(°C)+273T(K)=(37+273)K=310K

Formula

The rate constant is calculated using the formula,

k=AeEaRT

Where,

• k is the rate constant

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