# The reaction 2 B → C + 2D is found to be zero-order when run at 990°C. If it takes 4.4 × 10 2 s for an initial concentration of B to go from 0.50 M to 0.20 M , what is the rate constant for the reaction? What is the half-life of the reaction under these conditions?

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

Chapter
Section

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343
Chapter 13, Problem 13.112QP
Textbook Problem
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## The reaction 2 B → C + 2D is found to be zero-order when run at 990°C. If it takes 4.4 × 102 s for an initial concentration of B to go from 0.50 M to 0.20 M, what is the rate constant for the reaction? What is the half-life of the reaction under these conditions?

Interpretation Introduction

Interpretation:

The half –life of the reaction has to be calculated.

Concept Introduction:

Half-life for zero order reactions:

The time taken by the concentration of reaction to get reduced of its original concentration is called as half-life reaction.

The half-life for zero order reactions depends on the initial concentration of the reactant.

The half-life period of zero order reactions gets shorter as the zero-order reaction proceeds.

The equation of half life for zero order reaction is given as,

t1/2=[A]02k

To calculate the half –life of the reaction

### Explanation of Solution

The rate law for a zero order reaction can be given as,

[A]=-kt+[A]0

Rate constant = 4.4×10-2s

Initial concentration =  0.50Mto0.20M

The rate constant is calculated as,

0.20M=-k+4.4×102s+0.50Mk=(0.50M)-(0.20M)4.4×102sk=6

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