Explanation Given: Rate = k [A] 1/2 Calculation: (a) We can simply use the exact same method of integration.. We will use [A] n and find a general rate law for some order n. rate = k [ A ] n rate = d [ A ] d t d [ A ] d t = − k [ A ] n d [ A ] [ A ] n = − k d t ∫ A 0 A d [ A ] [ A ] n = − ∫ t 0 t k t ( 1 − ( n − 1 ) ) ⋅ ( 1 [ A ] n − 1 ) A 0 A = − k t t 0 t 1 [ A ] n − 1 − 1 [ A ] 0 n − 1 = ( n − 1 ) k t 1 [ A ] n − 1 = 1 [ A ] 0 n − 1 + ( n − 1 ) k t In our example, we are told that n =1/2, so we simply substitute the value of n to find the final integrated rate law. 1 [ A ] n − 1 = 1 [ A ] 0 n − 1 + ( n − 1 ) k t 1 [ A ] 1 2 − 1 = 1 [ A ] 0 1 2 − 1 + ( 1 2 − 1 ) k t 1 [ A ] − 1 2 = 1 [ A ] 0 − 1 2 − 1 2 k t [ A ] 1 2 = [ A ] 0 1 2 − 1 2 k t (b) Now we can find the value of t 1/2 where half of the material is remaining...

Pearson eText for Chemistry: structures and Properties -- Instant Access (Pearson+)

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ISBN: 9780136951537

Author: Nivaldo Tro

Publisher: PEARSON+

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Chapter 14, Problem 114E

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To determine: The integrated rate law for the half-order reaction and the half-life expression for the half-order reaction.

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Chapter 14, Problem 113E

Chapter 14, Problem 115E

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Pearson eText for Chemistry: structures and Properties -- Instant Access (Pearson+)

Ch. 14 - Explain why lizards become sluggish in cold...Ch. 14 - Why are reaction rates important (both practically...Ch. 14 - Using the idea that reactions occur as a result of...Ch. 14 - Using the idea that reactions occur as a result of...Ch. 14 - What units are typically used to express the rate...Ch. 14 - Why is the reaction rate for reactants defined as...Ch. 14 - Explain the difference between the average rate of...Ch. 14 - Consider a simple reaction in which a reactant A...Ch. 14 - How is the order of a reaction generally...Ch. 14 - For a reaction with multiple reactants, how is the...

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The integrated rate law for the half-order reaction and the half-life expression for the half-order reaction.

Solution Summary: The author explains how to determine the integrated rate law and the half-life expression for the reaction.

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To determine: The integrated rate law for the half-order reaction and the half-life expression for the half-order reaction.

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Chapter 14 Solutions