Chapter 14.4, Problem 14.5CYU

### Chemistry & Chemical Reactivity

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

Chapter
Section

### Chemistry & Chemical Reactivity

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

# Sucrose, a sugar, decomposes in acid solution to give glucose and fructose. The reaction is first-order in sucrose, and the rate constant at 25 °C is k = 0.21 h‒1. If the initial concentration of sucrose is 0.010 mol/L, what is its concentration after 5.0 h?

Interpretation Introduction

Interpretation: The concentration after five hours has to be given.

Concept introduction:

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

Rate=-Δ[A]Δt=k[A]

The integrated rate law equation can be given as,

ln[A]t[A]o=-kt

The above expression is called integrated rate law for first order reaction.

Explanation

As the reaction process follows first-order, the integrated law of first order reaction follows,

â€‚Â Given:[Sucrose]initialÂ =Â 0.010Â mol/L[Sucrose]finalÂ =Â ?kÂ =Â 0.21Â Â h-1Â tÂ =Â 5.0Â hTherefore,ln[sucrose]t[Sucrose]0Â =Â -kÂ tln([sucrose]t0.010Â mol/L)Â =Â -(0.21Â Â h-1)(5

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