   Chapter 14.4, Problem 14.5CYU

Chapter
Section
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,

Given:[Sucrose]initial = 0.010 mol/L[Sucrose]final = ?k = 0.21  h-1 t = 5.0 hTherefore,ln[sucrose]t[Sucrose]0 = -k tln([sucrose]t0.010 mol/L) = -(0.21  h-1)(5

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