9th Edition
Steven S. Zumdahl
ISBN: 9781133611097




9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

Upon dissolving InCl(s) in HCl, In+(aq) undergoes a disproportionation reaction according to the following unbalanced equation:

In + ( a q ) In ( s ) + In 3+ ( a q )

This disproportionation follows first-order kinetics with a half-life of 667 s. What is the concentration of In+(aq) after 1.25 h if the initial solution of In+(aq) was prepared by dissolving 2.38 g InCl(s) in dilute HCl to make 5.00 × 102 mL of solution? What mass of In(s) is formed after 1.25 h?

Interpretation Introduction

Interpretation: The disproportionation reaction of In+ and its half-life is given. The mass of InCl(s) dissolved in HCl to prepare a given volume of solution is also given. By using these values, the concentration of In+ and the mass of In(s) formed after 1.25h is to be determined.

Concept introduction: The half-life is defined as the time required for the concentration of reactant to be reduced to one-half of its initial value.

The integrated rate law for the first order reaction is given by,


To determine: The rate constant for the given reaction, the concentration of In+ , mass of In(s) formed after 1.25h .




Half-life of In+ is 667s .


The rate constant for the first order reaction is calculated using the formula,



  • k isthe rate constant.
  • t1/2 isthe half-life.

Substitute the values of t1/2 in the above equation.


Mass of InCl(s) is 2.38g .

Volume of dilute HCl is 500mL .

The molar mass of InCl(s) is 150.271g/mol .


The number of moles is calculated using the formula,


Substitute the values of given mass and molar mass of InCl(s) in the above equation.


Volume of dilute HCl is 500mL .

Number of moles of InCl(s) is 0.0158mol .

The conversion of milliliter (mL) into liter (L) is done as,


Hence, the conversion of 500mL into liter is,



The molarity of In+(aq) is calculated using the formula,


Substitute the values of volume and moles in the above equation.


This is the initial concentration of In+(aq) .

The time of reaction is 1.25h .

There are 3600s in one hour. Hence, number of seconds in 1.25h is,


The initial concentration is 0

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