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: 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 1.25 h 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,

ln[A]=−kt+ln[A]0

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

Explanation

Given

Half-life of In+ is 667 s .

Formula

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

k=0.693t1/2

Where,

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

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

k=0.693t1/2=0.693667 s=0.001 s−1_

Mass of InCl(s) is 2.38 g .

Volume of dilute HCl is 500 mL .

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

Formula

The number of moles is calculated using the formula,

Number of moles=Given massMolar mass

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

Number of moles=Given massMolar mass=2.38 g150.271 g/mol=0.0158 mol_

Volume of dilute HCl is 500 mL .

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

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

1 mL=10−3 L

Hence, the conversion of 500 mL into liter is,

500 mL=(500×10−3) L=0.5 L

Formula

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

Molarity of In+=Moles of In+Volume of solution

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

Molarity of In+=Moles of In+Volume of solution=0.01580.5 L=0.0316 M_

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

The time of reaction is 1.25 h .

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

1.25 h=1.25×3600 s=4500 s

The initial concentration is 0