Chapter 5, Problem 5.78QP

Interpretation Introduction

Interpretation:

The given inter halogen compounds have to be arranged in increasing order of percentage of fluorine by mass.

Concept introduction:

Percent composition by mass of each element present in a compound is known as the compound’s percent composition by mass.

$\begin{array}{l}\text{Percent}\text{by}\text{mass}\text{of}\text{an}\text{element}\text{=}\frac{\text{n}\text{×atomic}\text{mass}\text{of}\text{element}}{\text{molecular}\text{or}\text{formula}\text{mass}\text{of}\text{compound}}\text{×100\%}\\ \text{Where}\text{n}\text{is}\text{the}\text{number}\text{of}\text{atoms}\text{of}\text{the}\text{element}\text{in}\text{a}\text{molecule}\text{or}\text{formula}\text{unit}\text{of}\text{the}\text{compound}\end{array}$

Answer to Problem 5.78QP

The percentage of fluorine by mass of given inter halogen compounds was arranged in the increasing order as,

${\text{IF}}_{\text{5}}{\text{<BrF}}_{\text{5}}{\text{<ClF}}_{\text{3}}{\text{<ClF}}_{\text{5}}$

${\text{IF}}_{\text{5}}$ contains the smallest percentage of fluorine by mass.

Explanation of Solution

Percent composition by mass: Percent composition by mass of each element present in a compound is known as the compound’s percent composition by mass.  The formula is expressed mathematically as follows:

$\begin{array}{l}\text{Percent}\text{by}\text{mass}\text{of}\text{an}\text{element}\text{=}\frac{\text{n}\text{×atomic}\text{mass}\text{of}\text{element}}{\text{molecular}\text{or}\text{formula}\text{mass}\text{of}\text{compound}}\text{×100\%}\\ \text{Where}\text{n}\text{is}\text{the}\text{number}\text{of}\text{atoms}\text{of}\text{the}\text{element}\text{in}\text{a}\text{molecule}\text{or}\text{formula}\text{unit}\text{of}\text{the}\text{compound}\end{array}$ By using the above formula, percentage fluorine by mass of interhalogen compounds is calculated as follows:

$\begin{array}{l}\text{Percent}\text{by}\text{mass}\text{of}\text{\%}\text{F}\text{in}{\text{ClF}}_3\text{=}\frac{\text{3×atomic}\text{mass}\text{F}\text{in}\text{}\text{amu}}{\text{molecular}\text{mass}\text{of}{\text{ClF}}_3\text{in}\text{amu}}\text{×}\text{100\%}\\ \text{=}\frac{\text{3}\times \text{18}\text{.9984}\text{amu}}{92.448\text{amu}}\text{×}\text{100\%}\\ \text{=}61.\text{62}\text{\%}\end{array}$

$\begin{array}{l}\text{Percent}\text{by}\text{mass}\text{of}\text{\%}\text{F}\text{in}{\text{BrF}}_5\text{=}\frac{\text{5×atomic}\text{mass}\text{F}\text{in}\text{}\text{amu}}{\text{molecular}\text{mass}\text{of}{\text{BrF}}_5\text{in}\text{amu}}\text{×}\text{100\%}\\ \text{=}\frac{\text{5×18}\text{.9984}\text{amu}}{\text{174}\text{.894}\text{amu}}\text{×}\text{100\%}\\ =54.31\%\end{array}$

$\begin{array}{l}\text{Percent}\text{by}\text{mass}\text{of}\text{\%}\text{F}\text{in}{\text{IF}}_{\text{5}}\text{=}\frac{\text{5×atomic}\text{mass}\text{F}\text{in}\text{}\text{amu}}{\text{molecular}\text{mass}\text{of}{\text{IF}}_5\text{in}\text{amu}}\text{×}\text{100\%}\\ \text{=}\frac{\text{5×18}\text{.9984}\text{amu}}{\text{221}\text{.89}\text{amu}}\text{×}\text{100\%}\\ \text{=}\text{42}\text{.79\%}\end{array}$

$\begin{array}{l}\text{Percent}\text{by}\text{mass}\text{of}\text{\%}\text{F}\text{in}{\text{ClF}}_5\text{=}\frac{\text{3×atomic}\text{mass}\text{F}\text{in}\text{}\text{amu}}{\text{molecular}\text{mass}\text{of}{\text{ClF}}_5\text{in}\text{amu}}\text{×}\text{100\%}\\ \text{=}\frac{5\times \text{18}\text{.9984}\text{amu}}{130.445\text{amu}}\text{×}\text{100\%}\\ \text{=}72.82\text{\%}\end{array}$

Conclusion

The percentage fluorine by mass of interhalogen compounds was arranged in the below order:

${\text{IF}}_{\text{5}}{\text{<BrF}}_{\text{5}}{\text{<ClF}}_{\text{3}}{\text{<ClF}}_{\text{5}}$