Chapter 17, Problem 17.93P

Interpretation Introduction

Interpretation

Highly toxic disulfur decafluoride decomposes by a free radical process: ${\text{S}}_{\text{2}}{\text{F}}_{\text{10}}\text{(g) }\underset{}{\overset{}{\rightleftharpoons }}{\text{ SF}}_{\text{4}}{\text{(g) + SF}}_{\text{6}}\text{(g)}$. In a study of the decomposition, ${\text{S}}_{\text{2}}{\text{F}}_{\text{10}}$ was placed in a 2.0 L flask and heated to ${\text{100}}^{\text{o}}\text{C}$; ${\text{[S}}_{\text{2}}{\text{F}}_{\text{10}}\text{]}$ was 0.50 M at equilibrium. More ${\text{S}}_{\text{2}}{\text{F}}_{\text{10}}$ was added, and when equilibrium was retained, the concentration of ${\text{S}}_{\text{2}}{\text{F}}_{\text{10}}$ was 2.5 M. How the concentrations change of ${\text{[SF}}_{\text{4}}\text{]}$ and ${\text{[SF}}_6\text{]}$ affects the equilibrium has to be determined.

Concept Introduction

Law of Chemical Equilibrium

The equilibrium constant is the product of molar concentrations of the product which is raised to its stoichiometric coefficients divided by the product of molar concentrations of the reactant which is raised to its stoichiometric coefficients.

Equilibrium Constant

Consider a reaction,

    $\text{aA+bB}\iff \text{cC+dD}$

    Forward reaction rate ${\text{K}}_{\text{f}}$= ${\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{B}}$

    Backward reaction rate ${\text{K}}_{\text{b}}$= ${\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}$

    At equilibrium, the rate of forward reaction = rate of backward reaction

    ${\text{K}}_{\begin{array}{l}\text{eq}\\ \end{array}}\text{=}\frac{{\text{K}}_{\text{f}}}{{\text{K}}_{\text{b}}}$

  $\frac{{\text{K}}_{\text{f}}}{{\text{K}}_{\text{b}}}\text{=}\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{B}}}$

    ${\text{K}}_{\text{eq}}\text{=}\frac{{\text{K}}_{\text{f}}}{{\text{K}}_{\text{b}}}\text{=}\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{B}}}$    

    ${\text{K}}_{\text{eq}}$ is the equilibrium constant.