Chapter 15, Problem 15.157MP

Interpretation Introduction

Interpretation:

The $pH$ and equilibrium concentration of all the speciesshould be determined

Concept introduction:

• $pH$is defined as the negative logarithm of the hydrogen ion of the solution
  $pH=-\log \left[H_3{O}^{+}\right]$
• Molarity of a solution is defined as the number of moles of solute per litreof solution
  $Molarity=\frac{Numberofmoles}{Volumr\left(ml\right)}\times 1000$
• The general gas equation obtained by combining $Boyle\text{'}s$ law , $Charle\text{'}s$ law and $Avagadro\text{'}s$ law is known as ideal gas equation From $Boyle\text{'}slaw$

  We get, $V\propto \frac{1}{P}$

  From $Charle\text{'}slaw$

  We get, $V\propto T$

  From $Avagadro\text{'}slaw$

  We get, $V\propto n$

  Now by combining these three law we get
  
  $\begin{array}{l}V\propto \frac{nT}{P}\\ V=\frac{nRT}{P}\\ PV=nRT\end{array}$

  Where $n=Numberofmoles$

  $\begin{array}{l}P=pressure\\ V=Volume\\ T=temperature(K)\\ R=universalgascons\tan t=0.0821Latm/K/mol\end{array}$

• Strong acid dissociates completely in solution and therefore, the molar concentration of $H^{+}$ ion in the solution is same as that of the acid itself.But the weak acid are not completely dissociated and the relative strength of the weak acid can be compared in terms of their dissociation or ionization constant.The dissociation equilibrium of an acid HA, may be represented as
  $H{A}_{\left(aq\right)}+H_2{O}_{\left(l\right)}\rightleftharpoons H_3{O}^{+}{}_{\left(aq\right)}+A^{-}{}_{\left(aq\right)}$

  Applying law of equilibrium
  
  $K=\frac{\left[H_3{O}^{+}\right]\left[A^{-}\right]}{\left[HA\right]\left[H_{2}O\right]}$

  Since water is present in a large quantity its concentration remains practically constant, the concentration of water may be combined with K to give another constant $K_a$.
  
  $\begin{array}{l}K\left[H_{2}O\right]=\frac{\left[H_3{O}^{+}\right]\left[A^{-}\right]}{\left[HA\right]}\\ K_a=\frac{\left[H_3{O}^{+}\right]\left[A^{-}\right]}{\left[HA\right]}\end{array}$

  Where $K_a$ is the dissociation constant