Chapter 4, Problem 128AP

Because the Acid-base and precipitation reactions discussed in this chapter all involve ionic species, their progress can be monitored by measuring the electrical conductance of the solution. Match each of the following reactions with one of the diagrams shown here. The electrical conductance is shown in arbitrary units.

$\begin{array}{l}\text{(1)}\hfill \\ \text{A 1}\text{.0 }M\text{ KOH solution is added to 1}\text{.0 L of 1}\text{.0 }M{\text{ HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\text{.}\hfill \\ \left(\text{2}\right)\hfill \\ \text{A 1}\text{.0 }M\text{ NaOH solution is added to 1}\text{.0 L of 1}\text{.0 }M\text{ HCl}\text{.}\hfill \\ \left(\text{3}\right)\hfill \\ \text{A 1}\text{.0 }M{\text{ BaCl}}_{\text{2}}\text{ solution is added to 1}\text{.0 L of 1}\text{.0 }M{\text{ K}}_{\text{2}}{\text{SO}}_{\text{4}}\text{.}\hfill \\ \left(\text{4}\right)\hfill \\ \text{A 1}\text{.0 }M\text{ NaCl solution is added to 1}\text{.0 Lof 1}\text{.0 }M{\text{ AgNO}}_{\text{3}}\text{.}\hfill \\ \left(\text{5}\right)\hfill \\ \text{A 1}\text{.0 }M{\text{ HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\text{ solution is added to 1}\text{.0 L of 1}\text{.0 }M{\text{ NH}}_{\text{3}}\text{.}\hfill \end{array}$

Interpretation Introduction

Interpretation:

Thegiven reactions, which involve ionic species, are to be matched with the given graphs that is electrical conductance versus volume..

Concept Introduction:

A material consists of transferable particles that contain an electric charge in order to carry electricity. This phenomenon is known as electrical conductance.

The representation of the number of moles of solute per liter of solution is known as molarity.

Answer to Problem 128AP

Solution: The reactions are matched to the given diagram as follows:

$\begin{array}{cccc}\text{Diagram}& & \text{Reaction}& \\ \text{a}& & 2\text{and 4}& \\ \text{b}& & 5& \\ \text{c}& & 3& \\ \text{d}& & 1& \end{array}$

Explanation of Solution

Given information: The reactions thatinvolve ionic species aregiven as follows:

$\text{A}\text{1}\text{.0 M KOH}$ solution is added to $\text{1}\text{.0 L}$ of $\text{1}{\text{.0 M HC}}_2{\text{H}}_{\text{3}}{\text{O}}_2$.

$\text{A}\text{1}\text{.0 M NaOH}$ solution is added to $\text{1}\text{.0 L}$ of $\text{1}\text{.0 M HCl}$.

$\text{A}\text{1}{\text{.0 M BaCl}}_2$ solution is added to $\text{1}\text{.0 L}$ of $\text{1}{\text{.0 M K}}_2{\text{SO}}_2$.

$\text{A}\text{1}\text{.0 M NaCl}$ solution is added to $\text{1}\text{.0 L}$ of $\text{1}{\text{.0 M AgNO}}_3$.

$\text{A}\text{1}{\text{.0 M HC}}_2{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}$ solution is added to $\text{1}\text{.0 L}$ of $\text{1}{\text{.0 M NH}}_{\text{3}}$.

The plot between electrical conductance and volume is represented as follows:

Atable is madefor each reaction, which consists of the volume of solution added. The conductance unit of a substance would be twice its molarity for the complete dissociation of the substance into $+1$ and $-1$ ions in the solution, and the conductance unit of the substance would be four times its molarity if the substance completely dissociates into $+2$ and $-2$ ions in the solution. The table for each reaction is represented as follows:

(1) ${\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\left(aq\right)+\text{KOH}\left(aq\right)\to {\text{KC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\left(aq\right)+{\text{H}}_{\text{2}}\text{O}\left(l\right)$.

$\begin{array}{ccc}\text{Volume}\left(\text{added}\right)& \text{Conductance}& \text{Unit}\\ 0\text{L}\left(\text{KOH}\right)& \left[{\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right]=1.0\text{M, }\left(\text{negligible}\text{ions, weak acid}\right)& 0\\ 1\text{L}\left(\text{KOH}\right)& \left[{\text{KC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right]=\frac{1.0\text{mol}}{2.0\text{L}}=0.50\text{M},\left({\text{C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_2{}^{-},{\text{K}}^{+}\right)& 1\\ 2\text{L}\left(\text{KOH}\right)& \begin{array}{c}\left[{\text{KC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M},\left({\text{C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_2{}^{-},{\text{K}}^{+}\right),\text{and}\\ \left[\text{KOH}\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M,}\left({\text{K}}^{+},{\text{OH}}^{-}\right)\end{array}& 1.3\end{array}$

(2) $\text{NaOH}\left(aq\right)+\text{HCl}\left(aq\right)\to \text{NaCl}\left(aq\right)+{\text{H}}_{\text{2}}\text{O}\left(l\right)$.

$\begin{array}{ccc}\text{Volume}\left(\text{added}\right)& \text{Conductance}& \text{Unit}\\ 0\text{L}\left(\text{NaOH}\right)& \left[\text{HCl}\right]=1.0\text{M, }\left({\text{H}}^{+},{\text{Cl}}^{-}\right)& 2\\ 1\text{L}\left(\text{NaOH}\right)& \left[\text{NaCl}\right]=\frac{1.0\text{mol}}{2.0\text{L}}=0.50\text{M},\left({\text{Na}}^{+},{\text{Cl}}^{-}\right)& 1\\ 2\text{L}\left(\text{NaOH}\right)& \begin{array}{c}\left[\text{NaCl}\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M},\text{and}\\ \left[\text{NaOH}\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M,}\left({\text{Na}}^{+},{\text{OH}}^{-}\right)\end{array}& 1.3\end{array}$

(3) ${\text{BaCl}}_2\left(aq\right)+{\text{K}}_{\text{2}}{\text{SO}}_4\left(aq\right)\to {\text{BaSO}}_4\left(s\right)+2\text{KCl}\left(aq\right)$.

$\begin{array}{ccc}\text{Volume}\left(\text{added}\right)& \text{Conductance}& \text{Unit}\\ 0\text{L}\left({\text{BaCl}}_2\right)& \left[{\text{K}}_2{\text{SO}}_4\right]=1.0\text{M, }\left({\text{2K}}^{+},{\text{SO}}_4{}^{2-}\right)& 4\\ 1\text{L}\left({\text{BaCl}}_2\right)& \left[\text{KCl}\right]=\frac{2.0\text{mol}}{2.0\text{L}}=1.0\text{M},\left({\text{K}}^{+},{\text{Cl}}^{-}\right)& 2\\ 2\text{L}\left({\text{BaCl}}_2\right)& \begin{array}{c}\left[\text{KCl}\right]=\frac{2.0\text{mol}}{3.0\text{L}}=\frac{2}{3}\text{M},\left({\text{K}}^{+},{\text{Cl}}^{-}\right),\text{and}\\ \left[{\text{BaCl}}_2\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M,}\left({\text{Ba}}^{2+},2{\text{Cl}}^{-}\right)\end{array}& 2.7\end{array}$

$\text{(4)NaCl}\left(aq\right)+{\text{AgNO}}_{\text{3}}\left(aq\right)\to \text{AgCl}\left(s\right)+{\text{NaNO}}_3\left(aq\right)$.

$\begin{array}{ccc}\text{Volume}\left(\text{added}\right)& \text{Conductance}& \text{Unit}\\ 0\text{L}\left(\text{NaCl}\right)& \left[{\text{AgNO}}_3\right]=1.0\text{M, }\left({\text{Ag}}^{+},{\text{NO}}_3{}^{-}\right)& 2\\ 1\text{L}\left(\text{NaCl}\right)& \left[{\text{NaNO}}_3\right]=\frac{1.0\text{mol}}{2.0\text{L}}=0.50\text{M},\left({\text{Na}}^{+},{\text{NO}}_3{}^{-}\right)& 1\\ 2\text{L}\left(\text{NaCl}\right)& \begin{array}{c}\left[{\text{NaNO}}_3\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M},\left({\text{Na}}^{+},{\text{NO}}_3{}^{-}\right),\text{and}\\ \left[\text{NaCl}\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M,}\left({\text{Na}}^{+},{\text{Cl}}^{-}\right)\end{array}& 1.3\end{array}$

${\text{(5) HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\left(aq\right)+{\text{NH}}_3\left(aq\right)\to {\text{NH}}_4{\text{C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_2$.

$\begin{array}{ccc}\text{Volume}\left(\text{added}\right)& \text{Conductance}& \text{Unit}\\ 0\text{L}\left({\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right)& \left[{\text{NH}}_3\right]=1.0\text{M, }\left(\text{negligible}\text{ions, weak base}\right)& 0\\ 1\text{L}\left({\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right)& \left[{\text{NH}}_4{\text{C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right]=\frac{1.0\text{mol}}{2.0\text{L}}=0.50\text{M},\left({\text{C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_2{}^{-},{\text{NH}}_4{}^{+}\right)& 1\\ 2\text{L}\left({\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right)& \begin{array}{c}\left[{\text{NH}}_4{\text{C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right]=\frac{1.0\text{mol}}{3.0\text{L}}=\frac{1}{3}\text{M}\\ \end{array}& 0.67\end{array}$

Hence, the evaluated data of these reactions are matched to the given diagrams as follows:

$\begin{array}{cccc}\text{Diagram}& & \text{Reaction}& \\ \text{a}& & 2\text{and 4}& \\ \text{b}& & 5& \\ \text{c}& & 3& \\ \text{d}& & 1& \end{array}$

Conclusion