Chapter 22, Problem 22.85P

(a)

Interpretation Introduction

Interpretation:

A balanced chemical equation for formation of sodium carbonate has to be written.

Explanation of Solution

The overall balanced equation is the sum of each step in the formation of sodium carbonate.

    $\begin{array}{l}{\text{2NaCl}}_{\text{(s)}}{\text{ + H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq) }}\underset{}{\overset{}{\to }}{\text{Na}}_{\text{2}}{\text{SO}}_{\text{4(aq)}}{\text{ + 2HCl}}_{\text{(g)}}\\ \\ {\text{Na}}_{\text{2}}{\text{SO}}_{\text{4(aq)}}\text{+}{\text{2C}}_{\text{(s)}}\underset{}{\overset{}{\to }}\cancel{{\text{Na}}_{\text{2}}{\text{S}}_{\text{(s)}}}\text{+}{\text{2CO}}_{\text{2(g)}}\\ \\ \cancel{{\text{Na}}_{\text{2}}{\text{S}}_{\text{(s)}}}{\text{ + CaCO}}_{\text{3(s)}}\underset{}{\overset{}{\to }}{\text{Na}}_{\text{2}}{\text{CO}}_{\text{3(s)}}{\text{ + CaS}}_{\text{(s)}}\\ \\ \text{Overall}{\text{CaCO}}_{\text{3(s)}}\text{+}{\text{Na}}_{\text{2}}{\text{SO}}_{\text{4(aq)}}\text{+}{\text{2C}}_{\text{(s)}}\text{+}{\text{2NaCl}}_{\text{(s)}}{\text{ + H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq) }}\\ \\ \underset{}{\overset{}{\to }}{\text{Na}}_{\text{2}}{\text{SO}}_{\text{4(aq)}}\text{+}{\text{2HCl}}_{\text{(g)}}\text{+}{\text{2CO}}_{\text{2(g)}}\text{+}{\text{Na}}_{\text{2}}{\text{CO}}_{\text{3(s)}}{\text{ + CaS}}_{\text{(s)}}.\end{array}$

(b)

Interpretation Introduction

Interpretation:

The standard enthalpy of calcium sulphide has to be determined.

Concept Introduction: 

Standard enthalpy of a reaction is the sum of the standard enthalpies of products minus sum of the standard enthalpies of reactants.

    ${\text{ΔH}}^{\text{ο}}{}_{\text{rxn}}\text{=}{\displaystyle \sum _{}^{}{\text{mΔH}}_{{}^{\text{f}}\text{(products)}}^{\text{o}}\text{-}}{\displaystyle \sum _{}^{}{\text{mΔH}}_{{}^{\text{f}}\text{(reactants)}}^{\text{o}}}$

Explanation of Solution

The standard enthalpy of calcium sulphide is determined as,

$\begin{array}{l}{\text{ΔH}}^{\text{ο}}{}_{\text{rxn}}\text{=}{\displaystyle \sum _{}^{}{\text{mΔH}}_{{}^{\text{f}}\text{(products)}}^{\text{o}}\text{-}}{\displaystyle \sum _{}^{}{\text{mΔH}}_{{}^{\text{f}}\text{(reactants)}}^{\text{o}}}\\ \\ {\text{ΔH}}^{\text{ο}}{}_{\text{rxn}}\text{=}{\text{[(1 mol Na}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}{\text{)(ΔH}}_{{}^{\text{f}}}^{\text{o}}{\text{Na}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}\text{)+ (2 mol HCl)}{\text{(ΔH}}_{{}^{\text{f}}}^{\text{o}}\text{HCl)}\text{+}{\text{(2 mol CO}}_{\text{2}}{\text{)(ΔH}}_{{}^{\text{f}}}^{\text{o}}{\text{CO}}_{\text{2}}\text{)}\\ \text{+}\left({\text{1 mol Na}}_{\text{2}}{\text{CO}}_{\text{3}}\right){\text{(ΔH}}_{{}^{\text{f}}}^{\text{o}}{\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}\text{)}\text{+ (1 mol CaS)}{\text{(ΔH}}_{{}^{\text{f}}}^{\text{o}}\text{CaS)]-}{\text{[(1 mol CaCO}}_{\text{3}}\text{)}{\text{(ΔH}}_{{}^{\text{f}}}^{\text{o}}{\text{CaCO}}_{\text{3}}\text{)}\\ \text{+}{\text{(1 mol Na}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(s)}}{\text{)(ΔH}}_{{}^{\text{f}}}^{\text{o}}{\text{Na}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(s)}}\text{)}\text{+ (2 mol C)}{\text{(ΔH}}_{{}^{\text{f}}}^{\text{o}}\text{C)}{\text{+ (2 mol NaCl)(ΔH}}_{{}^{\text{f}}}^{\text{o}}\text{NaCl)}\\ \text{+}{\text{ (1 mol H}}_{\text{2}}{\text{SO}}_{\text{4}}{\text{)(ΔH}}_{{}^{\text{f}}}^{\text{o}}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{)]}\\ \\ \text{351}\text{.8 kJ/mol = [(1 mol)(-}\text{1389}\text{.5 kJ/mol)+ (2 mol)}\text{(-92}\text{.31 kJ/mol)}\text{+ (2 mol)}\text{(-393}\text{.5 kJ/mol)}\\ \text{+}\text{(1 mol)}\text{(-1130}\text{.8 kJ/mol)}{\text{+ (1 mol)(ΔH}}_{{}^{\text{f}}}^{\text{o}}\text{CaS)]}\text{-}\text{[(1 mol)}\text{(-1206}\text{.9 kJ/mol)}\\ \text{+ (1 mol)}\text{(-1387}\text{.1 kJ/mol)}\text{+}\text{(2 mo)(0 kJ/mol) + (2 mol)(-411}\text{.1 kJ/mol)}\text{+}\text{(1 mol)(-907}\text{.51 kJ/mol)]}\\ \\ {\text{ΔH}}_{{}^{\text{f}}}^{\text{o}}\text{CaS}\text{=}\text{-480KJ}\text{.}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The overall reaction spontaneous or not has to be determined.

Explanation of Solution

The reaction is very endothermic; therefore it is probably not spontaneous even though the entropy change maybe expected to be positive. It will take a change in gibbs energy determination to know for sure.

(d)

Interpretation Introduction

Interpretation:

The mass of sodium carbonate has to be determined.

Explanation of Solution

The mass of sodium carbonate in the given reaction is calculated as,

$\begin{array}{l}{\text{Mass (g) of Na}}_{\text{2}}{\text{CO}}_{\text{3}}\text{ =}\text{(250}\text{. g NaCl)}\left(\frac{\text{1 mol NaCl}}{\text{58}\text{.44 g NaCl}}\right)\left(\frac{{\text{1 mol Na}}_{\text{2}}{\text{CO}}_{\text{3}}}{\text{2mol}\text{NaCl}}\right)\left(\frac{\text{105}\text{.99 g}{\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}}{\text{1 mol}{\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}}\right)\left(\frac{\text{73\%}}{\text{100\%}}\right)\\ \\ \text{=}{\text{165 gNa}}_{\text{2}}{\text{CO}}_{\text{3}}.\end{array}$