Chapter 9, Problem 9.101PAE

Interpretation Introduction

Interpretation: The additional data required to determine the ${\text{ΔH}}_{\text{f}}^{\text{0}}$ for silicon nitride based on the assumption that ${\text{ΔH}}^{\text{0}}$ for the following reaction is known.

$3C{O}_2(g)+S{i}_3{N}_4(s)\to 2Si{O}_2(s)+2N_2(g)+3C(s)$

Concept introduction:

• Chemical reactions proceed with the absorption (endothermic) or evolution (exothermic) of heat.
• Enthalpy change or the change in the energy of a chemical reaction can be deduced in terms of the enthalpy of formation of the products and reactants.
• The enthalpy of formation of any chemical system in its natural state is zero.

Answer to Problem 9.101PAE

Solution: The data showing the standard enthalpy of formation of solid silicon dioxide is required.

Explanation of Solution

The given reaction is:

$3C{O}_2(g)+S{i}_3{N}_4(s)\to 2Si{O}_2(s)+2N_2(g)+3C(s)$

Reaction enthalpy can be calculated using the following equation

$\Delta {\text{H}}_{\text{rxn}}^0={\displaystyle \sum {\text{n}}_{\text{products}}\Delta {\text{H}}_{\text{f}}^0{}_{\text{(products)}}\text{ - }{\displaystyle \sum {\text{n}}_{\text{reactants}}\Delta {\text{H}}_{\text{f}}^0{}_{\text{(reactants)}}}}\text{ -------(1)}$

n_products and n_reactants are the number of moles of products and reactants respectively

$\Delta {\text{H}}_{\text{f (products)}}^0\text{ and }\Delta {\text{H}}_{\text{f (reactants)}}^0$ are the standard heats of formation of the products and reactants respectively

Based on equation (1) for the given reaction we can write:

$\begin{array}{l}\Delta {\text{H}}_{\text{rxn}}^0=[2\times \Delta {\text{H}}_{\text{f}}^0{\text{(SiO}}_{\text{2}}\text{(s)) + 2}\end{array}$

$\begin{array}{l}\times \Delta {\text{H}}_{\text{f}}^0{\text{(N}}_{\text{2}}\text{(g)) + 3}\times \Delta {\text{H}}_{\text{f}}^0\text{(C(s)) ] - }\end{array}$

$\begin{array}{l}[3\times \Delta {\text{H}}_{\text{f}}^0{\text{(CO}}_{\text{2}}\text{(g)) + 1}\times \Delta {\text{H}}_{\text{f}}^0{\text{(Si}}_{\text{3}}{\text{N}}_2\text{(s))]}\end{array}$

$\begin{array}{l}{\text{N}}_{\text{2}}\text{(g), C(s) and CO2(g) are all present in their natural physical state}\text{. Hence, }\Delta {\text{H}}_{\text{f}}^0\text{ for these systems is 0}\text{. }\end{array}$

Therefore,

$\begin{array}{l}\Delta {\text{H}}_{\text{rxn}}^0=[2\times \Delta {\text{H}}_{\text{f}}^0{\text{(SiO}}_{\text{2}}\text{(s)) + 2}\times \Delta {\text{H}}_{\text{f}}^0\text{(0) + 3}\times \Delta {\text{H}}_{\text{f}}^0\text{(0) ] - }\end{array}$

$\begin{array}{l}[3\times \Delta {\text{H}}_{\text{f}}^0\text{(0) + 1}\times \Delta {\text{H}}_{\text{f}}^0{\text{(Si}}_{\text{3}}{\text{N}}_2\text{(s))]}\end{array}$

$\begin{array}{l}\Delta {\text{H}}_{\text{rxn}}^0=[2\times \Delta {\text{H}}_{\text{f}}^0{\text{(SiO}}_{\text{2}}\text{(s))]-[1}\times \Delta {\text{H}}_{\text{f}}^0{\text{(Si}}_{\text{3}}{\text{N}}_2\text{(s))]}\end{array}$

$\begin{array}{l}\Delta {\text{H}}_{\text{f}}^0{\text{(Si}}_{\text{3}}{\text{N}}_2\text{(s))}=[2\times \Delta {\text{H}}_{\text{f}}^0{\text{(SiO}}_{\text{2}}\text{(s))]}-\Delta {\text{H}}_{\text{rxn}}^0\end{array}$

Conclusion

The standard enthalpy of formation of solid silicon dioxide is required to calculate the enthalpy of formation of silicon nitride.