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# Calculating Heat of Reaction from Heat of Formation

## An application of Hess's Law

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Calculating Heat of Reaction from Heat of Formation

Credit: User:NIMSoffice/Wikipedia
Source: http://commons.wikimedia.org/wiki/File:HPHTdiamonds2.JPG
License: CC BY-NC 3.0

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### Calculating Heat of Reaction from Heat of Formation

An application of Hess’s law allows us to use standard heats of formation to indirectly calculate the heat of reaction for any reaction that occurs at standard conditions. An enthalpy change that occurs specifically under standard conditions is called the standard enthalpy (or heat) of reaction and is given the symbol ΔH\begin{align*}\Delta H^\circ\end{align*}. The standard heat of reaction can be calculated by using the following equation.

ΔH=nΔHf(products)nΔHf(reactants)

The symbol Σ is the Greek letter sigma and means “the sum of”. The standard heat of reaction is equal to the sum of all the standard heats of formation of the products minus the sum of all the standard heats of formation of the reactants. The symbol “n\begin{align*}n\end{align*}” signifies that each heat of formation must first be multiplied by its coefficient in the balanced equation.

 Substance ΔH∘f\begin{align*}\Delta H_f^\circ\end{align*} (kJ/mol) Substance ΔH∘f\begin{align*}\Delta H_f^\circ\end{align*} (kJ/mol) Al2O3(s) -1669.8 H2O2(l) -187.6 BaCl2(s) -860.1 KCl(s) -435.87 Br2(g) 30.91 NH3(g) -46.3 C (s, graphite) 0 NO(g) 90.4 C (s, diamond) 1.90 NO2(g) 33.85 CH4(g) -74.85 NaCl -411.0 C2H5OH(l) -276.98 O3(g) 142.2 CO(g) -110.5 P(s, white) 0 CO2(g) -393.5 P(s, red) -18.4 CaO(s) -635.6 PbO(s) -217.86 CaCO3(s) -1206.9 S(rhombic) 0 HCl(g) -92.3 S(monoclinic) 0.30 CuO(s) -155.2 SO2(g) -296.1 CuSO4(s) -769.86 SO3(g) -395.2 Fe2O3(s) -822.2 H2S(g) -20.15 H2O(g) -241.8 SiO2 -859.3 H2O(l) -285.8 ZnCl2 -415.89

#### Sample Problem: Calculating Standard Heat of Reaction

Calculate the standard heat of reaction (ΔH)\begin{align*}(\Delta H^\circ)\end{align*} for the reaction of nitrogen monoxide gas with oxygen to form nitrogen dioxide gas.

Step 1: List the known quantities and plan the problem.

Known

• ΔHf for NO(g)=90.4 kJ/mol\begin{align*}\Delta H{_f}^\circ \ \text{for NO}(\text{g})=90.4 \text{ kJ/mol}\end{align*}
• ΔHf for O2(g)=0 (element)\begin{align*}\Delta H{_f}^\circ \ \text{for O}_2 (\text{g})=0 \ (\text{element})\end{align*}
• ΔHf for NO2(g)=33.85 kJ/mol\begin{align*}\Delta H{_f}^\circ \ \text{for NO}_2(\text{g})=33.85 \text{ kJ/mol}\end{align*}

Unknown

• ΔH=? kJ\begin{align*}\Delta H^\circ=? \text{ kJ}\end{align*}

First write the balanced equation for the reaction. Then apply the equation to calculate the standard heat of reaction for the standard heats of formation.

Step 2: Solve.

The balanced equation is: 2NO(g)+O2(g)2NO2(g)\begin{align*}2\text{NO(g)}+\text{O}_2(\text{g}) \rightarrow 2\text{NO}_2(\text{g})\end{align*}

Applying the equation form the text:

ΔH=[2 mol NO2(33.85 kJ/mol)][2 mol NO(90.4 kJ/mol)+1 mol O2(0 kJ/mol)]=113 kJ

The standard heat of reaction is -113 kJ.

Step 3: Think about your result.

The reaction is exothermic, which makes sense because it is a combustion reaction and combustion reactions always release heat.

#### Summary

• Standard heats of reaction can be calculated from standard heats of formation.

#### Practice

Do the practice exercises at the link below:

#### Review

Questions

1. Is a Hess’ Law calculation a direct determination of a standard heat of reaction?
2. What is the purpose of the n\begin{align*}n\end{align*} in the equation?
3. What does \begin{align*}\sum\end{align*} stand for?

### Image Attributions

1. [1]^ Credit: User:NIMSoffice/Wikipedia; Source: http://commons.wikimedia.org/wiki/File:HPHTdiamonds2.JPG; License: CC BY-NC 3.0

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