The heat of reaction, also known as enthalpy of reaction, is the enthalpy change of a chemical reaction occurring at a constant pressure. Generally, it is determined as the energy required to release or produce one mole of a substance ^[1-4].

Formula ^[1-4]

Consider the following reaction.

aA + bB    →    cC + dD

The heat of reaction (ΔH_rxn) is given by

ΔH_rxn = [c ΔH_f^o(C)  +   d ΔH_f^o(D)]  –  [a ΔH_f^o(A)  +  b ΔH_f^o(B)]

The general expression for the heat of reaction is given by the difference between the sums of the enthalpies of formation of the products and the reactants.

ΔH_rxn = ΣnΔH_f^o (products) – ΣmΔH_f^o (reactants)

Where

n: Stoichiometric coefficients of the products

m: Stoichiometric coefficients of the reactants

Symbol: ΔH_rxn

Unit: kJ/mol

Characteristics

• ΔH_rxn can be positive or negative.
• A positive value indicates that the enthalpy of products is greater than that of the reactants. In other words, the reaction is endothermic and requires heat.
• A negative value indicates that the enthalpy of products is less than that of the reactants (see graph below). In other words, the reaction is exothermic and liberates heat.
• When the reaction occurs at standard temperature and pressure, the heat of reaction is denoted by the symbol ΔH_rxn^o. Standard temperature and pressure mean temperature of – 25 ˚C and pressure of 1 atm.

Examples

1. Let us take the example of the reaction between carbon (C) and oxygen (O₂) to form carbon dioxide (CO₂) ^[1-4].

C (s) + O₂ (g) → CO₂ (g)

The enthalpy of reaction is given by

ΔH_rxn^o = (1 mol) ΔH_f^o{CO₂(g)} – [(1 mol) ΔH_f^o{C(s)} + (1 mol) ΔH_f^o{O₂(g)}]

Because both C(s) and O₂(g) are in their natural and stable form, their enthalpies of formation are zero. Also, the standard enthalpy of formation values can be found in our other article.

Therefore,

ΔH_rxn^o = (1 mol) (-392.505 kJ/mol) – [(1 mol) (0) + (1 mol) (0)}

=> ΔH_rxn^o (CO₂) = -392.505 kJ/mol

2. Consider the reaction between methane (CH₄) and oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O).

CH₄ (g) + 2 O₂ (g) → CO₂ (g) + 2 H₂O (l)

ΔH_rxn^o = (1 mol) ΔH_f^o{CO₂(g)} + (2 mol) ΔH_f^o{H₂O (l)} – [(1 mol) ΔH_f^o{CH₄(g)} + (2 mol) ΔH_f^o{O₂(g)}]

=> ΔH_rxn^o = (1 mol) (- 393.5 kJ/mol) + (2 mol) (- 285.8 kJ/mol) – [(1 mol) (-74.81 kJ/mol) + (2 mol) (0)]

=> ΔH_rxn^o = -890.29 kJ/mol

How to Find Heat of Reaction Experimentally

The heat of reaction is usually determined by measuring the heat produced over time using a reaction calorimeter, such as a heat flow calorimeter. A calorimeter is an isolated system that maintains constant pressure. The following equation gives the amount of heat produced [1-4].

q = m c_P ΔT

Where,

q: Heat

m: Mass of the reactants

c_p: Specific heat of the reactants

ΔT: Change in temperature

The value of q is numerically equal to ΔH_rxn, provided we scale it to per mole. The process of measuring changes in enthalpy in this way is called calorimetry.

Example Problem

Calculate the heat of reaction when a given quantity of ethanol is burnt in air to increase the temperature of 400 g of water from 26 to 44 ˚C. The specific heat of water is 4.2 J/g.K.

Solution:

Given, m = 400 g                             c_P = 4.2 J/g.K                     ΔT = 44 ˚C – 26 ˚C = 18 ˚C

The amount of heat lost in the combustion process equals the heat gained by the water. Therefore, we use the following equation:

 q = m c_P ΔT

q = 400 g x 4.2 J/g.˚C x 18 ˚C

q = 30240 J or 30.24 KJ

The heat of reaction of ethanol is – 30.24 kJ.