# Calorimetry

An apparatus to measure heat changes in a chemical reaction is called calorimeter. It is a vessel which is immersed in a known volume of a liquid. If heat capacity of liquid (in which calorimeter is immersed) and heat capacity of calorimeter is known, we can measure the heat evolved in the process by measuring the changes in temperature. Measurements are made under two different conditions, i.e. at constant volume and at constant pressure. For measurement under constant volume, bomb calorimeter is used. For measurement under constant pressure, any open container can be used.

## ΔU Measurements

### Reaction Enthalpy

Reaction enthalpy is given by the symbol ΔrH

ΔrH = (sum of enthalpies of products) – (sum of enthalpies of reactants)

= ΣaiHproducts - ΣbiHreactants

Here, ai and bi are stoichiometric coefficients of products and reactants in the balanced chemical equation.

Standard Enthalpy of Reactions: It is the enthalpy change when all the participating substances are in their standard states. The pure form of a substance at 1 bar and at a specified temperature is called its standard state. For example: standard state of solid iron at 500 K is pure iron at 1 bar. Standard conditions are denoted by adding the supercript Θ (capital letter theta) to the symbol ΔH, e.g. ΔHΘ

Enthalpy of fusion: The enthalpy change accompanying melting of one mole of a solid substance in standard state is called standard enthalpy of fusion or molar enthalpy of fusion, ΔfusHΘ.

Enthalpy of Vaporization: The amount of heat required to vaporize one mole of a liquid at constant temperature and under standard pressure is called its standard enthalpy of vaporization or molar enthalpy of vaporization, ΔvapHΘ.

Enthalpy of Sublimation: The change in enthalpy on sublimation of one mole of a solid at constant temperature and under standard pressure is called standard enthalpy of sublimation, ΔsubHΘ.

### Standard Enthalpy of Formation

The standard enthalpy change for the formation of one mole of a compound from its elements in their most stable states of aggregation is called Standard Molar Enthalpy of Formation. The reference state of an element is its most stable state of aggregation at 25°C and 1 bar pressure. Following are some examples:

H2(g) + 1/2O2(g) → H2O(l)

ΔfHΘ = -285.8 kJ mol-1

C(graphite, s) + 2H2(g) → CH4 (g)

ΔfHΘ = -74.81 kJ mol-1

2C (graphite, s) + 3H2(g) + 1/2O2 → C2H5OH(l)

ΔfHΘ = -277.7 kJ mol-1

Standard molar enthalpy of formation (ΔfHΘ) is a special case of ΔrHΘ, where one mole of a compound is formed from its constituent elements. In above examples, 1 mole of each (water, methane and ethanol) is formed. Let us consider following reactions to understand this.

CaO(s) + CO2(g) → CaCO3(s)

In this reaction, calcium carbonate is formed from other compounds, and not from constituent elements. So, standard molar enthalpy of formation cannot be used for this reaction.

Hg + Br2(l) → 2HBr(g)

In this reaction, two moles of hydrogen bromide are formed from one mole of each element. So, expression for enthalpy of formation can be obtained by dividing all the coefficients in the balanced equation by 2.