# Heat of Vaporization

The Heat (or Enthalpy) of Vaporization is the quantity of heat that must be absorbed if a certain quantity of liquid is vaporized at a constant temperature. In a solution with both a vaporized and liquidized states, the kinetic energy of the vapor is higher than the kinetic energy of the liquid. Temperature follows kinetic energy, showing a lower temperature in the remaining liquid.

### Introduction

The Enthalpy of Vaporization is measured using constant temperature, meaning that something must be added to bring the lower temperature to the temperature of the solution prior to vaporization. To raise the temperature (and as a result, the kinetic energy), heat is added. The Enthalpy of Vaporization measures the amount of heat added, because it is the quantity that must be absorbed for a liquid to remain at constant temperature during vaporization. $$ΔH_{vap}$$ is expressed in kJ/mol.

$\Delta H_{vap} = H_{vapor} - H_{liquid}$

• $$\Delta H_{vap}$$ is the change in enthalpy of vaporization
• $$H_{vapor}$$ is the absolute enthalpy of the gas state of a compound or element
• $$H_{liquid}$$ is the absolute enthalpy of the liquid state of a compound or element

Enthalpies is a state function under a specific set of conditions, but cannot be measured directly, but the given difference has a unique value that can be measured. Because heat is added to the system to maintain the temperature, vaporization is an endothermic process, hence $$\Delta H_{vaporization}$$ is always positive.

### The Enthalpy of Condensation

Condensation is the opposite of vaporization, and therefore $$\Delta H_{condensation}$$ is also the opposite of $$\Delta H_{vap}$$. Because $$\Delta H_{vap}$$ is an endothermic process, where heat is lost in a reaction and must be added into the system from the surroundings, $$\Delta H_{condensation}$$ is an exothermic process, where heat is absorbed in a reaction and must be given off from the system into the surroundings.

$ΔH_{condensation} = H_{liquid} - H_{vapor} = -ΔH_{vap}$

Because $$ΔH_{condensation}$$, also written as $$ΔH_{cond}$$, is an exothermic process, its value is always negative. Moreover, $$ΔH_{cond}$$ is equal in magnitude to $$ΔH_{vap}$$, so the only difference between the two values for one given compound or element is the positive or negative sign.

Example

2.055 liters of steam at 100°C was collected and stored in a cooler container. What was the amount of heat involved in this reaction? The $$ΔH_{vap}$$ of water = 44.0 kJ/mol.

SOLUTION

1. First, convert 100°C to Kelvin.

°C + 273.15 = K
100.0 + 273.15 = 373.15 K

2. Find the amount involved (in moles).

$n_{water} = \dfrac{PV}{RT} = \dfrac{(1.0\; atm)(2.055\; L)}{(0.08206\; L\; atm\; mol^{-1} K^{-1})(373.15\; K)}$

$n_{water} = 0.0671\; mol$

3. Find $$ΔH_{cond}$$

$ΔH_{cond} = -ΔH_{vap}$

so

$ΔH_{cond} = -44.0\; kJ/mol$

4. Using the $$ΔH_{cond}$$ of water and the amount in moles, calculate the amount of heat involved in the reaction. To find kJ, multiply the $$ΔH_{cond}$$ by the amount in moles involved.

$(ΔH_{cond})(n_{water})$

$= (-44.0\; kJ/mol)(0.0671\; mol)$

$= -2.95\; kJ$

### Definitions of Terms

Vaporization (or Evaporation) the transition of molecules from a liquid to a gaseous state; the molecules on a surface are usually the first to undergo a phase change.

• Enthalpy: the amount of heat consumed or released in a system at constant pressure
• Kinetic Energy: the energy of a moving object measured in Joules
• Endothermic: when heat is added to a system from the surroundings, due to a decrease in heat in a reaction
• Exothermic: when heat from a system is given off into its surroundings, due to the increase in heat in a reaction
• Heat of Vaporization: the amount of heat required to evaporate a liquid
• System and its Surroundings: the system is the area in which a reaction takes place and the surroundings is the area that interacts with the system
• Condensation: the transition of molecules from a gaseous or vapor state to a liquid
• State Function (or Function of State): any property, such as temperature, pressure, enthalpy or mass, that has a unique value or number for the specific state of a system

### Heat of Vaporization

In a system, a liquid is boiled and some of the molecules are converted to gas. The Heat of Vaporization corresponds to the heat that the liquid lost when the molecules phase changed. The Enthalpy of Vaporization, conversely, is the amount of heat applied to the system to boil the liquid. As a result, the temperature of the liquid remained constant, while the given heat was absorbed to convert the molecules.

$ΔH_{vap} = \text{Heat of Vaporization}$

Example 2

If a liquid uses 50 Joules of heat to vaporize one mole of liquid, then what would be the enthalpy of vaporization?

SOLUTION

The heat in the process is equal to the change of enthalpy, which involves vaporization in this case

$q_{tot} = \Delta_{vap}$

so

$q_{tot} = 50 \; J= \Delta_{vap}$

So the enthalpy of vaporization for one mole of substance is 50 J.

### References

1. Petrucci, Ralph H., William S. Harwood, F. G. Herring, and Jeffry D. Madura. General Chemistry: Principles & Modern Applications. 9th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2007. 474.

### Contributors

• Nandini Bapat (UCD)