Enthalpy (H) of a thermodynamic system is an energy-like state function property that is equal to the total internal energy (U) and pressure-volume (PV) work whereas entropy is an intrinsic disorderness of a system under certain conditions. In thermodynamics, the change in enthalpy and entropy can be measured rather than their absolute values.

The term enthalpy was introduced by a Dutch Scientist, Heike Kamerlingh Onnes in 1909. The word enthalpy means ‘total heat content’. Enthalpy tells us how much heat is added or removed from the system. It is an important quantity because most of the reactions occur at constant pressure and it is used to measure the heat of a reaction.

The term entropy was introduced by the scientist Rudolf Clausius in 1850. This idea comes from the concept that heat always flows from hot to cold regions spontaneously which is equal to the entropy change. The concept of entropy develops from the fact that for energy to be converted to work, some dissipations must occur. This lost energy is called the ’entropy’.

Prerequisites |

Thermodynamics |

Internal energy vs Enthalpy |

How to find delta H? |

How to calculate heat of a reaction? |

## Enthalpy Vs Entropy

Enthalpy | Entropy |

It is a measurement of energy. | It is the measurement of the disorderness of a system. |

It is represented by H. | It is represented by S. |

It is the sum of internal energy and product of PV work. | It is the amount of heat transferred reversibly in and out of the system at a given temperature. |

H = U+PV | dS = d/T |

Its unit is KiloJoules/mole. | Its unit is Joules/Kelvin.mole. |

Change in enthalpy is equal to the energy supplied as heat at constant pressure. | In a spontaneous process, change in entropy will not be less in the direction of spontaneity. |

Enthalpy change in a cyclic process is zero. | Entropy change in a cyclic process is zero. |

Enthalpy is positive for endothermic processes. | Entropy is positive for spontaneous processes. |

Enthalpy is negative for exothermic processes. | Entropy is negative for non-spontaneous processes. |

According to the 1st law of thermodynamics, the energy of the universe is constant. | According to the 2nd law of thermodynamics, the entropy of the universe is always increasing. |

Systems favor minimum enthalpy. | Systems favor maximum entropy. |

There are some similarities between enthalpy and entropy as well which are such that, both enthalpy and entropy are

- State functions
- Extensive properties

## Enthalpy

Enthalpy is the amount of energy either lost or gained by the system. It can also be explained as the total energy contained inside a system.

According to the first law of thermodynamics, energy can neither be created nor be destroyed, it remains constant. So, we can say that the energy of the universe is constant.

If the energy of a system decreases, the surrounding energy increases, but the total energy remains constant and vice versa.

Enthalpy is represented by H.

It is the sum of internal energy and pressure-volume work.

H = U + PV

The absolute value of enthalpy cannot be determined but we can measure the change in enthalpy. These enthalpy changes are of several types.

**Related Topics**

### Enthalpy Change of Atomisation

It is the enthalpy change when one mole of gaseous atom(s) is formed from the element. It is denoted by ∆H_{atm}.

For example

Cs _{(s)} → Cs _{(g)}

∆H_{atm }= +76 KJ/mol

The value of enthalpy change is positive because this reaction is endothermic.

### Enthalpy Change of Solution

It is the amount of heat absorbed or liberated when a substance is dissolved in a solvent to form an infinitely dilute solution.

Enthalpy change of solution may be positive or negative and is denoted by ∆H_{sol}.

CaCl_{2 (s)} + aq → CaCl_{2 (aq)}

∆H_{sol }= -80 KJ/mol

### Enthalpy Change of Hydration

It is the change in enthalpy when one mole of gaseous ions is dissolved in water to form an infinitely dilute solution.

It is always negative and is denoted by ∆H_{hyd}.

Na_{(s) }+ H_{2}O_{(aq)} → NaOH_{(aq)} + 1/2H_{2 (g)}

∆H_{hyd} = -406 kJ/mol

### Enthalpy Change of Neutralization

It is the change in enthalpy when one mole of water is formed when a strong acid neutralizes a base.

It is denoted by ∆H_{neut}.

H_{2}SO_{4} + 2NaOH_{(aq)} → Na_{2}SO_{4 (aq)} + 2H_{2}O

∆H_{neut }= -55.8 kJ/mol

### Enthalpy change of Vaporization

The amount of heat required to convert one mole of a liquid into a gas is termed enthalpy change of vaporization (∆H_{vap}). It is also called heat of evaporation.

The heat of vaporization of water:

C_{2}H_{5}OH _{(liq) } → C_{2}H_{5}OH _{(gas)}

∆H_{vap } = -38.7 kJ/mol

## Entropy

Entropy is the measure of disorderness of the system. Entropy generally means disorderness which is analog to the variance in arrangements of particles. Entropy is represented by S.

In the case of solids, the particles are very close to each other because they are arranged in regular order, so solids have less entropy. The case of liquids is intermediate between solids and liquids whereas the particles are far away from each other in gases. They are more disordered so they have larger entropy.

S_{(s) }< S_{(liq)} <_{ }S_{(gas)}

Enthalpy usually runs opposite to the order of entropy increase but in some cases, entropy and enthalpy both increase e.g. endothermic processes like the dissolution of ammonium nitrate in water.

According to the 2nd law of thermodynamics, the entropy of the universe for a spontaneous process is always increasing as everything in the universe tends towards a more disordered state (stable) spontaneously.

S_{t} > 0

where,

S_{total}= S_{system}+ S_{surrounding}

We can never determine the absolute value of entropy. Instead, we can only determine the change in entropy.

Mathematically,

dS = dq_{rev} / T

At a given temperature heat is transferred reversibly in and out of the system.

S = q_{rev} /T

To calculate the difference in entropy between any two states of a system, we find a reversible path between them and integrate the energy supplied as heat at each stage of the path divided by the temperature at which heating occurs.

In the formula of entropy three terms are involved.

- Path function (q)
- q
_{rev}(reversible heat) - Temperature

### Heat (q) used for path functions

There are two ways of transfer of energy i.e. work and heat. Work is an organized way of transfer of energy so it does not change the entropy. On the other hand, heat is a random way of transfer of energy that causes a change in entropy.

**Reversible heat**

A reversible process is a slow process while an irreversible process is a fast one. If the transfer of heat takes place reversibly, the randomness increases. In fast heating (irreversible), heat is not uniformly distributed and some areas become more heated than others and the entropy changes are more than expected. That is why heat is added reversibly.

### Factors on which Entropy Depends

#### 1. Temperature

Entropy has a direct relationship with temperature.

When the temperature of a system increases, entropy increases too because the K.E of particles increases resulting in an increase in their movements due to which their randomness increases.

#### 2. Number of particles

Entropy has a direct relation with the number of particles. A greater number of particles means greater disorderness.

For example

- Decomposition of Dinitrogen tetroxide

N_{2}O_{4 } → 2NO_{2}

No. of particles increases from reactants to products and so does entropy.

- Chlorine gas (Cl
_{2})

Cl_{2 (gas)} → Cl_{2 (liq)}

Entropy decreases because chlorine gas is being converted into liquid.

#### 3. Effect of Dissolution

When a solute is added to a solvent, randomness increases, so entropy increases because solute-solute interactions are broken and all-new solute-solvent interactions are formed. For example, when sodium chloride (NaCl) dissolves in water, the ionic bonds present between Na & Cl is broken down and new bonds with the water molecule are formed.

However, there are some reactions where the change in entropy is zero because neither the state changes nor the number of particles.

Entropy change in solution is

CO _{(gas)} + H_{2}O _{(gas) } → CO_{2 (gas) }+ H_{2 (gas)}

Entropy change in solution is

ΔS = ΔS_{(products) }– ΔS_{(reactants)}

If,

ΔS_{p }< ΔS_{r} then, ΔS= negative

ΔS_{p} > ΔS_{r} then, ΔS= positive

The entropy change of the system can be calculated by using this relation.

ΔS_{(system)} = ΔS_{p }– ΔS_{r}

## Enthalpy vs Entropy in spontaneity

ΔG = ΔH – TΔS

Where ΔG is Gibbs free energy.

It refers to the physical and chemical processes that occur at constant temperature and pressure.

- If the Gibbs free energy change comes out positive, the reaction is non-spontaneous.
- If the Gibbs free energy change comes out negative, the reaction is spontaneous.
- If the Gibbs free energy change is zero, it means that the reaction is at equilibrium.

A general view of the criterion of spontaneity using enthalpy and entropy changes gives a better idea of spontaneous and non-spontaneous reactions.

Serial # | Enthalpy change(ΔH) | Entropy change(ΔS) | Gibbs Free energy change(ΔG) | Spontaneity |

1 | Positive (endothermic) | Positive (entropy change of product is greater than reactants) | Depends on temperature | Spontaneous at high temperature |

2 | Positive (endothermic) | Negative (entropy change of reactant is greater than the product) | Always positive | Non-spontaneous |

3 | Negative (exothermic) | Positive (entropy change of product is greater than reactants) | Always negative | Spontaneous |

4 | Negative (exothermic) | Negative (entropy change of reactant is greater than the product) | Depend on temperature | Spontaneous at low temperature |

**Explanation**

The relation between enthalpy and entropy needs to be described in four different cases:

For the endothermic process, ΔH is positive with positive entropy change, then ΔG depends on temperature. This process is spontaneous if (TΔS) is greater than ΔH when the temperature is high.

### 1. If Enthalpy (H) and Entropy (S) both are positive

If the values of enthalpy and entropy are assumed to be as;

Enthalpy change (ΔH) = 100kJ/mol

Entropy change (ΔS) = 100 J/K.mol = 0.1 KJ / K.mol

At a temperature = 10 K

ΔG = ΔH – TΔS

ΔG =100-(10)(0.1)

ΔG = 99 kJ/mol (+ve)

(Non-sponatneous reaction)

Now at temperature = 10000 K

ΔG = ΔH – TΔS

ΔG = 100-(10000)(0.1)

ΔG = -900kJ/mol (-ve)

(Sponatneous reaction)

### 2. If Enthalpy (H) is positive and Entropy (S) is negative

At Temperature = 10 K

ΔG = ΔH – TΔS

= 100 – (10) (-0.1)

= 101kJ/mol (+ve)

(Non-sponatneous reaction)

Now, at temperature = 10000 K

ΔG = ΔH – TΔS

= 100 – (10000) (-0.1)

= 1100kJ/mol (+ve)

(Non-sponatneous reaction)

### 3. If Enthalpy (H) is negative and Entropy (S) is positive

At temperature = 10 K

ΔG = ΔH – TΔS

= -100 – (10) (0.1)

= -101 kJ/mol (-ve)

(Sponatneous reaction)

Now at temperature = 10000 K

ΔG = ΔH – TΔS

= -100 – (10000) (0.1)

= -1100kJ/mol (-ve)

(Sponatneous reaction)

### 4. If Enthalpy (H) and Entropy (S) both are negative

At temperature = 10 K

ΔG = ΔH – TΔS

= -100 – (10) (-0.1)

= -99kJ/mol (-ve)

(Sponatneous reaction)

Now at T=10000 K

ΔG = ΔH – TΔS

= -100 – (10000) (-0.1)

= 900kJ/mol (+ve)

(Non-sponatneous reaction)

## Key Takaway(s)

## Concepts Berg

**Are enthalpy and entropy related?**

Enthalpy and entropy are related. Enthalpy is the internal energy or total heat content of a compound. Whereas entropy is the change in enthalpy per unit temperature. They are related as by the equation:

ΔG = ΔH – TΔS

**Which is more important enthalpy or entropy?**

Entropy is more important than enthalpy because when the temperature changes, a significant change is observed in entropy than enthalpy.

**Does entropy increase when enthalpy increases?**

Change in enthalpy also affects entropy. For an endothermic reaction, heat is absorbed from the surroundings, so, the entropy of the surroundings decreases. For exothermic reactions, heat is released to the surroundings, so, the entropy of the surroundings increases.

**Is entropy chaos?**

Entropy and chaos are similar terms. Entropy means disorder and the term chaos also means ‘disorder’, ‘perturbation’ confusion, or lack of order.

**Can entropy be negative?**

Entropy cannot be negative but a change in entropy can be negative only in the case of a non-spontaneous process. For example, during the condensation process, entropy decreases because gas is condensed back into a less entropy liquid.

**Is enthalpy negative or positive?**

Enthalpy change is positive for endothermic processes and negative for exothermic processes.

**Why do we need enthalpy?**

We need enthalpy because it tells us:

- The nature of reaction either endothermic or exothermic.
- The heat absorbed or desorbed by the system.
- Calculation of heat of reactions.

**What is the opposite of enthalpy?**

The opposite of enthalpy is entropy. Enthalpy is the total heat content of a system whereas entropy is a measure of the amount of disorder in the system.

**How to remember enthalpy vs entropy?**

Enthalpy is an amount of energy contained in a compound whereas entropy is a measure of disorderness within the compound. Gibb’s free energy provides a relationship between enthalpy and entropy.

**What is the enthalpy vs entropy for steam?**

Enthalpy of steam is the total heat content in one kilogram of steam. It is the sum of enthalpy of various states, liquid (water) and gas (vapor).

Entropy is defined as randomness in the molecule of a substance. Molecules of water in the form of vapor (steam) have the highest randomness than in the liquid state.

**What is the relationship between enthalpy and entropy?**

Enthalpy is the amount of energy released or absorbed in a system whereas, entropy is the measure of disorderness in a system.

Entropy is a change in enthalpy per unit temperature. Gibb’s free energy provides the relationship between enthalpy and entropy.

ΔG = ΔH – TΔS

**Enthalpy vs entropy vs free energy?**

ΔG = ΔH – TΔS

Gibb’s free energy is equal to the change in enthalpy minus the product of temperature and change in entropy of the system.

- If the Gibbs free energy change is positive, the reaction is non-spontaneous.
- If the Gibbs free energy change is negative, the reaction is spontaneous.
- If the Gibbs free energy change is zero, the reaction is at equilibrium.

**How can I understand entropy and enthalpy in terms of everyday examples?**

Examples of entropy are ice melting, dissolving sugar or salt in water and boiling water, etc.

Examples of enthalpy are refrigerator systems and hand warmers.

**What is the difference between enthalpy and energy?**

Energy is a state of matter. It is measured in joule whereas enthalpy is a form of energy. It is an energy change between two states. It is measured in Joules/mol.

**What is the significance of enthalpy?**

- Enthalpy tells us whether the reaction is endothermic or exothermic.
- From enthalpy, we can calculate the heat of the reaction.
- Enthalpy tells us how much heat is absorbed or is released by the system.

**What is enthalpy in layman’s terms?**

The word enthalpy comes from the Greek word ‘Enthalpos’ meaning ‘to put heat into’.

When changes in a system occur at constant pressure, it tells us how much heat and work were added or removed from the system. In this way, it also equals entropy.

**What is the difference between work and enthalpy?**

Enthalpy is the sum of internal energy plus the pressure-volume work.

The change in internal energy is the sum of heat transferred and is equal to the work done.

**What is the difference between activation enthalpy and the enthalpy of reaction?**

Activation enthalpy is an enthalpy difference between the transition state and ground state of reactants at constant temperature and pressure.

Enthalpy of reaction is a heat of reaction at constant pressure.

**What is the difference between the standard enthalpy of solution and standard enthalpy of hydration?**

The standard enthalpy of solution is the amount of heat absorbed or liberated when a substance is dissolved in a solvent to form an infinitely dilute solution.

Enthalpy change of solution may either be positive or negative.

MgCl_{2 (s)} + aq → MgCl_{2 (aq)}

∆H_{sol }= -55 KJ/mol

NaCl_{(s)} + aq → NaCl_{(aq)}

∆H_{sol }=+3.9kJ/mol

The enthalpy change of hydration is the change in enthalpy when one mole of gaseous ions are dissolved in water to form an infinitely dilute solution.

It is always negative.

Cl^{–}_{(s) }+ H_{2}O_{(aq) }→ Cl^{–}_{(aq)}

∆H_{hyd }= -364kJ/mol

**Is enthalpy H or Delta H?**

H is enthalpy which is equal to the sum of internal energy and product of pressure-volume work.

H=U+PV

Whereas ∆H is a change in enthalpy which is equal to the difference of enthalpy of product and enthalpy of reactants.

∆H= H_{f} – H_{i}

**What is the difference between heat and enthalpy**

Heat is a transfer of energy due to temperature differences whereas enthalpy is total heat content in a system. It is a change in heat at constant pressure.

If in case, the work done is zero then heat and enthalpy are interchangeable.

**How is enthalpy different from internal energy?**

Internal energy is the sum of kinetic energy and potential energy whereas enthalpy is the amount of heat evolved or absorbed during a chemical reaction.

**Is entropy proof of global warming?**

As entropy is a function of temperature. An increase in temperature leads to an increase in entropy. An increase in entropy means that more energy is spread out which increases global warming.

**What does negative enthalpy of formation mean?**

Negative enthalpy of formation means an exothermic reaction. It means that during the formation of compound energy is released which accounts for its stability.

Ca_{(s)}+ 1/2 O_{2(g) }→ CaO_{(s)}

∆H_{f }= -634.9 KJoule/mol

**What is meant by the entropy-driven reaction?**

Entropy-driven reactions mean that reaction takes place spontaneously. It necessarily means that the change in entropy is greater than zero.

∆S > 0

**What is the effect of pressure and temperature on enthalpy?**

When the temperature increases the kinetic energy of particles increases which increases its internal energy so enthalpy increases too.

Enthalpy occurs at constant pressure only.

**Why does a diamond have less entropy than graphite?**

Diamond is a crystalline solid which has a more ordered structure. This ordered structure is not present in graphite due to the free electrons. Diamond has less entropy than graphite due to this ordered structure.

**Does entropy depend upon pressure?**

Entropy is inversely proportional to pressure. According to Boyle’s law when pressure increases, the volume decreases meaning that the particles come close to each other and they become less spread out which decreases entropy.