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Entropy (Topic 13B)
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Enthalpy, , indicates heat absorbed or released in a reaction.
Exothermic reactions (negative ) are more likely feasible since they release energy, often resulting in a negative .
However, endothermic reactions (positive ) may be feasible at higher temperatures if compensates.
Entropy, is a measure of the dispersal of energy in a system. It quantifies the degree of disorder within a system.
Entropy reflects how energy is spread out within a system.
- High entropy means energy is more dispersed
- Low entropy indicates that energy is more concentrated.
Entropy increases as the disorder of a system increases. The more disordered a system is, the greater its entropy.
A system with high entropy has more ways of arranging particles and hence is more disordered. Conversely, a system with low entropy is more ordered.
In a solid, particles are arranged in a structured, fixed pattern, leading to lower entropy compared to liquids and gases where particles have freedom to move around.
Entropy plays a crucial role in understanding the stability of a system.
In thermodynamics, a system’s stability is often related to its entropy:
A process or reaction that leads to an increase in entropy is more entropically favourable. Nature tends to move towards states of higher entropy, as systems tend to evolve towards greater disorder over time.
Entropy in solids
Particle arrangement: In a solid, particles are tightly packed in a fixed, orderly structure, such as a crystalline lattice. The particles have limited movement and vibrate about fixed positions.
Energy distribution: Energy is not widely dispersed because the particles have little freedom to move. As a result, solids have low entropy.
Example: A crystal of sodium chloride at room temperature has relatively low entropy due to its highly ordered crystalline structure.
Entropy in liquids
Particle arrangement: In a liquid, particles are still close together but not in a fixed position. They can move around and slide past each other, giving liquids a fluid nature.
Energy distribution: There is more dispersal of energy compared to solids, leading to higher entropy. The particles have more freedom to move, but not as much as in a gas.
Example: Liquid water ( at room temperature has higher entropy than ice because the water molecules can move more freely.
Entropy in gases
Particle arrangement: In a gas, particles are far apart and move independently in all directions. There is no fixed structure, and the particles are in constant, random motion.
Energy distribution: Energy is highly dispersed because the particles have the greatest freedom of movement. As a result, gases have the highest entropy.
Example: Gaseous oxygen ( has very high entropy compared to liquid oxygen or solid oxygen because in the gaseous state the oxygen molecules are free to move throughout the entire volume of the container.
This graph shows how entropy changes as temperature increases across the solid, liquid and gas phases:
The graph shows that as a substance changes state there is a dramatic increase in entropy shown by the vertical lines (boiling and melting). This is linked to the change in particle arrangement.
The entropy increases gradually with temperature within a state. This is linked to increased vibration and/or motion of the particles and its relationship to the degree of disorder and energy dispersal increases.
Consider , the change in entropy, for the decomposition of copper carbonate :
In this reaction, a solid decomposes to produce a solid and a gas ). The number of gaseous molecules increases from zero to one.
The formation of a gaseous molecule from a solid significantly increases the system’s entropy because the gas molecules are much more disordered and have more freedom to move than solid particles.
Consider , the change in entropy, for the synthesis of ammonia from nitrogen and hydrogen in the Haber process:
In this reaction, four moles of gas – one mole of – and three moles of react to produce two moles of ammonia gas.
The total number of gaseous molecules decreases from four to two, which means the entropy of the system decreases.
Fewer gas molecules result in less disorder and a lower entropy state.
Consider dissolving ammonium nitrate in water.
There is an increase in entropy, as the solid dissolves into ions in solution, creating disorder, which drives the reaction.
This endothermic reaction, absorbs thermal energy, cooling the surroundings.
The increase in entropy makes the reaction feasible despite a positive enthalpy change. It is only spontaneous above a given temperature.
Consider the reaction between ethanoic acid and ammonium carbonate.
This reaction releases gas, significantly increasing disorder
The reaction is also mildly exothermic making it feasible and spontaneous at all temperatures.
Consider the complete combustion of magnesium metal.
The reaction is highly exothermic, . This reaction releases energy as heat and light.
The reaction shows a reduction in entropy, : a gaseous reactant converts to a solid product.
This reaction is only feasible below a certain (very high) temperature.
The reaction is not spontanious at r.t.p. due to a high activation energy.
Consider the mixing of solid barium hydroxide with solid ammonium chloride.
This is a highly endothermic reaction, absorbing enough thermal energy from the surroundings to reduce the environmental temperature to below the freezing point of water.
The magnitude of the entropy increase when solid products are fully converted to gases and liquids is so large that the reaction is feasible despite a highly positive .
The reaction is only spontanious above certain temperatures.
The change in entropy, for a chemical reaction or physical process is calculated using:
where:
- = change in entropy
- = entropy of the products
- = the entropy of the reactants.
A positive change in entropy, indicates that the disorder of the system increases, which increases the likelihood of a spontaneous process.
The total entropy change in a reaction is expressed as:
where refers to the entropy change within the reactants and products, and accounts for the heat exchanged with the environment.
This relationship shows how both the reaction’s internal changes and the effect on surroundings influence the reaction’s spontaneity.
depends on the heat exchanged with the surroundings and is calculated using the formula:
where:
- is the enthalpy change of the reaction
- is the temperature in kelvin.
Exothermic reactions release heat energy to the surroundings.
The increase in temperature of the surroundings correlates to increase . Reaction releasing heat can compensate for a negative ensuring that is always positive.
Endothermic reactions take heat energy from the surroundings.
The decrease in the temperature of the surroundings correlates to a reduction in . must be positive therefore a positive is necessary for feasibility.
The spontaneity of a reaction is influenced by the sign of .
For a reaction to be spontaneous, must be positive. Even if is negative, a sufficiently large positive can result in a positive , making the reaction spontaneous.
This highlights the importance of considering both system and surroundings in determining the feasibility of reactions under given conditions.
A reaction’s feasibility is based on changes in enthalpy , entropy, , and the temperature, of the system.
We calculate feasibility using the Gibbs free energy equation:
When is negative, the reaction is feasible (spontaneous).
Both and influence the outcome; is the heat exchange at constant pressure, and represents the effect of entropy at a given temperature.
Entropy, , measures system disorder; reactions increasing disorder (positive ) are more likely feasible, especially at higher temperatures where becomes more significant.
is the product of entropy and temperature, highlighting entropy’s influence as temperature rises. When the value of is negative, favouring feasibility.
The sign of determines whether a process is feasible (spontaneous):
(negative ): The process is feasible, meaning it can occur spontaneously without external input.
(positive ): The process is not feasible, meaning it will not occur spontaneously.
: The system is at equilibrium, and the process has no net tendency to occur in either direction.
In order to calculate , first determine .
You may be provided with values for (enthalpy change) and (entropy change) or you may need to calculate them based on given data.
Convert the units:
Ensure that the units of are compatible. Often, is given in , in and can be or .
To make them compatible:
- Convert from into by dividing by 1000.
- Convert from into by adding 273.
Apply the Gibbs free energy equation:
Now, substitute the values into the Gibbs free energy equation:
can tell us if a reaction is thermodynamically feasible, but it does not provide any information about the rate of the reaction.
A reaction with a negative might occur so slowly that it is effectively not happening within any practical time frame. This is often due to a high activation energy barrier.
Activation energy, , is the minimum energy required for reactants to form the transition state before converting into products.
Even if , a high activation energy can make the reaction proceed very slowly.
Limitations of – diamond to graphite conversion
The conversion of diamond to graphite is thermodynamically feasible at standard conditions because graphite is the more stable form of carbon: .
Despite being thermodynamically feasible, the process is extremely slow because of the very high activation energy required to break the strong covalent bonds in diamond.
As a result, diamonds do not spontaneously turn into graphite at room temperature.
Limitations of – decomposition of hydrogen peroxide
The decomposition of hydrogen peroxide, , into water and oxygen has a negative at all temperatures and is therefore thermodynamically feasible.
Without a catalyst, this reaction is slow because of the high activation energy. Hydrogen peroxide can be safely stored at room temperature for a number of months. However, adding a catalyst like manganese dioxide significantly lowers the activation energy, making the reaction proceed rapidly.
Limitations of – the rusting of iron
The rusting of iron is thermodynamically feasible, as it has a negative below a threshold temperature; it is exothermic but shows a reduction in entropy.
The reaction rate is slow under normal conditions, which is why rusting is not immediate. However, the presence of water and salt can lower the activation energy and increase the reaction rate, making the rusting process occur faster.
In any chemical reaction, the total entropy change, , is the sum of the entropy changes in the system and the surroundings.
Entropy measures the level of disorder or randomness, so reactions that increase disorder lead to positive entropy changes within the system.
The total entropy change is an important factor in determining whether a reaction is spontaneous, as it reflects the overall change in disorder for both the system and its surroundings.
The total entropy change is always positive.
The relationship between Gibbs free energy, , and the equilibrium constant, , is crucial in understanding reaction feasibility.
The equation connects these Gibbs free energy to the equilibrium constant, where is the gas constant and is the temperature in kelvin.
If a reaction is spontaneous at constant temperature and pressure, it has a negative . The value of must be positive meaning that must be greater than one.
The equation demonstrates how Gibbs free energy is influenced by the equilibrium constant.
When is large, , it indicates that products are favoured at equilibrium, leading to a positive value for and a negative .
Conversely, when is small, , reactants are favoured, resulting in a negative value for and a positive .
For reactions with a large equilibrium constant, , the concentration of products at equilibrium is much greater than that of reactants.
This correlates with a negative , meaning the forward reaction is spontaneous under the given conditions.
The larger the value of , the more favourable the forward reaction, reinforcing the concept that a large corresponds to a significant driving force toward products.
For reactions with a small equilibrium constant the concentration of reactants at equilibrium is much greater than that of products.
This correlates with a positive , meaning the reaction is not spontaneous under the given conditions.
A small value of (below one) means the reaction does not proceed significantly toward products.