Name: entropy and spontaneous change
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 49 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Chemistry

CH.7

CH.7.d

Second Law of Thermodynamics

According to the first law of thermodynamics, the energy change in a system is equal and opposite to the energy change of the surroundings. 
When an ice cube, the system, is added to a cup of hot tea, the surroundings, the ice melts while the tea becomes cooler. The heat gained by the ice cube is equal to the heat lost from the tea. Energy is conserved no matter the direction of heat transfer.
However, adding an ice cube would never make the tea hotter because the amount of heat transferred does not determine which way the heat flows.
The associated change in entropy must be considered to explain the direction of heat transfer and other spontaneous reactions.
The second law of thermodynamics states that the entropy of the universe, which is the total entropy of both the system and surroundings, increases for all spontaneous processes. This means that the &#916;S of the universe, the difference between the entropy of the universe&#8217;s final and initial states, must be greater than zero.
As entropy is a measure of energy dispersal, a process where the energy of the universe is more dispersed in the final state than in the initial will be spontaneous.
When an ice cube melts, the water molecules change from an ordered solid to a more disordered liquid state with a positive change in the entropy of the system; when water freezes into ice, the &#916;S of the system is negative.
However, for these processes to be spontaneous, the entropy of the universe must increase, so the difference between whether these processes are spontaneous must be in the surroundings.
When water freezes, it releases heat to the surroundings, increasing the energy dispersal of the surroundings. The &#916;S of the surroundings must be positive and greater in magnitude than the &#916;S of the system for the &#916;S of the universe to be positive.
Pure water will only freeze spontaneously at temperatures below 0 &#176;C. This is because the heat transferred to the surroundings at low temperatures will result in a greater change in entropy than the same heat transferred at higher temperatures.
The magnitude of &#916;S of the surroundings is directly proportional to the heat transferred by the system and inversely proportional to the temperature T.
Thus, for any process occurring at a constant temperature and pressure, the &#916;S of the surroundings is equal to the heat transferred to the surroundings, divided by the temperature in kelvin.

second law of thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (&#916;S &#62; 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the system and surroundings comprise everything, that is, the universe, and so the following is true:
<img alt="Chemical equilibrium equations; &#931;FX=0, MA=0; mathematical diagram; reaction analysis." src="/files/ftp_upload/11424/11424_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
To illustrate this relation, consider again the process of heat flow between two objects, one identified as the system and the other as the surroundings. There are three possibilities for such a process:
<ol>
	<li>The objects are at different temperatures, and heat flows from the hotter to the cooler object. This is always observed to occur spontaneously. Designating the hotter object as the system and invoking the definition of entropy yields the following:</li>
</ol>
<img alt="Static equilibrium, &#931;Fx=0 diagram, illustrating balanced forces and torque in a mechanical system setup." src="/files/ftp_upload/11424/11424_Equation_2.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq2" />
The magnitudes of &#8722;qsys and qsys are equal, their opposite arithmetic signs denoting loss of heat by the system and gain of heat by the surroundings. Since Tsys &#62; Tsurr in this scenario, the entropy decrease of the system will be less than the entropy increase of the surroundings, and so the entropy of the universe will increase:
<img alt="Chemical structure diagram of serotonin molecule; includes nitrogen, oxygen, and hydrogen atoms." src="/files/ftp_upload/11424/11424_Equation_3.png" style="text-align: center; height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
<ol>
	<li value="2">The objects are at different temperatures, and heat flows from the cooler to the hotter object. This is never observed to occur spontaneously. Again designating the hotter object as the system and invoking the definition of entropy yields the following:</li>
</ol>
<img alt="Three-dimensional hydrogen orbital diagrams showing electron probability density distributions." src="/files/ftp_upload/11424/11424_Equation_4.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
arithmetic signs of qsys denote the gain of heat by the system and the loss of heat by the surroundings. The magnitude of the entropy change for the surroundings will again be greater than that for the system, but in this case, the signs of the heat changes (that is, the direction of the heat flow) will yield a negative value for &#916;Suniv. This process involves a decrease in the entropy of the universe.
<ol>
	<li value="3">The objects are at essentially the same temperature, Tsys &#8776; Tsurr, and so the magnitudes of the entropy changes are essentially the same for both the system and the surroundings. In this case, the entropy change of the universe is zero, and the system is at equilibrium.</li>
</ol>
<img alt="Mohr-Coulomb stress circle diagram; equations; geotechnical analysis; static equilibrium evaluation." src="/files/ftp_upload/11424/11424_Equation_5.png" style="text-align: center; height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq5" />
These results lead to a profound statement regarding the relation between entropy and spontaneity known as the second law of thermodynamics: all spontaneous changes cause an increase in the entropy of the universe. A summary of these three relations is provided in the table below.
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td colspan="2" style="color: black; border: 1px solid black; text-align: center;">The Second Law of Thermodynamics</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">&#916;Suniv &#62; 0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">spontaneous</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">&#916;Suniv &#60; 0</td>
			<td style="color: black; border: 1px solid black; text-align: center;"> nonspontaneous (spontaneous in opposite direction) </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">&#916;Suniv = 0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">at equilibrium</td>
		</tr>
	</tbody>
</table>
For many realistic applications, the surroundings are vast in comparison to the system. In such cases, the heat gained or lost by the surroundings as a result of some process represents a very small, nearly infinitesimal, fraction of its total thermal energy. For example, combustion of a fuel in air involves transfer of heat from a system (the fuel and oxygen molecules undergoing reaction) to surroundings that are infinitely more massive (the earth&#8217;s atmosphere). As a result, qsurr is a good approximation of qsys, and the second law may be stated as the following:
<img alt="Static equilibrium diagram; &#931;Fx=0, &#931;Fy=0, &#931;M=0; showing forces and torques in physics study." src="/files/ftp_upload/11424/11424_Equation_6.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq6" />
This equation is useful to predict the spontaneity of a process.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/16-3-the-second-and-third-laws-of-thermodynamics">Openstax, Chemistry 2e, Chapter 16.2: The Second and Third Law of Thermodynamics</a>.

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes ...

Education

JoVE Core

Thermodynamics

KEY TERMS AND CONCEPTS

entropy and spontaneous change

Entropy and spontaneous change are linked through the entropy of the universe. Entropy is a thermodynamic property that helps predict whether a process will happen on its own. Processes with an increase in system entropy, or ΔS &gt; 0, are often spontaneous, but there are many exceptions.

To make a better prediction, entropy changes must include both the system and the surroundings. In thermodynamics, the system plus the surroundings make up the universe. When heat moves between two objects, the direction of heat flow and the temperatures of the objects determine the sign of the entropy change.

If the two objects are at different temperatures and heat flows from the hotter object to the cooler one, the process is spontaneous. If the hotter object is the system, it loses heat and the surroundings gain the same amount. Because Tsys is greater than Tsurr, the entropy decrease of the system is smaller than the entropy increase of the surroundings, so ΔSuniv increases.

If heat flows from the cooler object to the hotter one, the process is not spontaneous. Using the same setup, the system gains heat and the surroundings lose heat. In this case, the entropy change of the universe is negative, so the process involves a decrease in the entropy of the universe.

When the two objects are at essentially the same temperature, the entropy changes are nearly equal in size. Then ΔSuniv is zero, and the system is at equilibrium. These three cases lead to the second law of thermodynamics: spontaneous changes increase the entropy of the universe, while nonspontaneous changes decrease it.

For many real situations, the surroundings are much larger than the system. Then the heat gained or lost by the surroundings is only a tiny part of its total thermal energy. Combustion of a fuel in air is one example, because a reacting fuel-oxygen system transfers heat to the much larger atmosphere. In this case, qsurr is a good approximation of qsys, and the second law can be used to predict whether a process is spontaneous.

Entropy and Spontaneous Change

spontaneity

Spontaneous Change in Matter and Energy

Spontaneous change in matter and energy happens naturally under certain conditions. A nonspontaneous process will not occur unless it is driven by a continual input of energy from an outside source. Under a given set of conditions, processes also tend to move in one direction rather than the other. Water flows downhill on its own, so that is a spontaneous process. Water flowing uphill needs a pump, so that is nonspontaneous. Iron in the earth’s atmosphere will corrode, but rust does not turn...

entropy

Entropy in Matter and Energy Changes

Entropy describes how energy and matter are spread through a system. It is a thermodynamic state function, so it can change when a physical or chemical change occurs. When entropy increases, disorder increases. When entropy decreases, disorder decreases. A change in entropy is written as ΔS = Sf - Si. The concept is also linked to microstates, which are the specific arrangements of the locations and energies of all atoms or molecules in a system. Boltzmann’s relation, S = k ln W, connects...

Entropy and spontaneous change are linked through the entropy of the universe. Entropy is a thermodynamic property that helps predict whether a process will happen on its own. Processes with an increase in system entropy, or ΔS &gt; 0, are often spontaneous, but there are many exceptions. To make a better prediction, entropy changes must include both the system and the surroundings. In thermodynamics, the system plus the surroundings make up the universe. When heat moves between two objects,...

third law of thermodynamics

Entropy at Absolute Zero

The third law of thermodynamics links entropy to absolute zero. A pure, perfectly crystalline solid with no kinetic energy at 0 K has only one microstate. Because there is only one possible arrangement for its identical atoms or molecules, its entropy is zero. This limiting case sets the entropy scale for real substances. Careful calorimetric measurements can be used to find how entropy changes with temperature and to calculate absolute entropy values under specific conditions. Standard...

standard entropy change for a reaction

Calculating Entropy Change from Tables

Entropy is a state function, so the standard entropy change of a chemical reaction can be found from standard molar entropy values in a table. The reaction entropy, written as ΔS°rxn, is calculated by subtracting the total entropy of the reactants from the total entropy of the products. The balanced equation matters because the stoichiometric coefficients set how many moles of each substance are included. A table of standard entropies gives values in J/mol·K for substances such as graphite,...

gibbs free energy

Predicting Spontaneity with Gibbs Energy

Gibbs free energy helps predict whether a process is spontaneous under constant temperature and pressure. It is a thermodynamic property based on the system’s enthalpy and entropy. Chemists also call it free energy, and it is a state function. The idea was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. Unlike the second law approach, it uses system properties only. That makes it a useful shortcut when tracking both the system and the surroundings is...

effects of temperature on free energy

Temperature and Spontaneous Processes

Temperature can change whether a process is spontaneous. In chemistry, spontaneity means a process can happen on its own under a given set of conditions. Phase changes are one clear example, and some chemical reactions also change spontaneity as temperature changes. The relationship uses free energy change, enthalpy change, and entropy change. Entropy is a measure of disorder in the system. The key equation shows that the sign of free energy depends on the signs of enthalpy and entropy, and in...

calculating standard free energy changes

Using Formation Data to Find Free Energy

Standard free energy change is the free energy change for a reaction under standard conditions of 1 bar pressure and 298 K. Free energy is a state function, so its value depends only on the starting and ending states of the system. That makes it possible to calculate standard free energy changes from tabulated thermodynamic data. One common method uses standard enthalpy and entropy values to find standard free energy change, ΔG°. Another method uses standard free energies of formation, ΔGf°,...

free energy changes for nonstandard states

free-energy-changes-for-nonstandard-states

Predicting Spontaneity with Reaction Quotient Q

Free energy under nonstandard conditions depends on the reaction quotient, Q, and the standard free energy change. Nonstandard conditions mean that concentrations are not 1 M or pressures are not 1 bar. The relation links the gas constant R, the absolute temperature T in kelvin, and Q. It can be used to predict whether a process is spontaneous under a given set of conditions. The reaction quotient, Q, helps show the status of a reversible reaction. It is based directly on the balanced chemical...

free energy and equilibrium

Predicting Reaction Direction with Free Energy

Free energy and equilibrium help predict which way a chemical reaction will move. A negative value of ΔG means the forward reaction is favored. A positive value means the reverse reaction is favored. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the system is at equilibrium. The reaction quotient, Q, helps show whether a reaction must move forward or backward to reach equilibrium. Q is the numerical value of the mass action expression for the system. If Q is less...

key terms and concepts

Learn how entropy, heat flow, and the surroundings determine spontaneity. Explore when ΔSuniv is positive, negative, or zero in thermodynamics.

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High School

CHEM.13

CHEM.13.A

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CH.7.a

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phase-transitions-vaporization-and-condensation

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CH.7.b

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CH.7.c

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Third Law of Thermodynamics

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CH.7.e

Catalysis

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The student will investigate and understand that thermodynamics explains the relationship between matter and energy. Key ideas include rates of reactions depend on catalysts and activation energy;

CH.7.f

The student will investigate and understand that thermodynamics explains the relationship between matter and energy. Key ideas include enthalpy and entropy determine the extent of a reaction.

CH.7.g

Entropy and Spontaneous Change

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