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# Absolute Entropy and Entropy Change

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Entropy is seen all around us in the sciences: physics, chemistry, astronomy, and more. In our general review of entropy, we covered how the measure of disorder within a system and how we can use entropy to observe and figure out where energy goes relative to a system.

But entropy isn't a static property. Just like the systems that it describes, entropy changes. Not only that, different properties that entropy contributes to can reveal valuable characteristics within a system. In this lesson, we're going to cover these higher-level qualities in which entropy plays a role.

• In this lesson, we'll cover how to calculate entropy change within a system.
• Then, we'll learn what absolute entropy is and how we calculate it as well.
• Afterward, we'll step through a table of standard entropies for common substances and elaborate on what trends we can see and why they exist.
• Lastly, we'll tie everything together with a few examples and cover how each of these concepts is thermodynamically significant and how they actually describe a system.

## Entropy Change Formula

Total Entropy, or just entropy, is a measure of the disorder of a system and its surroundings. A system and its surroundings are referred to as the "universe" in thermodynamics.

Any process that occurs without the input of energy from the surroundings, a spontaneous process, is characterized by the following:

• For all processes, there is a natural tendency for components in a system to break down and break down, leading to an increase in disorder.

• A spontaneous process is the result of an overall increase in disorder.

• When order occurs in one place, this order is then used to create order in another place.

• Disorder always increases in any universe (a system and its surroundings).

We can formulate the above observations in the following statement,

The second law of thermodynamics, a law stating that the total entropy of a system and its surroundings always increases for a spontaneous process." 1

The second law can be restated in a form that refers only to the system. As a spontaneous change in the system takes place, the creation of entropy takes place. As heat (q) flows into the system, entropy also flows into the system. The relation of heat (q) and the absolute temperature (T)can be shown to be related to the entropy change through the following inequality

$$\Delta{S}>\frac{q}{T}:\,\,\,\,\,\,(spontaneous\,process)$$

This application of the second law of thermodynamics to the system can be restated in words:

...for a spontaneous process at a given temperature, the change in entropy of the system is greater than the heat divided by the absolute temperature." 1

The above formula for the system entropy can be made exact when applied to a system at equilibrium:

$$\Delta{S}=\frac{q}{T}:\,\,\,\,\,\,(equilibrium\,process)$$

For example, in a system that absorbs heat in the process of melting, ΔHfusion, such as when ice melts to liquid water, the entropy can be shown to be equal to:

$$\Delta{S}=\frac{\Delta{H_{fusion}}}{T}$$

## Standard Entropy Change Formula

In our introductory lesson on entropy, we briefly discussed how to calculate the total change in entropy by subtracting a proportionally correct representation of the reactants from the products. If you want to see examples of how this is done, you can see our lesson on Entropy here. As a reminder, the formula looks like this:

$$\Delta{S^\circ}=\Sigma\,n\Delta{{S^\circ}_{products}}-\Sigma\,m\Delta{{S^\circ}_{reactants}}$$

Where Σ is the summation symbol and n and m are the stoichiometric coefficients of the balanced equation for products and reactants, respectively. The standard entropy change of products is ΔS°products, while the standard entropy change of reactants is ΔS°reactants.

The summation symbol, Σ, instructs us to add: for example, $$\Sigma_{i=1}^4a_1=a_1+a_2+a_3+a_4$$, means the first term is, a, index, 1, added to, a, index, 2, added to, a, index, 3, and finally we end with, a, index, 4.

This formula takes advantage of the fact that we're working with standard entropies. Recall that the entropy values that are experimentally determined are standardized at a common temperature and pressure: 298 K and 1 atm, respectively. Because of this, we can use the formula above to deduce the total standard entropy change in the chemical reaction.

In the previous lesson, we went through a few simple examples where we took some given entropies, plugged them into the formula, and discovered what the total standard entropy change was within the system. If you would like to see these examples, refer to that lesson.

However, questions that involve entropy on the AP Chemistry exam will be less about whether or not you can use the formula correctly and more about applying the formula when it comes to concepts you've already learned. To drive this point home, we'll cover a more difficult entropy problem that you might see on the AP exam.

Find the total standard entropy change when liquid pentane undergoes a total combustion reaction to completion. Use the table of common standard entropies provided in the third section of this lesson to help you.

Explanation:

We know that a combustion reaction always involves the products water and carbon dioxide. We can also deduce that pentane has the formula C5H12 from the acyclic saturated hydrocarbon formula CnH(2n+2), Where n is the number of carbon atoms, for example, pentane has five carbon atoms in its formula.

We also know that, lastly, combustion reactions always use oxygen gas as a reactant. Therefore, we have a formula of the following:

$$C_5H_{12\,(l)}+O_{2\,(g)} \rightarrow H_2O_{(g)}+CO_{2\,(g)}$$

After balancing, we have a chemical reaction that looks like this.

$$C_5H_{12\,(l)}+8O_{2\,(g)} \rightarrow 6H_2O_{(g)}+5CO_{2\,(g)}$$

Then, we use our overall standard entropy change formula in the following formula.

$$\Delta{S^\circ}=\Sigma\,n\Delta{{S^\circ}_{products}}-\Sigma\,m\Delta{{S^\circ}_{reactants}}$$

$$\Delta{S^\circ}=[(6\,mol\,H_2O_{(g)}\cdot 188.8\frac{J}{K\cdot mol}+(5\,mol\,CO_{2\,(g)}\cdot 213.8\frac{J}{K\cdot mol})]$$

$$-[(1\,mol\,C_5H_{12\,(l)}\cdot 263.5\frac{J}{K\cdot {mol}})]+(8\cdot O_{2\,(g)}\cdot 205.2\frac{J}{K\cdot mol})]$$

Then,

$$\Delta{S^\circ}=296.7\frac{J}{K}$$

This means that our final answer for the entropy change is 296.7 J/K.

This problem is a good example of an AP Chemistry question. It requires you to have knowledge of the formula of hydrocarbons, different types of reactions (how combustion reactions work), balancing chemical equations, and how to calculate overall standard entropy. Hopefully, this problem helps you to understand that AP Chemistry entropy problems won't always be as simple as plugging values into a formula.

## Absolute Entropy Definition

We've been working with standard entropies that have been set to 298 K and 1 atm to allow for easy comparison. However, this isn't the only way that entropy is measured. You might have heard of the concept of absolute zero, which is the coldest conceivable temperature: 0 K. At this temperature, all entropy within a system disappears. This means that at T = 0 K, S = 0. Chemists exploit the fact that entropy and temperature are related and conceived of the measurement of absolute entropy.

Absolute entropy is the total amount of entropy acquired when a pure substance is warmed from absolute zero to a specific temperature.

Recall that standard entropies are standardized at 298 K. This means that standard entropy is really just the absolute entropy for a substance at 298 K. Actually calculating absolute entropy is a matter of measuring heat capacity continuously as the object in question is heated from absolute zero to the desired temperature.

## Standard Entropy Table

Some of the molecules commonly dealt with in AP Chemistry are listed below. In order to help, here's a table of standard entropies for common substances that you can refer back to. All substances are assumed to be in gaseous form unless otherwise stated.

 Molecule Standard Entropy (J/K) C (graphite) 5.7 CH4 186.3 C2H6 229.6 C5H12 (l) 263.5 C5H12 348.0 C6H12O6 (glucose) 212.0 CO 197.7 CO2 213.8 H2 130.7 H2O(l) 69.9 H2O 188.8 He 126.2 N2 191.6 NH3 192.5 O2 205.2

## Entropy Change Formula Thermodynamics

By this point in your study of AP Chemistry, you should have a cursory understanding of the three laws of thermodynamics. In order to truly understand why entropy works in the way it does, relating everything we've learned to the three laws paints a picture that's easier to comprehend.

Over the past two lessons, we've learned that entropy is a measure of general randomness or disorder within a system. We've also learned some physical and chemical indicators that can be used to predict entropy. In reality, all we're doing with these indicators are measuring the properties of particles throughout different transformations and measuring how "disordered" the system is based on that.

Next, we learned about how there are standard entropies that have been standardized to a common temperature and pressure (298 K and 1 atm, respectively) to allow for easy comparison and to allow for an easier method of calculating entropy change throughout a reaction. We also learned that you can measure entropy without standardization.

Absolute entropy is the total amount of entropy needed to heat an object from absolute zero (where entropy and temperature are equal to zero) to the desired temperature. This also implies that the absolute entropy of an object at 298 K is its standard entropy.

Now that we've briefed you on all of this, where do the three laws come into play?

1. The first law of thermodynamics states that energy can't be created or destroyed. This is the law of energy conservation, which you should be well versed in by now. This doesn't apply nearly as much to the concept of entropy as the other two laws do.

2. The second law of thermodynamics states that the energy and matter of the universe are constantly dispersing and becoming more disordered. Sound familiar? This law is really saying that the entropy of the universe is always increasing. This means that we can derive that nature tends towards disorder through the second law. This concept was discussed at length in the first lesson on Entropy.

3. The third law of thermodynamics states that a system's entropy is zero at a temperature of absolute zero (0 K). This law implies that the opposite is true as well: increasing the temperature of a system increases entropy. From this law, we can derive the definition of absolute entropy.

Hopefully, breaking down the three laws of thermodynamics helps to solidify your understanding of why entropy functions the way it does. The universe may be disordered, but your understanding of entropy shouldn't be!

## Absolute Entropy and Entropy Change - Key takeaways

• Entropy is a measure of the disorder of a system and its surroundings. A system and its surroundings are referred to as the "universe" in thermodynamics.
• Absolute entropy is the total amount of entropy acquired when a pure substance is warmed from absolute zero to a specific temperature.
• The first law of thermodynamics states that energy can't be created or destroyed.
• The second law of thermodynamics states that "...the total entropy of a system and its surroundings always increases for a spontaneous process".1
• The third law of thermodynamics states that a system's entropy is zero at a temperature of absolute zero (0 K).

Absolute entropy is the total amount of entropy acquired when a pure substance is warmed from absolute zero to a specific temperature. However, entropy is  a measure of the disorder of a system and its surroundings. A system and its surroundings are referred to as the "universe" in thermodynamics.

Absolute entropy is the total amount of entropy acquired when a pure substance is warmed from absolute zero to a specific temperature.

For a reaction, the formula for absolute entropy is: $$\Delta{S^\circ}=\Sigma\,n\Delta{{S^\circ}_{products}}-\Sigma\,m\Delta{{S^\circ}_{reactants}}$$

Where:

• $$\Sigma$$ is the summation symbol
• n and m are the stoichiometric coefficients of the balanced equation

The formula for entropy of a reaction is: $$\Delta{S^\circ}=\Sigma\,n\Delta{{S^\circ}_{products}}-\Sigma\,m\Delta{{S^\circ}_{reactants}}$$

The symbol for entropy is S. ΔS is the change in entropy and ΔS°  is the change in standard entropy.

## Absolute Entropy and Entropy Change Quiz - Teste dein Wissen

Question

What is absolute entropy?

Absolute entropy is the total amount of entropy acquired when a pure substance is warmed from absolute zero to a specific temperature.

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Question

What is the second law of thermodynamics?

The second law of thermodynamics, a law stating that the total entropy of a system and its surroundings always increases for a spontaneous process.

Show question

Question

Does heat flow into a system increase the entropy of the system?

Yes

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Question

True or False: For all processes, there is a natural tendency for components in a system to break down and break down, leading to an increase in disorder.

True

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Question

True or False: Increasing the heat of a system decreases the entropy?

False

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Question

True or False: Disorder always increases in any system?

False

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Question

True or False: The entropy always increases in the universe?

True

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Question

True or False: Order in one place leads to the creation of order in other parts of the system

True

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Question

What is the first law of thermodynamics?

The first law of thermodynamics states that energy can't be created or destroyed.

Show question

Question

What is the second law of thermodynamics?

The second law of thermodynamics states that the energy and matter of the universe are constantly dispersing and becoming more disordered.

Show question

Question

What is the third of thermodynamics?

The third law of thermodynamics states that a system's entropy is zero at a temperature of absolute zero (0 K)

Show question

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