Video: Identifying the Term That Is the Measure of the Change in Disorder or Randomness of a System in a Set of Terms

Which of the following is the measure of the change in disorder or randomness of a system? [A] Enthalpy change [B] Entropy change [C] Standard enthalpy of formation [D] Activation energy [E] Specific heat capacity

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Video Transcript

Which of the following is the measure of the change in disorder or randomness of a system? A) Enthalpy change, B) entropy change, C) standard enthalpy of formation, D) activation energy, or E) specific heat capacity.

In this question, we’re being asked to identify a property that tells us about the change in disorder or randomness in a system. So let’s take a look through our answer choices to see which one best fits this description.

Mathematically, enthalpy is equal to the internal energy plus the product of the pressure times volume. A change in enthalpy tells us how much thermal energy was exchanged between the system and the surrounding environment as the result of a process or chemical reaction. If energy was transferred to the system from the surroundings, that indicates a positive change in enthalpy. And if energy was transferred to the surroundings from the system, that indicates a negative change in enthalpy. Enthalpy doesn’t tell us about changes in disorder or randomness. So this isn’t the answer that we’re looking for.

Entropy has to do with the number of arrangements of particles in the system. If there are more ways to arrange the particles in a system, that means that that system has a greater entropy.

For example, let’s compare a substance that’s a solid to a substance that’s a gas. When the substance is a solid, there’s more order to how the particles are arranged. After all, when the substance is a solid, the particles have to be stuck together in order to be a solid. If the particles were arranged randomly in the container, the substance wouldn’t be a solid anymore.

The opposite is true for a gas. In a gas, the particles can be arranged in any way in the container. And the substance will still be a gas. This means that a gas has more arrangements of the particles. We could draw a few of these arrangements for our system of seven gas particles. But there would be many, many more. We could come up with more than one way to arrange the particles of our solid. But because there’s more order in the solid and the particles all have to be stuck together, there’s going to be more ways to arrange the gas particles in general.

Because there’s more ways to arrange the gas particles, a gas will usually have more entropy than a solid. Let’s say that we have a process where a substance goes from a solid to a gas, such as the sublimation of CO₂. We could calculate the change in entropy for this process. Because gases have more entropy than solids do, we would expect this process to have a positive change in entropy.

Entropy isn’t technically a measure of the change in disorder or randomness. It’s closer to a measurement of probability. But changes in disorder or randomness are certainly reflected by changes in entropy, as there’s more ways to be disordered or random.

When the system was a more ordered solid, there was fewer ways to arrange the particles. So that system had less entropy. When the system was the more random and disordered gas, there were more ways to arrange the particles. So that system had more entropy. So it seems answer choice b, an entropy change, is the answer that we’re looking for. But let’s look through our other answer choices so we understand what they are.

The standard enthalpy of formation is the energy that’s needed to form a substance from its constituent elements. For example, we could form carbon dioxide from its constituent elements, carbon and oxygen. The standard enthalpy of formation for carbon dioxide is negative 393.5 kilojoules per mole.

The activation energy is the energy that’s needed to start a reaction. For example, let’s imagine that we have a general reaction of the form A reacts to form B. The energy of our reactants is higher than the energy of our products. So we expect this to be a spontaneous reaction. But there’s still some amount of energy that’s needed to start the reaction, to get over this hump in the diagram. And that amount of energy is the activation energy.

The specific heat capacity is the energy that’s needed to increase the temperature of a substance per one gram of substance per one degree Celsius. Different substances have different specific heat capacities. For example, water has a very high specific heat capacity, which means it takes a lot of energy to increase the temperature of water. This is why on a hot day your pool can be a relatively stable and comfortable temperature. But the surrounding concrete will be hot enough to burn your feet.

In this question, we needed to identify which was the measure of the change in disorder or randomness of a system. This is the change in entropy because entropy tells us the number of ways that we can arrange the particles in our system. And there are more ways to arrange particles in a disordered or random manner than there are in ordered one.

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