# Video: Identifying the Reaction for Which the Entropy of the System Will Decrease in a Set of Balanced Chemical Reaction Equations

Which of the following is not a state function? [A] The amount of thermal energy transferred [B] Enthalpy [C] Viscosity [D] Density [E] Free energy

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### Video Transcript

Which of the following is not a state function? A) The amount of thermal energy transferred, B) Enthalpy, C) Viscosity, D) Density, or E) Free energy.

A state function is a property that depends only on the current state of the system, not the path that’s taken to get to that state. For example, let’s imagine that we’re climbing a mountain. There’s going to be a number of paths that we can take up the mountain that go from the base of the mountain to the summit. Here I’ve drawn two different paths. In path A, we go directly up the mountain. And in path B, we take a more zigzagy route.

In both cases, the change in altitude is the same. We’re going from the base of the mountain to the summit of the mountain. This makes the change in altitude a state function, since the change in altitude was the same no matter which path we took up the mountain. However, we can imagine that the time it takes to go up the mountain with the more direct path A would be shorter than the time it takes to go up the mountain with path B. Because the time it takes to go up the mountain depends on the path you take, the change in time is not a state function.

There are many properties that you’re familiar with that are state functions. For example, let’s imagine that we take some ice and we melt it so that we get some water at some temperature, pressure, and volume. We could also imagine that we cool down some water vapor or steam to get the same amount of water at the same temperature, pressure, and volume. Since the temperature, volume, and pressure of the water is the same but we can take different paths to get to that state, temperature, volume, and pressure are all state functions.

Now, let’s take a look at a chemical reaction. This reaction represents the combustion of octane, which occurs inside a car that runs on gasoline. When we burn octane in a vehicle, some of the energy that’s released as a result of the reaction is used to power the vehicle. When energy is being used to power something, we call that work. Whatever energy from this reaction that is left over and isn’t being used to power the vehicle will be transferred to the environment in the form of heat or thermal energy.

Instead of using the octane to power a vehicle, we could also imagine simply burning the octane in some container. In this case, none of the energy that’s being released as a result of this reaction is being used to power anything. All of the energy is just being transferred to the environment in the form of thermal energy or heat. In both cases, regardless of how we choose to burn the octane, the total change in energy as a result of this reaction is the same. This makes the change in total energy or the internal energy of our system a state function. As it didn’t matter how we chose to burn the octane, the total change in energy is the same.

However, the amount of thermal energy that’s transferred to the environment or the amount of work are not state functions, as the amount that you get is dependent on how you choose to perform the reaction. When we chose to burn the octane in the car, we were able to get work, but we weren’t able to get work when we just burned the octane in a container. So, we’ve already determined the correct answer to this problem. The amount of thermal energy that is transferred is not a state function because it depends on how you choose to do a reaction. But let’s take a look at our other answer choices, so we understand why they are state functions.

Let’s take a look at viscosity and density first. To do this, I’m going to refer to our example from earlier where we can make water by either melting ice or cooling steam. Regardless of how you got the water, whether you melted the ice or cooled the steam, the viscosity and density are simply properties of the water. This makes both viscosity and density state functions. Enthalpy is equal to the internal energy of the system plus the product of the pressure times the volume. We’ve already discussed how the internal energy of a system is a state function, and also how pressure and volume are state functions. Since enthalpy is a function that is made of other state functions, it must be a state function too.

The case for the free energy is similar. We’ve already discussed how both enthalpy and temperature are state functions. The entropy is a state function as well, as it is related to the number of configurations, which would not change depending on how you choose to get to a state. Since the free energy is a function made of other state functions, it is also a state function. Another way we could see the enthalpy and free energy are state functions is by looking at a process such as a chemical reaction that has different ways of getting from the reactants to the products. But as we’ve already determined, from our list, the only thing that is not a state function is the amount of thermal energy that is transferred.