Which of the following is the change in enthalpy due to the formation of a substance from its constituent elements in their standard states, per mole of a substance? A) enthalpy change, B) entropy change, C) standard enthalpy of formation, D) activation energy, or E) specific heat capacity.
In this question, we’re interested in a change in enthalpy. So there’s several answer choices that we can eliminate right off the bat, including an entropy change, activation energy, and the specific heat capacity. In particular, we’re interested in the change in enthalpy due to the formation of a substance from its constituent elements in their standard states.
For example, we could form carbon dioxide from its constituent elements carbon and oxygen. The standard state of carbon is graphite, and the standard state of oxygen is oxygen gas. So the formation of carbon dioxide from its constituent elements in their standard states would be carbon as graphite plus oxygen gas reacting to form carbon dioxide gas. The enthalpy change associated with forming carbon dioxide from its standard states is negative 393.5 kilojoules per mole. This change in enthalpy is the standard enthalpy of formation for carbon dioxide. These standard enthalpies of formation are tabulated values that we can look up. They’re useful because we can use Hess’s law to calculate the enthalpy change of a reaction that we’re interested in.
So say, for example, we wanted to know the change in enthalpy for this reaction, which is the burning of octane in the presence of oxygen which produces carbon dioxide and water. We could look up the standard enthalpies of formation for each of the chemical species present in this reaction and use those to calculate the enthalpy change for this reaction. This enthalpy change for the reaction that we calculate using the standard enthalpies of formation would be an example of an enthalpy change that answer choice A is referring to. This change in enthalpy would be reflected by the amount of energy that’s transferred from the system to the surroundings as a result of this reaction. So the change in enthalpy due to the formation of a substance from its constituent elements in their standard state is the standard enthalpy of formation.
But let’s look through the other answer choices B, D, and E, just so we know what they are. Entropy has to do with the number of arrangements that the particles in your system can have. If a system has more arrangements of particles, that means that it has more 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, the particles have to be arranged in a specific way in order for the substance to be a solid. But when the substance is a gas, the particles can be arranged in almost any way in the container and the substance will still be a gas. Just for our system of six gas particles, we could think of many ways to arrange these particles and the substance would still look like a gas.
Though we could think of more than one way to arrange those particles of the solid, it would be far fewer than the number of arrangements that we could come up with for the gas. Since we can arrange the particles of a gas in more ways than we could arrange the particles of a solid, a gas generally has more entropy than a solid does. If we had a process where a substance goes from a solid to a gas such us in the sublimation of CO₂, that process would have a positive entropy change because a gas has more entropy than a solid does. The activation energy is the energy that’s needed to start a reaction.
Let’s say that we have some general reaction where A reacts to form B. According to this diagram, A is higher in energy than B is. So we would expect this reaction to be favorable. But there’s still some amount of energy that we need to get over this hill to go from A to B. And that amount of energy is the activation energy. The specific heat capacity is the energy that’s needed to raise the temperature of a substance per one gram of a substance per one degree Celsius. If a substance has a high specific heat capacity, that means it’s going to take a lot of energy to raise the temperature of that substance.
For example, water has a high specific heat capacity compared to many other substances. Which is why when it’s hot outside, your pool can be a relatively comfortable and stable temperature, but the surrounding concrete will be hot enough to burn your feet. But as we’ve discussed, this question was asking us to identify what the change in enthalpy due to the formation of a substance from its constituent elements in their standard states is. And that is the standard enthalpy of formation.