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Here, we begin to think about a specific definition of heat energy known as "enthalpy". It's an important thermodynamic quantity used within chemistry
Previously, we’ve looked at heat and work. Heat is the movement of energy microscopically. A system will lose its energy, by transferring kinetic and potential energy to its surroundings by microscopic collisions. On the flip side of that coin, there’s work, which is energy that’s transferred because something expands, or compresses. Expansion must work against a force, which requires energy. This is going to combine to give us a definition of energy used in chemistry known as enthalpy. So, to recap so far we have a system. It has an internal energy, U, which is going to change . All of that change in energy is accounted for by work plus heat, but we don’t quite know how it’s going to be distributed.
There are two extremes here. we can do things at constant volume. Here, only the pressure will change. If we lock everything off in a solid, sealed container, which is completely inflexible, then pressure changes, but volume doesn’t. And if there’s no change in volume, no work is done. The internal energy change is accounted for only by heat exchange. So that’s the easier extreme to think about. We can also do a chemical reaction at constant pressure. Here, volume can change freely, so there’s no limit on the work that can be done. Alternatively, there could be a path between the two extremes where both pressure and volume alter freely.
In any of these cases, the internal energy change is only dependent on the initial and final states of the system. It doesn’t matter what the pathway is. It doesn’t matter if volume or pressure, or neither, is fixed. And in any of those cases, the first law of thermodynamics still holds true. The internal energy change, Delta U, is accounted for entirely by the sum of heat and work. So, in this lecture we’re going to look at constant pressure; here, a system is completely open to the environment. Imagine a chemical reaction bubbling and giving off gas – that gas has to perform work against the pressure of the atmosphere. So, let’s look at what this means just with the mathematics for now.
We’ve got the first law of thermodynamics. The internal energy change is accounted for by heat and by work. We also know that work is pressure times volume. A positive change in volume, an expansion, means work is done by the system, so energy is removed, so it’s equal to negative of the pressure times volume change. We’re then going to combine those equations adding in a subscript p to say that this is, very specifically, heat at a constant pressure. This is usually what you’ll see in thermodynamics a lot. There a subscripts under certain values, but all these do is tell you something useful about conditions.
We can also rearrange this, to find that q, the heat transferred, is equal to the internal energy change, plus that work done. This is a new heat quantity that becomes very useful in chemistry. It’s labelled H. And it’s referred to as enthalpy. Just like other forms of energy, enthalpy is a thermodynamic state function. Its value depends only on the starting state and the final state, and is independent of the pathway. And this function is equal to the heat transferred, by a chemical reaction, at a particular temperature at a fixed pressure. And, most of the time, in chemistry, we just measure enthalpy. It’s really convenient to measure directly. We don’t even care that much about the components of it.
But where do we use it? let’s look at exothermic reactions. A reaction that is exothermic, as you might know already, is one where heat flows out of the system. It’s generating heat. Now, this is where your instinct and intuition may be a little wrong. If something feels warm, you might think its energy is going up. But that heat you can feel, or the heat that causes a thermometer to go up, is heat coming from or leaving the system. Its internal energy must be going down. So, the heat, q, or enthalpy change, delta H is negative. Remember, these numbers describe the state of the system. A negative means energy is flowing from it, because it represents the internal energy going down.
With that in mind we can flip it to see endothermic reactions. In this case, heat flows into the system, and the energy of the system increases. That means the enthalpy, or heat effect, is positive. The way we often try to visualise these changes is with an energy level diagram. We have a scale up the Y axis that represents energy. Here, we’re specifically looking at the enthalpy of the system. Enthalpy, remember, being the sum of the internal energy, and its pressure multiplied by volume. So it’s the internal energy, plus the energy required for the system to make room for itself. Now, the weird bit is that the absolute values here cannot be known.
So if we have a set of reactants, it doesn’t matter what the absolute location of it is. The various things that go into the internal energy are either too complicated to know, or not relevant. So it’s not a value we can know. But… we can consider the relative location of the products. If heat is released from the system we know that the products are lower in enthalpy. This is because enthalpy is a state function. It’s a value that’s associated with the state of a system at a particular time. And any change to it, is accounted for by heat. In this case, heat lost.
But if the reaction consumes heat, meaning it feels colder as it draws in energy from the surroundings, the products will be higher in enthalpy and Delta H is positive. Just remember that this is a function, or a measure of heat, and it’s the case at constant pressure. This brings us to the end of enthalpy. It’s basically just a fancy word for how much a chemical reaction can increase the reading on a thermometer, but it’s also a precise term for how that works at constant pressure.

Internal energy changes

An internal energy change is a state function. It is a function only of the initial state of the system, and the final state.

[Delta U=U_2-U_1]

The first law of thermodynamics says that this change must entirely be accounted for by heat exchanged with the system, and work done by or to the system.

[Delta U=q+w]

At constant volume, there can be no work done because the system cannot expand. Therefore internal energy change is entirely accounted for by heat.

At the other extreme, constant pressure, work can be done, but only the volume change needs to be accounted for.

An intermediate case, where pressure and volume may change is more difficult to account for in a single step.

Defining enthalpy

Knowing the first law of thermodynamics and the definition work:

[Delta U=q+w w=-pDelta V]

We can combine these to define internal energy change as a function of heat and volume change at constant pressure:

[Delta U=q-pDelta V]

And then rearrange this for what it means for heat to transfer in and out of the system at constant pressure.

[q=Delta U+pDelta V]

We call this heat exchange, under constant pressure conditions, enthalpy. It is still just heat exchanged – i.e., collisions at the microscopic level – but it is a specific definition that has a lot of uses within chemistry.

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Introduction to Thermodynamics

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