Enthalpy (`H`) is an another measure of energy. Enthalpy is defined by the following relation:
`H=U+PV`
Where `U` is the internal energy of the system in `J`, `P` is the pressure in `"atm"`, and `V` is the volume in `L`.
Most of the time, we're interested in the change in enthalpy. This is expressed as the following:
`DeltaH = DeltaU + Delta(PV)`
Which is equivalent to saying
`DeltaH =DeltaU + PDeltaV + VDeltaP`
Since most reactions are performed under atmospheric pressure (`1 "atm"`), `DeltaP=0.` This simplifies the expression to become:
`DeltaH = DeltaU + PDeltaV`
Recall from the first law states that `DeltaU = q+ w = q -PDeltaV`. Plugging this into the `DeltaU` for the previous equation, we can give this following relation:
`DeltaH = q -PDeltaV + PDeltaV= q`
For systems under constant pressure.
We can therefore define enthalpy. The change in enthalpy (`DeltaH`) is defined as (`DeltaU + Delta(PV)`). For the enthalpy of a system under constant pressure, the change in enthalpy (`DeltaH`) is simply equal to `q`, the change in heat. Enthalpy is a convenient way of calculating the energy of a system undergoing a reaction, since most reactions are under constant pressure. Make sure you're able to follow all of the above steps!
Enthalpy is used primarily to calculate the energy of chemical reactions. In the 20th century, an astonishing effort from many scientists collaborating resulted in a library of enthalpy values for almost every known molecule. These are called heats of formation and correspond to the amount of heat released when a specific molecule is formed from its constituent elements.
For example, the `DeltaH_(f)` of `HBr` has been found to be `(-36.29 "kJ")/"mol"`. This means that in the process of forming a mole of `HBr` from its constituent elements `H_2` and `Br_2`, `(36.27 "kJ")/"mol"` is released. This relates back to an earlier concept that bonds forming released energy. It turns out that the energy released during the formation of a molecule is the heat of formation! If this sounds unfamiliar, check out the last section of this post:
Additionally, here is a table of enthalpy values from Wikipedia:
Take a quick look at the table. You may notice that the `DeltaH_f` of some molecules is 0. This brings us to the following rule:
The `DeltaH_f` of an element in its standard state is 0, where the standard state of an element is the state of the element under `1 "atm"` and `298 K`.
This is also known as STP or Standard Temperature and Pressure. `O_(2(g))` is the standard state of oxygen because oxygen is a diatomic gas at `1 "atm"` and `298 K`. In other words, whenever an element is in its standard state (`H_(2(g)),O_(2(g)), Al_((s))`), the `DeltaH_f` of that element is equal to 0. This makes sense, since the element is already in its most stable state and has no energy to release.
In order to calculate the total change in enthalpy of a reaction, we use the following, somewhat intimidating, equation:
`DeltaH= n∑DeltaH_(f,"products")^°-n∑DeltaH_(f,"reactants")^°`
Where n is the number of moles
The equation looks complicated due to the summations, but it's really not. In "plain English," it says that the total change in enthalpy is equal to the total heats of formations of the products minus the total heats of formations of the reactants. This'll become clear after this example:
#1. Calculate the change in enthalpy for the following reaction:
`2H_2O_((l)) + O_(2(g)) rArr 2H_2O_(2(l))`
First step is to find the heats of formation for each molecule in the reaction. From the wikipedia link earlier, we find that:
`DeltaH_(f,H_2O_((l)))=(286 "kJ")/"mol"`
`DeltaH_(f,O_(2(g)))=0`
`DeltaH_(f,H_2O_(2(l)))=(-188 "kJ")/"mol"`
From the equation, we know that `DeltaH = 2DeltaH_(f,2H_2O_(2(l))) - (2DeltaH_(f, H_2O_((l)))+1DeltaH_(f,O_(2(g))))`
`DeltaH = 2((-188 "kJ")/"mol")-(2((286 "kJ")/"mol")-0) = -948 kJ`
Answer: `-948 kJ`
Notice that the enthalpy released is negative. Since `DeltaH=q`, this means that the reaction is exothermic.
1. Enthalpy is another measure of the energy of a system.
2. For constant pressure conditions, `DeltaH=q`
3. Enthalpy is used often to calculate changes in energy because most chemical reactions take place under constant pressure.
4. The standard state of an element is the state of matter that the element is in while under standard conditions (`1 "atm"` and `298 K`)
5. The standard heat of formation corresponds to the energy required to form the molecule from its constituents in their standard states.
6. The `DeltaH_f` of an element in its standard state is 0.