dH is a state function which means one only needs to know the initial and final states to calculate a change in enthalpy; it does not matter how the change occurs.

Heating water is an example of process that is path independent. Let's say in lab two students have to heat a sample of water from 23 °C to 60 °C.

The heat transfered to the water is

q = n s dT

Since the process is at constant pressure, and only PV work is being done, q is qp. Thus,

dH = n s dT

One student carefully heats 20 g of water from 23 °C to 60°C.

Determine the dH for this process.

dH = n s dT

dH = (20g)(4.184 J g-1K-1)(60 - 23)K

dH = 3096 J

Another student puts 20 g of water over a microburner and goes outside for (insert bad habit here)...

The sample of water went from 23 °C to 75 °C.

Before the student can continue with the experiment the sample of water must be cooled to 60 °C.

Determine the dH for this process.

To heat the water from 23 to 75 °C the amount of heat that when in is

dH = n s dT

dH = (20g)(4.184 J g-1K-1)(75 - 23)K

dH = 4351 J

But the water had to cool back to 60 °C, and while the water was cooling heat was released.

dH = n s dT

dH = (20g)(4.184 J g-1K-1)(60 - 75)K

dH = -1255 J

So, dH was 4351 J to get to 75 °C but on the way back to 60 °C 1255 J were released.

dH = 4351 + -1255 = 3096 J

The energy that was actually transfered to the water is determined by comparing the initial and final states. Student 2 transfered extra energy into the water, but it was released by the water to the surroundings when it cooled; so, in the end, students 1 and 2 transfered the same amount of energy to the water.

What we have just demonstrated, by example, is Hess's Law. Hess's Law holds for dH of any process.

Typically, chemists use Hess's Law to determine dH for reaction for a variety of reasons; the experiment may be difficult, dangerous, or impossible, or we may be making a survey to determine which reactions release the amount of heat we want.