Enthalpy is a thermodynamic property of a system. It is the sum of the internal energy added to the product of the pressure and volume of the system. It reflects the capacity to do non-mechanical work and the capacity to release heat.
Enthalpy is denoted as H; specific enthalpy denoted as h. Common units used to express enthalpy are the joule, calorie, or BTU (British Thermal Unit). Enthalpy in a throttling process is constant.
Enthalpy– is the internal energy added to the product of pressure and volume:
H– enthalpy
U– internal energy
PV– pressure (volume)
H= U + PV
Enthalpy Formulas
H = E + PV
where H is enthalpy, E is internal energy of the system, P is pressure, and V is volume
d H = T d S + P d V
Enthalpy Derivation
When the system changes at constant pressure, the change in enthalpy, ∆H, is ∆H= ∆(U + PV)
It can be written as: ∆H= ∆U + P∆V
There is no ∆ in P because pressure is constant.
Enthalpy Change of Reaction: Combustion
Combustion of a compound is the enthalpy change which occurs when one mole of the compound is burned completely in oxygen under standard conditions, and with everything in its standard state.
Example: Calculate the enthalpy change of combustion for the reaction where 0.65g of propan-1-ol as completely combusted and used to heat up 150g of water from 20.1 to 45.5
Step 1: Calculate the energy change for the amount of reactants in the test tube.
ΔT = 45.5 – 20.1 = 25.4
Q = m x cp x ΔT
Q = 150 x 4.18 x 25.4
You use the mass of the water in the calorimeter here not the mass of the mass of the alcoholJ
Q = 15925.8J
Step 2: Calculate the number of moles of the alcohol combusted
Moles of propan-1-ol = mass/Mr
Moles = 0.65/60 (you’ll need to calculate the Mr yourself)
Moles = 0.01083 mol
Step 3: Calculate the ΔH per mole.
ΔH = q/n
ΔH = 15925.8 /0.01083
= 1470073 J mol-1
= 1470000 kJ mol-1
= 14700 kJ mol-1 to 3sf
Remember to the correct sign, this reaction is EXOTHERMIC as the temperature RISES so the sign will be negative
= -14700 kJ mol-1 to 3sf
Enthalpy Change of Reaction: Decomposition
Decomposition is one of the most common types of chemical reactions. In this reaction, a compound is broken down into smaller chemical pieces:
In equations, enthalpy is denoted by the capital letter H, while specific enthalpy is lowercase h. Its units are usually joules, calories, or BTUs.
The change in enthalpy is directly proportional to the number of reactants and products, so you work this type of problem using the change in enthalpy for the reaction or by calculating it from the heats of formation of the reactants and products and then multiplying this value times the actual quantity (in moles) of material that is present.
Enthalpy Problem
Hydrogen peroxide decomposes according to the following thermochemical reaction:
H2O2(l) → H2O(l) + 1/2 O2(g); ΔH = -98.2 kJ
Calculate the change in enthalpy, ΔH, when 1.00 g of hydrogen peroxide decomposes.
Solution
This sort of problem is solved by using a table to look up the change in enthalpy unless it’s given to you (as it is here). The thermochemical equation tells us that ΔH for the decomposition of 1 mole of H2O2 is -98.2 kJ, so this relationship can be used as a conversion factor.
Once you know the change in enthalpy, you need to know the number of moles of the relevant compound to calculate the answer. Using the Periodic Table to add up the masses of hydrogen and oxygen atoms in hydrogen peroxide, you find the molecular mass of H2O2 is 34.0 (2 x 1 for hydrogen + 2 x 16 for oxygen), which means that 1 mol H2O2 = 34.0 g H2O2.
Using these values:
ΔH = 1.00 g H2O2 x 1 mol H2O2 / 34.0 g H2O2 x -98.2 kJ / 1 mol H2O2
ΔH = -2.89 kJ
Answer
The change in enthalpy, ΔH, when 1.00 g of hydrogen peroxide decomposes = -2.89 kJ
It’s a good idea to check your work to make sure the conversion factors all cancel out to leave you with an answer in energy units. The most common error made in the calculation is accidentally switching the numerator and denominator of a conversion factor. The other pitfall is significant figures. In this problem, the change in enthalpy and mass of sample both were given using 3 significant figures, so the answer should be reported using the same number of digits.
References: https://www.thoughtco.com/enthalpy-change-example-problem-609553
https://www.thoughtco.com/definition-of-enthalpy-605091
Evaluating Change In Enthalpy 