brodidit for students
Home / Notes / Class 11 / Chemistry / Thermochemistry
Thermochemistry: Class 11 Chemistry
System and surroundings, state functions, first law of thermodynamics, internal energy and enthalpy, exothermic and endothermic changes, standard enthalpies, calorimetry, Hess's law and bond enthalpies with calculations.
Key points
Thermochemistry is the study of heat changes during chemical reactions and physical changes. A system is the part of the universe being studied, and everything else is the surroundings. An open system exchanges matter and energy, a closed system exchanges only energy, and an isolated system exchanges neither.
A state function depends only on the initial and final states of the system and not on the path taken. Pressure, volume, temperature, internal energy and enthalpy are state functions. Heat (q) and work (w) are not state functions. Energy is measured in joules (J) or kilojoules (kJ), and 1 cal = 4.184 J.
The first law of thermodynamics states that energy can be neither created nor destroyed, only changed from one form to another. The mathematical form is ΔU = q + w. Here ΔU is the change in internal energy, q is heat absorbed by the system and w is work done on the system. Heat absorbed and work done on the system are positive. Heat released and work done by the system are negative.
For a gas, the work done by expansion against a constant pressure is w = −PΔV. At constant volume no pressure volume work is done, so ΔU = qv. Internal energy U is the total of kinetic and potential energies of all the particles in the system. Its absolute value cannot be measured, only its change.
Enthalpy is defined as H = U + PV. At constant pressure the heat absorbed or released equals the enthalpy change: ΔH = qp. The relation between ΔH and ΔU is ΔH = ΔU + ΔnRT, where Δn is the change in moles of gas. When no gases are involved or Δn = 0, ΔH ≈ ΔU.
An exothermic reaction releases heat to the surroundings and has a negative ΔH. Combustion and neutralisation are examples. The products have less enthalpy than the reactants. An endothermic reaction absorbs heat and has a positive ΔH, for example the decomposition of CaCO₃ and the dissolving of ammonium nitrate. A thermochemical equation gives the balanced equation, states of matter and the value of ΔH, such as H₂(g) + ½O₂(g) → H₂O(l), ΔH = −285.8 kJ.
Standard enthalpy changes are measured at 298 K and 1 atm with substances in their standard states. The common types are:
- Enthalpy of formation (ΔHf°): heat change when 1 mole of a compound is formed from its elements in their standard states. It is zero for an element in its standard state.
- Enthalpy of combustion (ΔHc°): heat released when 1 mole of a substance burns completely in oxygen.
- Enthalpy of neutralisation: heat released when 1 mole of water is formed from an acid and a base. For strong acid and strong base it is about −57 kJ per mole of water.
- Enthalpy of atomisation, fusion, vaporisation and solution: heat changes for those processes per mole.
Calorimetry measures heat changes. Heat absorbed or released by a substance is q = mcΔT, where m is the mass, c the specific heat capacity and ΔT the temperature change. For water c = 4.18 J g⁻¹ K⁻¹. In a bomb calorimeter, a substance burns in a sealed steel vessel under oxygen, and the heat raises the temperature of water and the apparatus. Heat released = C × ΔT, where C is the heat capacity of the calorimeter. This gives ΔU. A simple coffee-cup calorimeter at constant pressure is used for solutions to give ΔH.
Hess's law of constant heat summation states that the total enthalpy change of a reaction is the same whether it takes place in one step or in several steps. It follows from enthalpy being a state function. It is used to find ΔH for reactions that cannot be measured directly, for example C + ½O₂ → CO, by adding or subtracting known thermochemical equations. When an equation is reversed, the sign of ΔH changes. When it is multiplied by a number, ΔH is multiplied too.
From enthalpies of formation: ΔH°reaction = ΣΔHf°(products) − ΣΔHf°(reactants), each multiplied by its coefficient. From enthalpies of combustion the order is reversed: ΔH°reaction = ΣΔHc°(reactants) − ΣΔHc°(products).
Bond enthalpy (bond energy) is the energy needed to break one mole of a particular bond in gaseous molecules. Breaking bonds absorbs energy and forming bonds releases energy. ΔH(reaction) = Σ bond enthalpies of bonds broken − Σ bond enthalpies of bonds formed. The result is an estimate because bond enthalpies are average values.
The Born-Haber cycle applies Hess's law to the formation of an ionic solid such as NaCl. It links the enthalpy of formation to atomisation of the metal, ionisation energy, bond dissociation of the non-metal, electron affinity and lattice energy. Lattice energy is the energy released when one mole of an ionic solid forms from its gaseous ions. A larger lattice energy means a more stable crystal.
Study tip: In Hess's law problems, write the target equation first and arrange the given equations so that each substance appears on the correct side, then add. Always write the sign and unit (kJ or kJ mol⁻¹) in the final answer. Learn the definitions of the standard enthalpies word for word because they are asked often.
Definitions and flashcards
Say the meaning first, then open the card to check.
System
The part of the universe chosen for study
State function
A property that depends only on the initial and final states, not the path
Internal energy
The total kinetic and potential energy of the particles of a system
Enthalpy
The heat content of a system, H = U + PV
Exothermic reaction
A reaction that releases heat, with negative ΔH
Endothermic reaction
A reaction that absorbs heat, with positive ΔH
Enthalpy of formation
Heat change when 1 mole of a compound forms from its elements in their standard states
Hess's law
The enthalpy change of a reaction is the same whether done in one step or many
Bond enthalpy
Energy needed to break 1 mole of a bond in the gas phase
Lattice energy
Energy released when 1 mole of an ionic solid forms from its gaseous ions
Formula sheet
| Name | Formula | What it means |
|---|---|---|
| First law | ΔU = q + w | Change in internal energy |
| Work of expansion | w = −PΔV | Work done on a gas at constant pressure |
| Enthalpy | ΔH = ΔU + ΔnRT | Δn = change in gas moles |
| Heat change | q = mcΔT | c of water = 4.18 J g⁻¹ K⁻¹ |
| Enthalpy of reaction | ΔH° = ΣΔHf°(products) − ΣΔHf°(reactants) | Uses standard enthalpies of formation |
| Bond enthalpy | ΔH = Σ(bonds broken) − Σ(bonds formed) | Estimate for gaseous reactions |
Short questions with model answers
These are the kind of questions asked for 2, 3 and 5 marks. Try each one before opening the answer.
What is a state function? Give two examples. (2 marks)
It is a property whose value depends only on the present state of the system, not on how that state was reached. Enthalpy and internal energy are examples.
State the first law of thermodynamics and write its equation. (2 marks)
Energy can neither be created nor destroyed, only converted from one form to another. The equation is ΔU = q + w, where q is the heat absorbed by the system and w the work done on the system.
Differentiate between exothermic and endothermic reactions. (3 marks)
An exothermic reaction releases heat to the surroundings, so ΔH is negative and the surroundings warm up (combustion). An endothermic reaction absorbs heat from the surroundings, so ΔH is positive and the surroundings cool down (dissolving NH₄NO₃).
State Hess's law and explain why it is true. (5 marks)
The total enthalpy change of a chemical reaction is the same whether it occurs in one step or through several steps, provided the initial and final conditions are the same. It is true because enthalpy is a state function, so the change depends only on the initial and final states. The law is used to find enthalpies that cannot be measured directly, such as the formation of CO from carbon and oxygen.
Define standard enthalpy of formation. What is its value for an element? (3 marks)
It is the enthalpy change when one mole of a compound forms from its elements in their standard states at 298 K and 1 atm. For an element in its standard state it is zero.
How is a bomb calorimeter used to find the heat of combustion? (3 marks)
A known mass of the substance is burned in excess oxygen in a sealed steel bomb placed in water. The rise in the temperature of the water is measured. The heat released equals the heat capacity of the calorimeter multiplied by the temperature rise, which gives the heat per gram or per mole.
Numericals with worked steps
Find the heat needed to raise the temperature of 200 g of water from 25 °C to 45 °C. (c = 4.18 J g⁻¹ °C⁻¹)
- ΔT = 45 − 25 = 20 °C
- q = mcΔT = 200 × 4.18 × 20
- q = 16720 J = 16.72 kJ
Answer: 16.72 kJ
Given C + O₂ → CO₂, ΔH = −393.5 kJ and CO + ½O₂ → CO₂, ΔH = −283.0 kJ, find ΔH for C + ½O₂ → CO.
- Keep the first equation: C + O₂ → CO₂, −393.5 kJ
- Reverse the second: CO₂ → CO + ½O₂, +283.0 kJ
- Add: C + ½O₂ → CO
- ΔH = −393.5 + 283.0 = −110.5 kJ
Answer: ΔH = −110.5 kJ
Find ΔH for CH₄ + 2O₂ → CO₂ + 2H₂O(l). ΔHf: CH₄ = −74.8, CO₂ = −393.5, H₂O(l) = −285.8 kJ mol⁻¹.
- ΣΔHf (products) = −393.5 + 2(−285.8) = −393.5 − 571.6 = −965.1
- ΣΔHf (reactants) = −74.8 + 2(0) = −74.8
- ΔH = −965.1 − (−74.8) = −890.3 kJ
Answer: ΔH = −890.3 kJ
Estimate ΔH for H₂ + Cl₂ → 2HCl. Bond enthalpies (kJ mol⁻¹): H-H 436, Cl-Cl 242, H-Cl 431.
- Bonds broken: 436 + 242 = 678 kJ
- Bonds formed: 2 × 431 = 862 kJ
- ΔH = 678 − 862 = −184 kJ
Answer: ΔH = −184 kJ (exothermic)
A system absorbs 500 J of heat and does 200 J of work on the surroundings. Find ΔU.
- q = +500 J
- Work done by the system, so w = −200 J
- ΔU = q + w = 500 − 200 = 300 J
Answer: ΔU = +300 J
Common mistakes
- Getting the sign of ΔH wrong. Exothermic reactions have negative ΔH.
- Forgetting to change the sign of ΔH when a thermochemical equation is reversed, or to multiply it when the equation is multiplied.
- Reversing products and reactants in the formation enthalpy formula. It is products minus reactants.
- Taking the enthalpy of formation of an element such as O₂ or Cl₂ as non-zero.
- Using grams instead of moles when the ΔH is given per mole.