Internal Energy (Higher Tier)

Definition of Internal Energy

Internal energy is the total energy stored within the particles of a substance. This energy includes two main parts:

• Kinetic energy due to the motion of particles (atoms, ions or molecules).
• Potential energy stored in the chemical bonds between atoms and in the forces between particles.

The energy stored in bonds is a key part of internal energy. When chemical bonds form, energy is stored; when bonds break, energy is absorbed.

Internal energy is a microscopic property — it relates to the energy of particles inside the substance, not the energy of the substance as a whole moving or positioned.

Changes in Internal Energy

Internal energy changes when energy is transferred to or from a substance. This can happen in two main ways:

• Heating: Energy transferred by heating increases the internal energy, raising the kinetic energy of particles (they move faster) and/or changing the potential energy (changing the arrangement of particles).
• Doing work: Energy can be transferred by work done on or by the system, such as gas expanding or compressing, which changes internal energy.

During state changes (melting, boiling, freezing, condensing), internal energy changes without a change in temperature because energy is used to break or form bonds between particles, altering potential energy.

For example, when ice melts, energy is absorbed to break hydrogen bonds between water molecules, increasing potential energy but not kinetic energy, so temperature stays constant.

For instance, heating 1 mole of ice at 06C to melt it requires energy to break bonds without changing temperature, increasing internal energy.

Energy Transfers in Reactions

Chemical reactions involve breaking and making bonds, which changes the internal energy of the system:

• Breaking bonds requires energy input because bonds hold atoms together; energy must be absorbed to overcome these forces.
• Making bonds releases energy because atoms form stable arrangements, releasing stored potential energy.

The overall energy change in a reaction depends on the balance between energy absorbed breaking bonds and energy released making bonds:

Overall energy change = energy absorbed breaking bonds 0minus0energy released making bonds

If more energy is absorbed breaking bonds than released making bonds, the internal energy of the system increases. If more energy is released making bonds, the internal energy decreases.

For example, in the reaction of hydrogen and oxygen to form water, energy is absorbed to break H00H and O00O bonds but more energy is released forming O00H bonds, resulting in a net energy release.

Energy Diagrams and Calculations

Energy profile diagrams show how the internal energy of a system changes during a reaction:

• The vertical axis represents internal energy.
• The horizontal axis represents the progress of the reaction from reactants to products.

The diagram shows:

• Bond breaking at the start, requiring energy input.
• Bond making later, releasing energy.

The difference in height between reactants and products shows the overall energy change (internal energy change).

Bond energies are average values for the energy needed to break one mole of a specific bond in the gas phase. They allow calculation of internal energy changes:

Energy change (kJ/mol) = Total energy absorbed breaking bonds 0minus0Total energy released making bonds

For example, to calculate the energy change for a reaction:

• Sum the bond energies of all bonds broken (energy absorbed).
• Sum the bond energies of all bonds formed (energy released).
• Subtract the energy released from the energy absorbed.

A positive result means the reaction absorbs energy (internal energy increases). A negative result means the reaction releases energy (internal energy decreases).

Example: Calculate the internal energy change for the reaction:

$\mathrm{H_2 + Cl_2 \rightarrow 2HCl}$

Bond energies (kJ/mol): H00H = 436, Cl00Cl = 243, H00Cl = 431

Energy absorbed breaking bonds = 436 (H00H) + 243 (Cl00Cl) = 679 kJ

Energy released making bonds = 2 1 0431 (H00Cl) = 862 kJ

Energy change = 679 0minus0 862 = 0183 kJ (energy released, internal energy decreases)