Energy Transfers (College Board AP® Chemistry): Revision Note

Conservation of Energy

• All forms of energy can be converted from one form to the other, for example:

  • Sunlight feels warm because radiant energy is converted to thermal energy in the skin

  • When a ball rolls down a hill, the potential energy in the ball is converted to kinetic energy

  • Batteries convert stored chemical energy into electrical energy

• All of these conversions and transfers proceed in accord with one of the most important observations in science:

Energy can be neither created nor destroyed

• During a chemical or physical process, any energy lost by the system must be gained by the surroundings and vice versa

• This important observation, that energy is conserved, is known as the first law of thermodynamics

  • In a thermodynamic sense, this law is summarized as: “the total quantity of energy in the universe is assumed constant”

Internal Energy, E

• To apply the first law of thermodynamics to chemical systems, we must consider all sources of energy in the system being studied

  • These are typically kinetic and potential energy

• The internal energy, E, of a system is the sum of all the kinetic and potential energies of the components of the system

  • We generally do not know the numerical value of a system’s internal energy

• However, during a chemical reaction, we can measure the change in internal energy, ΔE, of the system

  • This is mathematically defined as:

ΔE = E_final - E_intial

• From the above relationship, we can define the direction of energy transfer between the system and surroundings during a physical or chemical change

  • A positive ΔE value indicates E_final* > E*_initial, which means energy is gained by the system from the surroundings

  • A negative ΔE value indicates E_final* < E*_initial, which means the system loses energy to the surrounding

• It is important to note that in keeping with the first law of thermodynamics, any increase in the energy of the system is accompanied by a decrease in the energy of the surroundings, and vice versa

Relationship between ΔE, Heat (q) and Work (w)

• Any energy exchange between a system and its surroundings is observed in the form of heat or work

• Hence, changes in the magnitude of the internal energy, Δ*E*, of a system could either be in the form of:

  • Heat added or removed from the system

  • Work done on or by the system

• This relationship allows us to mathematically define the first law of thermodynamics

  • When a system undergoes any chemical or physical change, the change in internal energy, Δ*E*, is the sum of the heat added to or released from the system, q, and the work done on or by the system,w

ΔE = q + w

• It is important to take note of the sign conventions associated with work and heat in determining the value of ΔE

  • When heat is gained by the system; q is positive

  • When heat is lost by the system; q is negative

  • When work is done by the system; w is negative

  • When work is done on the system; w is positive

Specific Heat Capacity

• When a substance is heated and does not change phase, its temperature rises

• However, the magnitude of the temperature change produced by a given quantity of heat varies from substance to substance

• The temperature change experienced by a substance when heat is absorbed is dependent on its heat capacity

  • Heat capacity, C, is defined as the heat required to raise the temperature of a substance by 1 K or 1 °C

  • The greater the heat capacity of an object, the greater the amount of heat required to produce a given temperature increase

  • It is measured in J K^-1 or J °C^-1

• For a pure substance, the heat capacity is defined in terms of a specified amount of the substance

  • For one mole of a substance, the heat capacity is known as molar heat capacity

  • For one gram of a substance, the heat capacity is known as specific heat capacity, c

• The specific heat capacity of a substance can be experimentally determined using the following variables:

  • Mass of substance, m

  • Temperature change, ΔT

  • Quantity of heat, q

• Calorimetry experiments measure the heat transferred by recording the temperature change of a known mass of a substance, often water, in an insulated container (a calorimeter)

• The relationship between the specific heat capacity, temperature change, mass of substance and quantity of heat is mathematically defined as:

c = $\frac{\mathbf{q}}{\mathbf{(}\mathbf{m}\mathbf{\times }\mathbf{\Delta }\mathbf{T}\mathbf{)}}$

• Rearranging gives:

q = m × c × ΔT

• Where:

  • q is the heat transferred (J)

  • m is the mass of the substance whose temperature changes (g)

  • c is its specific heat capacity (J g^-1 °C^-1)

  • ΔT is its temperature change (°C or K)

• Specific heat capacity is measured in J g^-1 °C^-1 or J g^-1 K^-1

• Molar heat capacity is measured in J mol^-1 °C^-1 or J mol^-1 K^-1

Energy Changes of a System

• Changes in the energy of a system can be explained by phase transitions which occur in the system

• Important phase transitions which can be used to demonstrate energy changes that occur from the heating and cooling of a system include:

  • Melting / Freezing

  • Evaporation / Condensation

  • Sublimation / Deposition

Phase changes and energy

Energy changes in phase transitions

A graphical representation of the effect of energy changes in a system and the change in the state of matter

Melting and freezing

• The particles in a solid system are arranged in more or less fixed positions with respect to one another and closely arranged to minimize the energy of the system

• When heat is added to this system, the temperature of the solid increases

  • This increases the kinetic energy of the particles until they are able to move relative to one another

  • Consequently, the solid begins the process of melting

  • The temperature at which this occurs is known as the melting point

• Melting is also known as fusion and the amount of heat required for this process is known as the heat of fusion

  • For example, the heat of fusion for ice is 6.01 kJ/mol

• On the other hand, in a liquid system, the cooling of the system will result in a decrease in the temperature of the liquid

  • This results in a decrease in the energy of the particles and the change of the liquid to a solid

  • This process is referred to as freezing

• For a particular substance, the energy released when it freezes is equal in magnitude to its heat of fusion, but opposite in sign

• In general,

  • The process of melting involves an increase in the energy of the system and is considered to be endothermic

  • The freezing process involves a decrease in the energy of the system and is considered to be exothermic

Evaporation and condensation

• Similar to the process of melting, heating a liquid system increases the energy of the system

  • The particles of the liquid will experience an increase in their kinetic energy

  • This process is known as evaporation and the heat required for this is known as the heat of vaporization

  • The heat of vaporization is used to measure the strength of intermolecular forces that exist within the liquid

• It is important to differentiate between evaporation and boiling

  • Evaporation is slower and occurs at the surface of the liquid

  • Boiling is faster and occurs throughout the liquid

  • Evaporation cools the liquid that is left, because the most energetic particles escape; during boiling the temperature stays constant because heat is supplied as fast as the liquid absorbs it

    • For example, stepping out of a swimming pool or a warm shower feels cool because the water on the skin absorbs its heat of vaporization from the body as it evaporates

  • Condensation describes the process by which a gas is changed to a liquid

    • It occurs as a result of a decrease in the energy of the gas particles

    • For example, dew is formed by the condensation of water vapor in the air on cool surfaces

  • In general, for any given substance:

    • The heat of condensation is equal in magnitude to the heat of vaporization but opposite in sign

    • Heat of condensation is exothermic and negative while vaporization is endothermic and positive

Sublimation and deposition

• Sublimation describes the process by which the particles of solids are directly converted to gas without going through the liquid phase

  • For example, solid iodine molecules are converted to gas when heated

  • The heat of sublimation is the sum of the heat of vaporization and the heat of fusion

ΔH_sub = ΔH_fus + ΔH_vap

• On the other hand, the process by which gas molecules are converted to solids is known as deposition

  • Frost is solid water formed by direct condensation of water vapor from the atmosphere without first forming liquid water

  • Snow is formed by a similar process in the upper atmosphere

• Similar to the heat of condensation and vaporization

  • The heat of deposition is an exothermic process

  • The heat of sublimation is an endothermic process

  • The heat of deposition is equal in magnitude but opposite in sign to the heat of sublimation

Changing Chemical Systems

• Energy changes in chemical systems are observed through three processes:

  • Heating/Cooling

  • Phase Transition

  • Chemical Reaction

Heating and cooling curves

• When heat is added at a constant rate to a solid material at a temperature below its melting point, the following effects are observed:

  • A constant rate of increase in the temperature of the solid until it begins to melt

    • During this process, there is an increase in the average kinetic energy of the particles, so the temperature rises

  • When melting begins, the temperature remains constant until all of the solid is converted to liquid

    • A constant temperature shows that the kinetic energy of the particles remains constant while the potential energy increases

    • The heat added is used to overcome the intermolecular forces present in the substance

  • The temperature of the liquid starts increasing at a constant rate until it starts to boil

    • Similar to the beginning of the heating process, the average kinetic energy of the particles increases as more heat is added

  • When boiling begins, the temperature remains constant until all of the liquid is converted to gas

    • Again, the average kinetic energy remains the same as the heat added is used to overcome the intermolecular forces between the particles of the liquid

  • The temperature of the gas, then, increases at a constant rate

• All of these processes can be summarized in a heating curve as shown below:

Heating curve

Diagram of a typical heating curve of a sample from the solid state on the left to the gaseous state on the right. The temperature of the sample increases as heat is added except during the change of phase which are represented by segments BC and DE

• From segments AB, CD and EF of the heating curve

  • Heat added only raises the temperature and can be calculated from the product of the specific heat capacity, the mass and the temperature change; q = m × c × ΔT

  • The slope of these lines can be used to compare the specific heat capacities of the solid, liquid and gaseous phases of the sample

    • The greater the specific heat capacity, the less the slope of the line

    • This means that more heat is required to change the given quantity of the sample by one degree

    • This is seen on the heating curve for water: liquid water has a greater specific heat capacity than ice, so the liquid section is less steep

• In segments BC and DE

  • The temperature remains constant during these phase changes because the added energy is used to overcome the attractive forces between molecules rather than to increase their average kinetic energy

  • The heat involved during these processes is known as the heat of fusion and the heat of vaporization respectively

  • The longer the lines, the greater the value of heat required to change the phase

  • Generally, the heat of vaporization is greater than the heat of fusion

    • This is because boiling must overcome nearly all of the attractions between the particles, while melting overcomes only some of them

• A cooling curve is the reverse of a heating curve with similar features except we start with a gas sample and end with a solid

  • Cooling involves the process of removing heat from the sample

Chemical reactions

• Many chemical reactions are accompanied by heat exchange between the system and the surroundings

• Consider a system in which a chemical reaction occurs

  • Before the reaction, the system and surroundings are at the same temperature, say 25 °C

  • As soon as the reaction begins, the temperature changes

• If the temperature of the system decreases, then energy flows from the surroundings to the system

  • The system has absorbed heat and q is positive

  • When the reaction stops, heat continues to flow until the system returns to the temperature of its surroundings

• If the temperature of the system increases, then energy flows from the system to the surroundings

  • In this case, the system has evolved heat and q is negative