MCAT General Chemistry Chapter 7: Thermochemistry

Systems vs. Surroundings

• System: that matter that is being observed; the total amount of reactants and products in a chemical reaction 

• Surroundings: everything outside of the system 

  • The boundary between system and surroundings is based on what phenomena is being tested 

Isolated System

•  the system cannot exchange energy (heat and work) or matter with the surrounding 

  • Ex.: insulated bomb calorimeter

Closed System

• the system can exchange energy (heat and work) but not matter with surroundings 

  • Ex: a steam radiator 

Open System

•  the system can exchange both energy (heat and work) and matter with the surroundings 

  • Ex: a pot of boiling water 

Process

•  describes a system experiencing a change in one or more properties

  • Are uniquely identified by some property that is constant throughout

  • Allow us to simplify the first law of thermodynamics 

The First Law of Thermodynamics

Equation 7.1: The first law of thermodynamics

ΔU = Q -W 

W = -PV

• Q = heat added

• W= work

• ΔU = internal energy 

Isothermal Process

•  occur when the system’s temperature is constant 

  • Total internal energy of system (U) is constant, ΔU = 0

  • Q = W ; heat added = work done by system

Adiabitic Process

occur when no heat is exchanged between the system and the environment 

• Thermal energy of the system is constant throughout 

• When Q=0, change in internal energy = work done on the system  ΔU = -W

Isobaric Process

occur when the pressure of the system is constant 

• Do not alter the first law but appear as a flat line on the P-V graph 

  

Isovolumetric Process

the system experiences no change in volume 

•  Change in internal energy = heat added to system; ΔU = W

• Is a vertical line on the P-V graph

Spontaneous Processes

• One that can occur by itself without have to be drive by energy from an outside source; can be calculated from Gibbs free energy 

• Do not necessarily happen quickly or go to completion; many reach an equilibrium with dynamically stable concentrations of reactants and products 

• Often spontaneous reactions are coupled to nonspontaneous reactions to provide energy for nonspontaneous reactions 

Relating Keq and Q (reaction quotient)

• Q < K_eq then reaction proceeds spontaneously until equilibrium is reached

• Q > K_eq then reaction proceeds spontaneously in reverse direction until equilibrium is reached

State Functions

• describe the system in an equilibrium state; cannot describe the process 

  • Include pressure, density, temperature, volume, enthalpy, internal energy, Gibbs free energy, and entropy 

Standard Conditions

• Defined for measuring the enthalpy, entropy, and Gibbs free energy

• 25℃ (298°K), 1 atm pressure, 1 M concentration

• Here, the most stable of substance is its standard state 

  • Common MCAT ex.: H₂ (g), H₂O (l), NaCl (s), O₂ (g) and C (s, graphite)

Standard Enthalpy, entropy, free energy

• are changes in these state functions that occur under standard conditions

  •  ΔH,  ΔS,  ΔG 

Phase Diagrams

• show the standard and nonstandard states of matter for a given substance in an isolated system 

  • Show temperatures and pressures at which a substance will be thermodynamically stable in a particular phase or in which particular phases will be in equilibrium

Lines of equilirbium (Phase diagram)

•  indicate temperatures and pressure of equilibria and divide the diagram into 3 phases 

  • liquids : found at moderate temperatures and moderate pressures

  • Gases: found at high temperatures and low pressures

  • Solids: found at low temperatures and high pressures 

Triple point (phase diagram)

•  point at which three phase boundaries meet 

Critical Point (phase diagram)

• point at which there is no distinction between liquid and gas phases 

Phase Changes

•  are reversible

  • An equilibrium of phases will eventually be reached at any given combination of temperature and and pressure 

• are analogous to dynamic equilibria reversible chemical reactions 

  • Concentrations of each phase are constant because the amount of substance in one phase is equal to the amount of that substance in another phase

Evaporation or Vaporizatoin

• describes a point of gas liquid equilbrium

  • a point at liquid phase, when molecules near surface have enough kinetic energy to leave liquid phase and escape into gaseous phase ; process is known as

  • Temperature of substance in any phase is related to the average kinetic energy of the molecules that make up the substance 

Boiling

• specific type of vaporization where rapid bubbling an entrie liquid causes it to rapidly release as gas particles 

Temperature at which vapor pressure equals the ambient/external pressure is called boiling point

Condensation

• when escaping molecules from a solution exert countering pressure that forces a gas back into its liquid phase

  • Facilitated by lower temperature or higher pressure 

Fusion (melting)

availability of energy microstates increases as the temperature of the solid increases; molecules have greater freedom of movement and energy disperses

• describes when atoms in the solid phase absorb enough energy and their 3-D structure breaks down, allowing molecules to escape into liquid phase

  • The reverse is called solidification, crystallization, freezing

Melting or freezing point is the temperature at which these processes occur

Gas Solid Equilbirium

• sublimation : when a solid goes directly into the gas phase 

• Deposition: when a gas goes into the solid phase 

Distinction Between Heat and Termperature

• Temperature: related to the average kinetic energy of the particles of a substance 

  • Is related to the thermal energy (enthalpy) of the substance

• Heat (Q): the transfer of energy form one substance to another as a result of their differences in temperature

Zeroth Law of Thermodynamics

• implies that objects are in thermal equilibrium only when their temperatures are equal 

• says heat is process function because we can quantify how much thermal energy is transferred between two or more objects as a result of temp. Difference 

  • Endothermic: ΔQ > 0; system absorbs heat

  • Exothermic: ΔQ < 0 ; system loses heat 

• Enthalpy is equivalent to heat under constant pressure (usually context of MCAT problems)

Calorimetry

 process of measuring transferred heat 

Equation 7.2: Heat Absorbed

 q =mcΔT

M = mass

C = specific heat

ΔT - change in temperature 

Constant Pressure Calorimetry

• Atmospheric pressure is constant throughout the process; temperature can be measured as reaction progresses 

• Sufficient thermal insulation is necessary to ensure heat measured is accurate representation of of the reaction without gain or loss to environment

Constant Volume Calorimetry

• A hydrocarbon is placed in steel decomposition vessel which is filled pure oxygen gas 

• Vessel is placed in insulated container holding known mass of water 

• Material combusts in presence of oxygen

• Calorimeter is considered isolated from the rest of the universe 

  • System: sample plus oxygen and steel vessel

  • Surroundings: water 

  • Since no work is done, ΔU_system = ΔU_surroundings and q_system = -q_surr

Heating Curves

• Temperature rises until melting point/boiling point is reached, then temperature remains constant as compound is converted to the next phase 

• Once entire sample is converted, sample continues to rise again 

  • show that phase reactions do not undergo changes in temperature

Enthalpy or heat of fusion (ΔH_fus)

• must be used to determine the heat transferred during the phase change at solid liquid boundary

  • Solid to liquid: ΔH_fus will be positive

  • Liquid to solid: ΔH_fus will be negative 

Enthalpy or Heat of Vaporization (ΔH_vap)

•  must be used to determine the heat transferred during the phase change at liquid gas boundary

Equation 7.3: Heat of Vaporization 

Q = mL

M = mass 

L = latent heat (term for enthalpy of isothermal process)

Enthalpy

• Used to explain heat changes at a constant temperature 

• Can never be measured directly and can only be measured for certain spontaneous processes 

Equation 7.4: Enthalpy change of Reaction

ΔH_rxn = H_products -  H_reactants

• Positive ΔH_rxn = endothermic process

• Negative ΔH_rxn  = exothermic process 

Standard enthalpy of formation (ΔH°_f)

• The enthalpy required to produce one mole of a compound from its elements in their standard states

  • This means the ΔH°_f of an element in standard state is 0

Standard Heat of Reaction

Equation 7.5: Standard Enthalpy of Rxn

• The enthalpy change accompanying a reaction being carried out under standard conditions 

• ΔH°_rxn = ∑ΔH°_{f, products}  - ∑ΔH°_{f, reactants} 

Hess’s Law

• Property of the equilibrium state; process is irrelevant to change in enthalpy from one equilibrium to another 

• States that enthalpy changes of reactions are additive 

Bond Dissociation Energy

• explains Hess’ Law

• The average energy that is required to break a particular type of bone between atoms in the gas phase

  • Bond dissociation is an endothermic process

  • Bond formation is negative, exothermic process 

Bond Enthalpies (Bond dissociation energy)

Equation 7.6:

• ΔH°_rxn = ∑ΔH_{bonds broken}  - ∑ΔH_{bonds formed} = total energy absorbed - total energy released 

Standard heat of combustion (ΔH°_comb) 

• The enthalpy change associated with the combustion of a fuel 

• Require a reaction to be spontaneous and fast 

• MCAT combustion reactions for this occur in presence of atmospheric oxygen (some reactions can occur in presence of diatomic molecules)

  

Second Law of Thermodynamics

States that energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so

• describes entropy

Entropy

• the measure of the spontaneous dispersal of energy at a specific temperature 

  • Entropy can be localized/concentrated but this rarely happens spontaneously: work must be done to concentrate energy against spontaneity 

Change in Entropy (equation)

Equation 7.7: Change in Entropy 

ΔS = Q_rev / T

• Q_rev = heat gained or lost in a reversible process

• T = the temperature in kelvin 

  • Energy distributed into system = increase in entropy 

  • Energy distributed out of system = decrease in entropy 

Equation 7.8: 

ΔS _universe = ΔS _system + ΔS _surroundings > 0

• Explains how entropy of a universe is always increasing 

Entropy of Reaction

Equation 7.9 : 

ΔS°_rxn = ∑ΔS°_{f, products} - ∑ΔS°_{f, reactants} 

Gibbs Free Energy

• Is a state function that is combination of temperature, enthalpy, and entropy state functions 

• Any system will move in whichever direction results in a reduction of the gree energy of the system (towards equilibrium)

Calcuating Gibbs Free Energy

Equation 7.10: Gibbs Free Energy 

ΔG = ΔH - TΔS

• TΔS = the total amount of energy absorbed by a system when its entropy increases reversibly 

• ΔG < 0 = spontaneous (exergonic) reaction

• ΔG > 0 = non spontaneous (endergonic) reaction

• ΔG  = 0; system is in equilibrium

Phase Equilibria and Spontaneity

• Equilibria are states in which more than one phase exists 

• Change in Gibbs free energy must be equal to zero (ΔG =0) 

Effects on Spontaneity

• The rate of a reaction depend on the activation not ΔG 

  

Standard Gibbs Free Energy

• Describes free energy change of reactions under standard state conditions 

• Concentrations of any solutions in reaction are 1M

• Standard free energy of formation  of a compound, ΔG°_f ; 

  • The free energy change that occurs when 1 mole of a compound in its standard state is produced from its respective elements in their standard state  (under standard conditions)

  • Thus, ΔG°_f for any element under standard conditions is zero

Equation: 7.11

ΔG°_rxn = ∑ΔG°_{f, products} -  ∑ΔG°_{f, reactants} 

Free Energy (G), K_eq and Q

• We can derive the standard free energy change for a reaction from the equilibrium constant K_eq

• When a reaction begins, standard state conditions no longer apply 

• Value of equilibrium constant must be replaced with a value that is reflective of where the reaction is in its path toward equilibrium 

Main Point:

• Q denotes equilbrium when a rxn begins (no longer Keq)

• Keq used for standard state

Calculating Spontaneity From K_eq and Q

Equation 7.12: 

ΔG°_rxn = -RT ln K_eq

• The greater the value of K_eq the more spontaneous the reaction 

Equation 7.13: 

ΔG_rxn = ΔG°_rxn  + RT lnQ = RT ln(Q/K_eq)