Download Spontaneity, Entropy, and Gibbs Free Energy

Spontaneity, Entropy, and
Gibbs Free Energy
AP Chemistry
Ms. Grobsky
Where We Have Been and Where We
are Going
 How do we describe the shape of a molecule?
 Molecules have predictable shapes and polarities based on
minimizing repulsions and maximizing attractions
 Atoms more close together to lower energy and form bonds
 How is energy involved in a reaction?
 Energy is stored in bonds
 The heat content (enthalpy, H) of a system changes (ΔH)
during a reaction
 Endothermic – ΔH is + (uphill)
 Exothermic – ΔH is – (downhill)
Where We Have Been and Where We
are Going
 How rapidly does a reaction progress?
 Kinetics
 Reaction rates, activation energy, catalysts, reaction
mechanisms, temperature…
 The lower the activation energy (Ea), the faster a reaction
proceeds
 How far towards completion does a reaction occur?
 Equilibrium
 Opposing reactions occur at equal rates
 K >> 1 means product favored at equilibrium
 Why do reactions proceed in the first place?
Spontaneous Processes
 Spontaneous processes are
those that can proceed
without any outside
intervention GIVEN
SUFFICIENT ACTIVATION
ENERGY
 The gas in vessel A will
spontaneously effuse into
vessel B
 But once the gas is in both
vessels, it will NOT
spontaneously reverse
Spontaneous Processes
 Processes that are spontaneous in one direction are usually
nonspontaneous in the reverse direction under same conditions
 Rusting of a nail
 Breaking of an egg
Spontaneous Processes
 Processes that are
spontaneous at one
temperature may be
nonspontaneous at other
temperatures
 Above 0°C, it IS
spontaneous for ice to
melt
 Below 0°C, the reverse
process is spontaneous
(liquid water freezing)
Reversible Processes
 In a reversible process, the system changes in such a
way that the system and surroundings can be put
back in their original state by exactly reversing the
process
 Example
 Equilibrium processes are reversible and spontaneous in
both directions
 Changes are infinitesimally SMALL in a reversible
process
Irreversible Processes
 Irreversible processes cannot be undone by exactly
reversing the change to the system
 All spontaneous processes are irreversible
What Contributes to Spontaneity?
 Change in Enthalpy (ΔH)
 Defined as heat/energy absorbed or given off at a
constant pressure
 Change in Entropy (ΔS)
 Defined as a measure of randomness or disorder
 Cannot be directly measured
 Temperature of the Reaction (T)
 What is the temperature, or better said, the kinetic
energy of the particles in the reaction?
Enthalpy’s Contribution to
Spontaneity
 Many (but not all) spontaneous processes proceed with a DECREASE in
energy and are EXOTHERMIC (produces heat) at 25°C and 1 atm (STP)
 Not a direct correlation or a perfect explanation
 Endothermic (takes in heat) reactions that are non-spontaneous at
room temperature often become spontaneous at higher temperatures
 Increase in energy often increases spontaneity
 Example
 The decomposition of limestone (calcium carbonate) occurs at 1100 K and 1
atm
 At 25°C and 1 atm , this reaction does not occur
 In summary, ΔH contribution is tied to the temperature of the
reaction…
What about Entropy? What is It?
 Entropy can be thought of as a measure of the
molecular randomness or disorder of the system
 Change in entropy is denoted by ΔS
 First Law of Thermodynamics
 Energy in the universe is constant
 Energy cannot be created nor destroyed. It can only be
transformed
 Second Law of Thermodynamics
 Randomness or disorder of the universe is increasing
What are the Variables that
Affect Entropy?
Entropy on the Molecular Level
 What increases entropy?
 Adding particles
 Adding more particles increases the collisions and the
randomness of motion
 Adding energy/increasing temperature
 Velocity of particle motions is increased
 Increasing volume
 Particles are allowed to roam in greater space; thus, more
random motion
How is Entropy Affected by Physical
States?
 Entropy increases with the freedom of motion of
molecules
S (g) > S (l) > S (s)
 More energy means greater thermal disorder
 More freedom to move around in space means greater
positional disorder
What Happens to Entropy in
Solutions?
 Dissolution of a solid
 Ions have more entropy
 BUT, some water molecules have less entropy as they are
now grouped around the ions
 Usually, there is an overall increase in S
 The exception is very highly charged ions that make a lot of
water molecules align around them
Spontaneous Reactions and Entropy
The driving force for a
spontaneous process is an
increase in entropy of the
universe
Third Law of Thermodynamics
 At absolute zero, a pure substance exists as a perfect
crystal with no molecular movements
 No kinetic energy
 The entropy of a pure crystalline substance at absolute
zero is 0
Summary of the Three Laws of
Thermodynamics
 You can’t win, you can only break even
 You can only break even at T = 0
 You can’t reach T = 0
Calculating Entropy
 For a chemical reaction, the change in entropy (ΔS)
under standard conditions is calculated as:
0
∆𝑆𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
=
0
𝑛𝑆𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠
−
0
𝑛𝑆𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠
 Standard entropies, ∆𝑆 0 , are analogous to standard
enthalpies of formation, ∆𝐻𝑓0
 Molar entropy values of substances are in their standard
states
 25°C and 1 atm
 Units for S are generally J/mol∙K
Trends in Standard Entropies
 Standard entropies tend to increase with increasing
molar mass
 Larger and more complex molecules have greater
entropies
 Note for pure elements:
𝑆0 ≠ 0
∆𝐻0 = 0
Predicting Relative S0 Values of a
System
 Temperature changes
 S0 increases as the temperature rises
 Physical states and phase changes
 S0 increases as a more ordered phase changes to a less ordered phase
 Dissolution of a solid or liquid
 S0 of a dissolved solid or liquid is usually greater than the S0 of the pure
solute
 However, the extent depends upon the nature of the solute and solvent
 Dissolution of a gas
 A gas becomes more ordered when it dissolves in a liquid or solid
 Atomic size or molecular complexity
 In similar substances, increases in mass relate directly to entropy
 Increases in complexity (i.e. bond flexibility) relate directly to entropy
 Example
 NO has less entropy when compared to NO2 and N2O4
The Relation between Entropy and
Enthalpy
Introducing Gibb’s Free Energy
Introducing Gibb’s Free Energy
 Gibb’s Free Energy is defined as the energy available
in a system that is available to do useful work
 Standard free energies of formation, ∆𝐺𝑓0 , are
analogous to standard enthalpies of formation, ∆𝐻𝑓0
0
∆𝐺𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
=
0
𝑛𝐺𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠
−
0
𝑛𝐺𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠
Gibb’s Free Energy & Spontaneity
 So far, we have used ∆S to predict the
spontaneity of a process
 However, Gibb’s Free Energy is also related to
spontaneity and is especially useful in dealing
with the temperature dependence of
spontaneity
 If ∆G is negative, the FORWARD reaction is
spontaneous
 If ∆G is positive, the REVERSE reaction is
spontaneous
 If ∆G is 0, the system is at equilibrium!
Calculating ∆G
 ∆G can be calculated from ∆H and ∆S:
0
∆𝐺 = ∆𝐻𝑠𝑦𝑠
− 𝑇∆𝑆𝑠𝑦𝑠

This relationship holds true as long as the temperature and pressure
remain constant during the reaction
There are two parts to the free energy equation:



∆H – the enthalpy term

∆S – the entropy term
The temperature dependence of free energy comes from the entropy
term
The Effect of Temperature on ∆G and
Spontaneity
 By knowing the sign (+ or -) of ∆S and ∆H, we can get the sign
of ∆G and determine if a reaction is spontaneous
 High temperature favors the entropy term
 Low temperature favors the enthalpy term
Calculating ∆G
∆G =
0
∆Hsys
− T∆Ssys
 The ∆Hrxn can be calculated from ∆Hf at STP
 The ∆Srxn is also calculated from the ∆S0 at STP
 The Gibb’s equation allows you to calculate ∆G
and verify reaction spontaneity at other
temperatures
Gibb’s Free Energy and
Equilibrium
∆G, ∆G˚, and Keq



DG0 describes a reaction in standard state conditions
25°C, 1 atm
DG must be used when the reaction is NOT in standard state conditions
 ∆G is related to ∆G˚ via the equation:
∆G = ∆G˚ + RT ln Q
where
Q = Reaction quotient
R = Universal Gas Constant (8.314 J/K•mol)
T = Kelvin temperature
Qualitative Relationship Between the
Change in Standard Free Energy and the
Equilibrium Constant at a Given T
∆G = ∆G˚ + RT ln Q
∆G0
K
∆G0 = 0
K=1
∆G0 < 0
K > 1 (Product favored)
∆G0 > 0
K < 1 (Reactant favored)
• When ∆G0 = 0:
∆Gorxn = - RT ln K
• The larger the value of K, the more negative the value of ∆Gorxn
Relation between ΔG0 and K as
Predicted by ΔG0 = - RT ln K
ΔG0 = - RT ln K
Gibb’s Free Energy and Equilibrium
Position
DG0 < 0
DG0 > 0