Physical Chemistry Exam 2

Enthalpy
a thermodynamic quantity equivalent to the total heat content of a system.
H=U+PV
Molar Heat Capacity
The amount of (heat) energy necessary to raise the temperature of one mole of a substance by 1K
Internal Pressure (πT)
a measure of how the internal energy of a system changes when it expands or contracts at constant temperature. For an ideal gas, this equals 0
First Law of Thermodynamics
Energy cannot be created or destroyed
U=w+q
Plot an adiabat in P-V (molar volume) space?
(P2/P1)=(V1/V2)^γ-1
γ=Cp/Cv
Plot an adiabat in T- V (molar volume) space?
(T2/T1)=(V1/V2)^γ-1
γ=Cp/Cv
Molar Heat Capacity for Ideal Gas, Solid and Liquids, and Ideal Monatomic
Ideal Gas: Cp-Cv=R
Solids and Liquids: Cp = approximately Cv
Ideal Monatomic: U = 3/2 RT
Cp= 5/2R Cv= 3/2R
Extent of Reaction ξ “xi” (moles)
The extent to which a reaction proceeds
Positive if in forward reaction
Negative if in reverse reaction
How to find Limiting Reagents with Extent of Reaction
1. Find ξLR for every reactant
2. Pick the smallest ξLR
3. ni= 0 (because LR will be 0) = ni,o + Vi ξLR
Limiting Reagent
The compound that gets completely consumed in the reaction
Enthalpy of Reaction
The amount of heat released or absorbed when a mole of matter is transformed by a chemical reaction at Standard State Conditions

∆rH°=(dH/dξ)T,P

Standard State Conditions (°)
*Temperature isn’t part of SSC
Liquids: pure at 1 bar pressure
Solids: pure at 1 bar pressure
Gases: ideal at 1 bar pressure (No interactions between molecules)
Solutions: ideal solutions with 1 molality at 1 bar pressure (All interactions are the same)
Molarity vs Molality
Molarity = moles solute/liters of solution
Easier to do, temperature dependent

Molality= moles of solute/kg of solvent
Temperature independent

ai
species is dissociated as ions in solution
ao
species does not dissociate further into ions
∆rH Reaction
Reactants –> Products (exo/endo)
∆fH Formation
Elements –> 1 mole of compound (exo/endo) (majority is exo)
∆fusH Fusion
Solid –> Liquid (endo)
∆freH Freezing
Liquid –> Solid (exo)
∆vapH Vaporization
Liquid –> Gas (endo)
∆conH Condensation
Gas –> Liquid (exo)
∆subH Sublimation
Solid –> Gas (endo)
∆depH Deposition
Gas –> Solid (exo)
∆trsH Transition
Phase α –> Phase β (both exo and endo)
∆mixH Mixing
Pure Substances –> Mixture (both exo and endo)
∆solH Solution or Solvation
Solute and Solvent –> Solution (both exo and endo)
∆cH Combustion
1 Mole of Compound + O2 (exo)
CO2 + H2O + N2 + Others
Allotropes
Different molecular arrangements of a given element
ex) C (gr), C (dia)
Thermodynamic reference state
Element in its most stable phase and allotropic form at the temperature of interest
Formation Reactions (Enthalpy of Formations)
One mole of the compound of interest is made from its constituent elements in their most stable allotropic form and phase at the temperature of interest
Endothermic
∆H > 0 energy entering the system (intensive quantity, multiply by moles of extent of reaction to make extensive)
Exothermic
∆H < 0 energy leaving the system (intensive quantity, multiply by moles of extent of reaction to make extensive)
Hess’s Law
An observation that enthalpy is a state function calculating enthalpy changes at non-tabulated temperatures
Homonuclear Diatomics
HOFBrINCl
Finding Enthalpies of Reaction at a different temperature
MAMA BEAR: ∆rH°(T2) = ∆rH°(T1) + ∫(T1-T2) ∆rCp°dT
BABY BEAR: ∆rCp° = 0 then ∆rH°(T2) = ∆rH°(T1)
∆rCp° do the integral?
Calorimetry
A chemical reaction is run under adiabatic conditions (no heat transfer). Interconversion of chemical and thermal energy
Bomb Calorimetry Paths
Use internal energy (U) and Cv,tot
Solution Calorimetry Paths
Use enthalpy at standard state conditions (H°)
Cp°tot equals Cp°solution (mass x heat capacity) + Cp°instrument
Entropy (S)
Measure of the dispersal of energy in a system. As entropy increases there is more dispersal of energy. ∆S is a state function on any reversible path

∆vS°=SUM N – i=1 ViSi

Second Law of Thermodynamics
Take Zero: It is impossible to produce useful work from a heat engine connected to a single heat reservoir

Take One: in a spontaneous process, energy moves from being more “concentrated” to being more spread out and dispersed
-physically dispersed: light, high KE molecules dispersed over more available energy states

Take Two:
In a spontaneous process ∆S universe > 0 (irreversible)
In an equilibrium process ∆S universe = 0 (reversible)
An impossible process is one where ∆S universe < 0 ∆S is greater than or equal to 0 ∆S universe = ∆S system + ∆S surroundings

∆S in connection to q
Extensive: ∆S = q/T
Paths of Entropy/Energy Dispersal
Translations
Rotations
Intermolecular Forces
Vibrations
Electronic Energy
Carnot Cycle
– Ideal reversible closed thermodynamic cycle in which the working substance goes through isothermal and adiabatic paths to initial state. A heat engine converts thermal energy (heat) into useful work.

– Overall, ∆S = 0 is state function, and ∆U = 0

– Most efficient cycle that can be made!

Efficiency for Carnot Cycle ONLY
E = 1 – Tc/Th
Thermodynamic Definition of Temperature
Zero Kelvin is the temperature at which a reversible heat engine runs with perfect efficiency (can never achieve 0 K)

This sets the zero of our temperature scale! The triple point of water. Ttr = 273.16 K

How to calculate entropy changes in irreversible path
Find a different reversible path between the same states
How do we measure entropy of a system?
1. Think about enthalpy on an isobaric path. dH=CpdT
2. On an isobaric path dS=đq/T = Cpdt/T

Cpdt/T vs T graph gives us ∆S

Debye Function
used to model Cp at low temperatures. Find “a” using the lowest experimental Cp(T) value.
Cp=aT^3
Trouton’s Rule
∆vapS = 88 ± 5 J/molK

Example of an exception…
∆vapS of water is approximately 110 J/molK liquid H-bonding limits energy dispersal

In liquid water, hydrogen bonding limits the amount of translations and rotations the molecule can have. Thus, the jump to the gas phase is an even bigger jump in dispersal of energy.

Third Law of Thermodynamics (Nernst)
For reactions and phase transitions lim∆rS=0 as T approaches 0K
Third Law of Thermodynamics (Planck)
The entropy of a pure substance in perfect crystalline form is 0 J/molK at zero Kelvin
Third Law Reference of Entropy
Absolute Entropy at 0K = 0 J/molK
Reference for Enthalpy
formation reactions where we compare relative elements in their most stable phase and allotropic form at the temperature of interest
Forms of Energy
gravitational potential energy (PE)
electrical PE
chemical PE
thermal energy
sound
kinetic energy