C2301 Final Flashcards
Thermodynamics
Describes a system at macroscopic scale with respect to its bulk properties
Volume
Amount of space an object occupies or enclosed in a container
Pressure
Force exerted by a gas per unit area on the walls of a container
Pressure Units (4)
- Pascal
- Bar
- Atm
- Psi
Temperature
Average translational kinetic energy of a sample of molecules
Adiabatic boundary
Prevents heat transfer
Boyle’s Law, Charle’s Law, Avogadro’s Principle
Boyle: PV constant at constant n,T
Charle’s: V=constant x T, at constant n,P
Same for P
Avogadro: V=constant x n, at constant P, T
Ideal Gas Law
PV=nRT
Isotherm
P vs. V at constant T
Isobar
V vs. T at constant P
Isochor
P vs. T at constant V
Surface Plots
A 3D plot of P vs. V vs. T.
Combined Gas Law
P1V1/n1T1=P2V2/n2T2
Thermodynamic System
region of the universe with defined boundaries with which we study
Open system
Exchange matter and energy with surroundings
Closed system
Exchanges only matter
Isolated system
cannot exchange energy or matter
Extensive variables
Physical properties of a substance which depend on the amount of material present
Intensive Variables
Independent of amount of material present
Examples of extensive variables
V, mass, n, heat capacity, H, U, S, G, A
Examples of Intensive Variables
T, hardness, boiling point, density, concentration
Properties of Ideal Gases (4)
- Particles are point masses with no volume
- Exert no attractive or repulsive force on each other
- Obey ideal gas law exactly
- Infinitely compressible
Properties of Real Gases (6)
- Particles have a finite volume (cannot be infinitely compressed)
- Exert attractive and repulsive forces on each other
- Closely obey PV=nRT at low pressure and high temps
- Boyle T: repulsive and attractive forces cancel and the gas obeys ideal gas law exactly.
- At high P and low T molecular interactions cannot be ignored.
- Can be liquefied using pressure
What forces dominate at low P
Attraction
2 Points to remember about attraction
- As molecules come closer, attraction increase and decrease the potential energy
- At further separation distances, repulsions increase in strength and increase the potential energy
What are the two specific terms to the van der Waals equation and what do they represent/correct for?
a: relative strength of attractive intermolecular forces; corrects for reduction in P due to IM forces
b: total effective volume per mole of gas; corrects for size of molecule
Observations from the vDw eqn (4)
- Ideal gas law does not work well for high pressures
- Observed pressures are less than ideal pressures — attraction dominaes
- vDw eqn describes well up to 100bar
- As P increases, vDw does not work well, but it works better than the ideal gas law
What is a characteristiv of the Redlich-Kwong equation?
Sqrt(T) term
What is characteristic of the Beattie-Bridgman eqn?
A and B constants
What series does the virial equation employ?
Power series
Vapour Pressure
equilibrium pressure of a vapour above its liquid or solid
Phase Diagrams
P vs. T; show co-existence curves in which states exist at which pressure and T
Name of the 3 co-existence curves in a phase diagram
- Fusion curve
- Vaporization curve
- Sublimation curve
Triple Point
Equilibrium between solid, liquid, and vapour phases
Critical point
The point of critical temperature and pressure
Supercritical fluid
A state beyond the critical point where no distinct phase exists between a gas and liquid.
Properties of SCF (5)
- Effuse through solids (gas)
- Solvent properties (liquid)
- Small changes in P or T elicit large changes in density
- High heat capacities and compressibilities
- Low viscosities
Examples of supercritical fluid applications (2)
- scCO2 reduction
- Caffeine extraction
- scH2O is a green solvent
Why do SCFs not form hydrogen bonds?
The molecules have too much translational KE such that the H bonds easily break.
Compressibility Factor, Z
Describe how large the errors are; i.e. how far does the ideal gas law deviate from the van der Waals
When does Z=1 for a real gas?
At the Boyle Temperature
What dominates when Z<1?
Attraction
What dominates if Z>1?
Repulsion
Why does N have a low Z at low pressure but high Z at high P (isothermal)?
At low P, T drops and molecules have less KE to overcome attraction; i.e. gas becomes more compressible and Z decreases.
At high P, V is small; molecules are closer together which increases repulsions and Z.
What are reduced variables?
The quantity divided by their critical value
Why are reduced variables used?
To create a generality that does not depend on the arbitrary constants in the VdW eqn.
What are the 2 parts of the Law of Corresponding states?
- All gases with the same reduced T and P are in corresponding states; should occupy same reduced volume.
- This is useful in predicting experimental behaviour. All gases in corresponding states should have same Z.
What are the 5 ways that internal energy is described?
- Translational KE
- PE
- Molecular vibrations/rotations
- E stored in chemical bonds
- PE of interactions between molecules
First Formulation of the First Law
The internal E of a system is constant
Second Formulation of the First Law
In a closed or isolated system with no chemical reactions, E can only flow with the exchange of heat and work.
dU=q+w
System
part of the world of interest
Surroundings
Region directly adjacent to the system
Heat
The amount of E that flows across a boundary between the system and surroundings because of a T difference
3 Ways heat is transferred
- Conduction
- Convection
- Radiation
Transitory
Only appears during a change of state of the system (not related to initial/final)
Work
Any action that transfers E across the boundary between system and surroundings
Energy
Capacity of a system to do work
What quantities are transitory?
Heat and work
What quantity is non-transitory?
Energy
Reversible Process
System and environment can be restored to the same initial conditions from before the process occurred.
Irreversible Process
System and environment cannot be restored to their original states
Path Function
Depends on the path taken to arrive at the systems present state
State Functions
Pathway independent and have values determined by the state of the system
Boltzmann Distribution
Relative probability of finding a molecule/atom/electron in a specific energy state
Degrees of Freedom
Number of variables needed to describe motion of a particle completely
How many degrees of freedom for translational motion?
3 (x,y,z)
How many degrees of freedom for rotational motion?
2 (linear) or 3 (nonlinear)
Degrees of freedom for vibrational motion
Linear: 3N-5
Non-Linear: 3N-6
What are the 2 common experimental conditions to investigate with heat and what are they called?
Heat at constant P, qp, enthalpy
Heat at constant V, qV, internal energy
Heat Capacity
The measure of E needed to change the T of a substance a given amount (material and T dependent)
Shomate Equation
Describes the heat capacity of a substance at a specific T using curve fitting.
What is the relation between Cp and Cv for an Ideal Gas?
Cp=Cv+R
Why is Cp>Cv for gases?
At constant P, gas expands as T increases, and system does work on surroundings. As a consequence, not all of the heat flow into the system is used to increase dU. No work occurs at Cv, and all heat is used to increase dU.
What is the relation between Cp and Cv for liquids and solids?
Cp is approximately equal to Cv
Endothermic Process
heat flows into system from surroundings
Exothermic Process
heat flows out of system into surroundings
Define enthalpy
Enthalpy is the heat transfer by a system for a process occurring at constant P.
Internal Energy relation to Cv
dU=qv=CvdT
Enthalpy relation to Cp
dH=qp=CpdT
What is an assumption made when related enthalpy to Cp?
They are only valid if no chemical reactions or phase changes occur
Reversible adiabatic compression of a gas leads to heating or cooling?
Heating
Reversible adiabatic expansion of a gas leads to heating or cooling?
Cooling
Thermochemistry
Branch of thermo concerned with heat flow into or out of a reaction system
What do we consider E stored in chemical bonds?
Potential E
What are standard state conditions?
1atm, 25C, 1M
Standard Enthalpy of Reaction
Refers to the reaction of 1 mol of specified reaction at standard state
Standard Enthalpy of Formation
Enthalpy change of a reaction in which only 1 mol of the species of interest, with only pure elements in their most stable state are reactants, under standard state conditions.
Generalized enthalpy reaction of the following equation:
aA+bB = cC+dD
drH=c(dfH C)+d(dfH D) - a(dfH A) - b (dfH B)
Hess’s Law
The enthalpy change for any sequence of chemical reactions that sum to the overall reaction is the sum of the enthalpies of each individual reaction step.
Reaction Enthalpies not at Standard State
dH(T)=dH(298.15K)+ int(dCp(T))dT
What is constant during bomb calorimetry and what is measured?
Constant volume, dU
What is the main use for bomb calorimetry?
Determining the caloric content of food
How is the calorimeter constant determined in bomb calorimetry?
Use of a standard of known molar enthalpy of combustion, usually benzoic acid
Equation to calculate dH in bomb calorimetry (assuming we have already calculated dU)
dcH=dcU+d(PV)
What is another name of the constant pressure calorimeter?
Coffee-cup calorimeter
What type of enthalpy reactions are typically studied in constant pressure calorimetry?
Solvation
List the name of all phase changes.
- Melting: s - l
- Freezing: l - s
- Vaporization: l - g
- Condensation: g - l
- Sublimation: s - g
- Deposition: g - s
- Ionization: g - p
- Recombination: p - g
How is the enthalpy of sublimation related to the other enthalpies of phase changes?
dsubH=dmeltH+dvapH
What variable represents the isobaric volumetric thermal expansion coefficient and what is it equal to?
alpha, a=(1/V)(dV/dT)
What is the name of the variable kappa_T and what is the equation?
Isothermal compressibility,
kappa_T=(-1/V)(dV/dP)
Relation of partial differentials to exact differentials
Let b represent the symbol for a partial differential.
df=(bf/bx)dx+(bf/by)dy
How can the internal energy be written in terms of differentials (not necessarily exact)?
dU=d-q+PextdV
where d-q is an inexact differential
Relation of heat capacity at constant volume
dU/dT=Cv
What is the name of the relation defined by:
dU/dV=T(dP/dT)-P
Internal Pressure
Joule Experiment
Attempted to measure dU/dV for an ideal gas.
Joule experiment setup
Two interacting systems in a rigid adiabatic enclosure, with system 1 being the water bath and 2 being the volume within 2 vessels.
Joule-Thomson experiment
Seeks to measure dH/dV, far more accurate than the Joule experiment
Joule-Thomson experiment setup/process
Gas at initial P,V,T conditions flows from a high P cylinder into a low pressure cylinder. Gas is forced through a porous plug in which piston moves to maintain a constant P in each region. This causes a P drop across the plug and the T change is measured.
What is the name of a process occurring at constant enthalpy?
Isenthalpic
What is u_J-T?
Joule-Thomson coefficient
Limiting ratio of dT and dP
What dominates at positive u_J-T?
Attraction
What dominates at negative u_J-T?
Repulsions
What is the temperature at which the Joule-Thomson coefficient is 0?
Inversion Temperature
What approximation can be made for U and H for solids and liquids?
They can be considered a function of T alone
What is the direction of evolution of a system known as?
Spontaneous direction
What are the 2 formulations of the 2nd law?
- It is impossible for a system to undergo a cyclic process that turns all heat completely into work done on the surroundings.
- It is impossible for a process to occur that has the sole effect of removing a quantity of heat from an object at a lower T and transferring it to an object at a higher temperature.
Classical definition of entropy
Entropy is the amount of work not available to do work
What is the entropy for a cyclic process that is entirely reversible, and is this feasible?
dS=0, not feasible
Equation definition of entropy
dS=dqrev/T
Formal definition of the 2nd law
For any process proceeding in an isolated system, there is a unique direction of spontaneous change and dS>0 for the spontaneous process.
Is expansion of compression spontaneous?
Expansion
What is the equation representation of entropy for phase changes?
dvapS=dvapH/Tvap
Statistical definition of entropy
Measure of the degree to which energy is dispersed into the available E levels associated with random molecular motion.
Point
E spreads out more easily when the energy gap between adjacent levels is small.
Single particle microstate
Any particular E state of a single molecule; quantized unit combined trans, rot, and vib E states
N-particle microstate
Any quantized state of a whole system of molecules. Collection of single particle microstates.
What are the 5 rules for entropy and the number of N-particle microstates?
- At any given instant in time, total E of the system is dispersed throughout one N-particle microstate.
- In the next instant in time, total E is dispersed throughout a different N-particle microstate of equal energy
- Each accessible equal E N-particle microstate is equally possible
- Number of single particle microstates is large, the number of N-particle microstates is enormous
- Under a given set of conditions, the number of accessible N-particle microstates is the number of ways its thermal E can be dispersed among the different E levels of all its molecules
What is the Ludwig Boltzmann entropy equation?
S=kBln(omega)
If dS is positive, the system has changed from:
smaller number of N-particle microstates to larger number of N-particle microstates
As T increases, molecules have more energy and can populate higher E levels, causing:
Increase number of accessible N-particle microstates
What is the condition for entropy decrease in a system?
dStotal>0
Any process that occurs in the universe is spontaneous and leads to an increase of Stotal. What is this concept often referred to as?
TIme’s Arrow
3rd Law of Thermodynamics
The entropy of a pure, perfectly crystalline substance is 0 at 0K.
What is the number of microstates in a perfectly crystalline substance?
1
Residual entropy
Entropy at 0K for crystals that are not perfectly crystalline
What is the significance of entropy changes in chemical reactions?
They are important in determining equilibrium concentrations in a reaction.
How do absolute entropies differ from enthalpies?
Entropies of pure substances are not zero in their reference state.
What is the cyclic process in heat engines? (4 steps)
- Fuel intake
- Ignition and expansion
- Exhaust
- Compression
Can heat or work be entirely converted to the other?
Work
Does compression or expansion determine the max work for a reversible process?
Expansion
What is a carnot plot and how can it be used to determine the work of the cycle?
Cyclic plot of P vs. t of each of the 4 steps (isothermal compression, adiabatic expansion, isothermal expansion, and adiabatic compression). The area of the plot is the work done by the cycle.
What is the efficiency of a Carnot cycle?
Ratio of work output to the heat withdrawn from the reservoir.
e=-wcycle/qab
What is the work for each segment of the Carnot cycle (ideal gas)
Expansions: w<0
Compressions: w>0
The Clausius Inequality
TdS>=dq (reversible)
dS>dq/T (irreversible)
Hemholtz Energy
A=(U-TS)
Total exapansive and non-expansive work (total max work)
What is the formula for change in Hemholtz E?
dA=dU-TdS
Gibb’s Energy
Total maximum non-expansive work possible.
When is a system at equilibrium?
dA=0
When is GIbb’s E spontaneous?
dG<=0
Summarize: what do each of U, H, A, and G measure?
U: all kinetic and potential E.
H: heat flow into or out of system.
A: maximum total work a process can generate.
G: maximum non-expansive work a process can generate.
Summary of equations for U, H, A, and G (non-differential)
U=q+w
H=U+PV
A=U-TS=H-PV-TS
G=H-TS=U+PV-TS
Summary of equations of U, H, A, and G (differential form)
dU=tdS-PdV
dH=TdS-PdV+PdV+VdP=TdS+VdP
dA=TdS-PdV-TdS-SdT=-SdT-PdV
dG=TdS+VdP-TdS-SdT=-SdT+VdP
What quantities is each of U, H, A, and G dependent on (a result of the differential equations)
U (S,V)
H (S,P)
A (T,V)
G (T, P)
Maxwell relations (briefly explain)
State how U, H, A, and G vary with their natural state variables.
Does G increase or decrease with increase in T and P?
Decreases with increase in T, increase with increase in P
Chemical Potential
Change in Gibbs E of a mixture per mole of substance added at constant concentration.
Or, the chemical potential is the tendency of the system to donate a particle.
What is the Gibbs E of mixing?
Gfinal-Ginitial
What is the entropy of mixing?
dmixS=-dmixG/dT
What is the enthalpy of mixing?
dmixH=dmixG+TdmixS
What is the extent of reaction?
The number of moles the reaction is allowed to proceed to the right
What is the name of the conditions where the differential of Gibbs E of reaction in respect to the extent of reaction is 0?
Equilibrium position
In a simple reaction, what are the two contributions to Gibbs E?
- Unmixed substances
- Mixing
For what conditions does the differential of the Hemholtz E in respect to the extent of reaction equalling 0 correspond to an equilibrium position?
Constant V and T
Relation of Gibbs E and equilibrium constant
drG=-RTlnQp
What is the relation between Qp and Kp?
Kp is the special case of Qp where the reaction is at equilibrium and is called the thermodynamic equilibrium constant
Chemical Kinetics
Study of the rates and mechanisms of chemical reactions
Reaction Rate
Change in the extent of reaction with time
Rate of Reaction
in respect to the change in the number of moles of a given species with time
What must be assumed to discuss rate laws?
The reaction is homogeneous
True or False: the reaction order is related to stoichiometric coefficients.
False
How must all rate laws be determined?
Experimentally
Rate constant, k
Proportionality constant between the concentrations of reactants and the reaction rate.
General formula for the units of a rate constant in relation to the overall order, n
M^(1-n)s-1
What are the 2 methods for determining reaction orders? Briefly describe each.
- Isolation method: all reagents are provided in excess but one. The order with respect to that reagent can be determined.
- Method of Initial Rates: the concentration of a single reagent is changed while all others are held constant and initial rate is determined.
How do we measure the rate of a reaction? (2 categories)
- Chemical methods: chemical rxn initiated and periodically samples are taken out of rxn mixture and manipulated to terminate the rxn.
- Physical methods: a physical property of the system is measured/monitored as the rxn proceeds.
Reaction mechanism
Collection of individual kinetic processes or elementary steps involved in the transformation of reactants to products.
Elementary reaction steps
Single steps and a pathway/mechanism may contain one or more of these
Molecularity
Stoichiometric quantity of reactants involved (i.e. unimolecular has 1 reactant, bimolecular has 2, etc.)
When are the order and molecularity equivalent?
For elementary reaction steps
Integrated rate law expressions
Provide a predicted temporal evolution of the reactant/product concentrations that can be used in lieu of known rate expressions.
How can a first order rate law be expressed? (Choose linearly convenient form)
ln[A]=ln[A]0-kt
Half-Life
time for reactant concentration to decrease to half its initial value.
Half-life for first order equation?
t1/2=ln2/k
What is half life independent of?
Initial concentration
Second Order Type 1 Reaction
A reaction that is second order with respect to 1 reactant.
Second Order Type 2 Reaction
A reaction with 2 reactants that is 2nd order overall but first order with respect to each reactant.
What is the rate law for second order type 1?
1/[A]=1/[A]0+kefft
What is the effective rate constant?
keff=2k. Used for Second order type 1 reactions.
Half-life for second order type 1
t1/2=1/keff[A]0
Why are second order reactions dependent on [A]0?
Bimolecular reactions are dependent on the number of successful collisions taking place.
Rate law for second order type 2
1/[B]0-[A]0*ln([B]/[B]0/[A]/[A]0)=kt
What is the half life for second order type 2 reactions?
Concept of half-life does not exist.
Sequential First Order Reactions
Reactions that occur in a series of steps in which reactants are transformed into intermediate species until achieving a stable product
Intermediate
A product of one sequential step that is consumed in another
Maximum Intermediate species concentration eqn
tmax=(1/KA-kI)*ln(kA/kI)
Rate determining step
If one step is significantly slower than the other, it determines the rate of reaction
Euler’s Method in the Steady State Approximation
Determines the concentrations numerically as a function of time
Steady state approximation
When intermediate reactions are rapid, very little intermediate species will be detected in solution. Thus, the concentration of intermediate with respect to time can be considered 0.
When is the steady state approximation valid?
When the intermediate decay rate is greater than the rate of production
Yield (Kinetics)
Probability that a given product will be formed by the decay of the reactant
Arrhenius Expression
k=Ae^-Ea/RT
Graphical form of Arrhenius equation
ln(k)=ln(A)-Ea/RT
Apparent rate constant eqn
kapp=kA+kB