C2301 Final Flashcards
1
Q
Thermodynamics
A
Describes a system at macroscopic scale with respect to its bulk properties
2
Q
Volume
A
Amount of space an object occupies or enclosed in a container
3
Q
Pressure
A
Force exerted by a gas per unit area on the walls of a container
4
Q
Pressure Units (4)
A
- Pascal
- Bar
- Atm
- Psi
5
Q
Temperature
A
Average translational kinetic energy of a sample of molecules
6
Q
Adiabatic boundary
A
Prevents heat transfer
7
Q
Boyle’s Law, Charle’s Law, Avogadro’s Principle
A
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
8
Q
Ideal Gas Law
A
PV=nRT
9
Q
Isotherm
A
P vs. V at constant T
10
Q
Isobar
A
V vs. T at constant P
11
Q
Isochor
A
P vs. T at constant V
12
Q
Surface Plots
A
A 3D plot of P vs. V vs. T.
13
Q
Combined Gas Law
A
P1V1/n1T1=P2V2/n2T2
14
Q
Thermodynamic System
A
region of the universe with defined boundaries with which we study
15
Q
Open system
A
Exchange matter and energy with surroundings
16
Q
Closed system
A
Exchanges only matter
17
Q
Isolated system
A
cannot exchange energy or matter
18
Q
Extensive variables
A
Physical properties of a substance which depend on the amount of material present
19
Q
Intensive Variables
A
Independent of amount of material present
20
Q
Examples of extensive variables
A
V, mass, n, heat capacity, H, U, S, G, A
21
Q
Examples of Intensive Variables
A
T, hardness, boiling point, density, concentration
22
Q
Properties of Ideal Gases (4)
A
- Particles are point masses with no volume
- Exert no attractive or repulsive force on each other
- Obey ideal gas law exactly
- Infinitely compressible
23
Q
Properties of Real Gases (6)
A
- 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
24
Q
What forces dominate at low P
A
Attraction
25
2 Points to remember about attraction
1. As molecules come closer, attraction increase and decrease the potential energy
2. At further separation distances, repulsions increase in strength and increase the potential energy
26
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
27
Observations from the vDw eqn (4)
1. Ideal gas law does not work well for high pressures
2. Observed pressures are less than ideal pressures --- attraction dominaes
3. vDw eqn describes well up to 100bar
4. As P increases, vDw does not work well, but it works better than the ideal gas law
28
What is a characteristiv of the Redlich-Kwong equation?
Sqrt(T) term
29
What is characteristic of the Beattie-Bridgman eqn?
A and B constants
30
What series does the virial equation employ?
Power series
31
Vapour Pressure
equilibrium pressure of a vapour above its liquid or solid
32
Phase Diagrams
P vs. T; show co-existence curves in which states exist at which pressure and T
33
Name of the 3 co-existence curves in a phase diagram
1. Fusion curve
2. Vaporization curve
3. Sublimation curve
34
Triple Point
Equilibrium between solid, liquid, and vapour phases
35
Critical point
The point of critical temperature and pressure
36
Supercritical fluid
A state beyond the critical point where no distinct phase exists between a gas and liquid.
37
Properties of SCF (5)
1. Effuse through solids (gas)
2. Solvent properties (liquid)
3. Small changes in P or T elicit large changes in density
4. High heat capacities and compressibilities
5. Low viscosities
38
Examples of supercritical fluid applications (2)
1. scCO2 reduction
2. Caffeine extraction
3. scH2O is a green solvent
39
Why do SCFs not form hydrogen bonds?
The molecules have too much translational KE such that the H bonds easily break.
40
Compressibility Factor, Z
Describe how large the errors are; i.e. how far does the ideal gas law deviate from the van der Waals
41
When does Z=1 for a real gas?
At the Boyle Temperature
42
What dominates when Z<1?
Attraction
43
What dominates if Z>1?
Repulsion
44
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.
45
What are reduced variables?
The quantity divided by their critical value
46
Why are reduced variables used?
To create a generality that does not depend on the arbitrary constants in the VdW eqn.
47
What are the 2 parts of the Law of Corresponding states?
1. All gases with the same reduced T and P are in corresponding states; should occupy same reduced volume.
2. This is useful in predicting experimental behaviour. All gases in corresponding states should have same Z.
48
What are the 5 ways that internal energy is described?
1. Translational KE
2. PE
3. Molecular vibrations/rotations
4. E stored in chemical bonds
5. PE of interactions between molecules
49
First Formulation of the First Law
The internal E of a system is constant
50
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
51
System
part of the world of interest
52
Surroundings
Region directly adjacent to the system
53
Heat
The amount of E that flows across a boundary between the system and surroundings because of a T difference
54
3 Ways heat is transferred
1. Conduction
2. Convection
3. Radiation
55
Transitory
Only appears during a change of state of the system (not related to initial/final)
56
Work
Any action that transfers E across the boundary between system and surroundings
57
Energy
Capacity of a system to do work
58
What quantities are transitory?
Heat and work
59
What quantity is non-transitory?
Energy
60
Reversible Process
System and environment can be restored to the same initial conditions from before the process occurred.
61
Irreversible Process
System and environment cannot be restored to their original states
62
Path Function
Depends on the path taken to arrive at the systems present state
63
State Functions
Pathway independent and have values determined by the state of the system
64
Boltzmann Distribution
Relative probability of finding a molecule/atom/electron in a specific energy state
65
Degrees of Freedom
Number of variables needed to describe motion of a particle completely
66
How many degrees of freedom for translational motion?
3 (x,y,z)
67
How many degrees of freedom for rotational motion?
2 (linear) or 3 (nonlinear)
68
Degrees of freedom for vibrational motion
Linear: 3N-5
Non-Linear: 3N-6
69
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
70
Heat Capacity
The measure of E needed to change the T of a substance a given amount (material and T dependent)
71
Shomate Equation
Describes the heat capacity of a substance at a specific T using curve fitting.
72
What is the relation between Cp and Cv for an Ideal Gas?
Cp=Cv+R
73
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.
74
What is the relation between Cp and Cv for liquids and solids?
Cp is approximately equal to Cv
75
Endothermic Process
heat flows into system from surroundings
76
Exothermic Process
heat flows out of system into surroundings
77
Define enthalpy
Enthalpy is the heat transfer by a system for a process occurring at constant P.
78
Internal Energy relation to Cv
dU=qv=CvdT
79
Enthalpy relation to Cp
dH=qp=CpdT
80
What is an assumption made when related enthalpy to Cp?
They are only valid if no chemical reactions or phase changes occur
81
Reversible adiabatic compression of a gas leads to heating or cooling?
Heating
82
Reversible adiabatic expansion of a gas leads to heating or cooling?
Cooling
83
Thermochemistry
Branch of thermo concerned with heat flow into or out of a reaction system
84
What do we consider E stored in chemical bonds?
Potential E
85
What are standard state conditions?
1atm, 25C, 1M
86
Standard Enthalpy of Reaction
Refers to the reaction of 1 mol of specified reaction at standard state
87
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.
88
Generalized enthalpy reaction of the following equation:
aA+bB = cC+dD
drH=c(dfH C)+d(dfH D) - a(dfH A) - b (dfH B)
89
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.
90
Reaction Enthalpies not at Standard State
dH(T)=dH(298.15K)+ int(dCp(T))dT
91
What is constant during bomb calorimetry and what is measured?
Constant volume, dU
92
What is the main use for bomb calorimetry?
Determining the caloric content of food
93
How is the calorimeter constant determined in bomb calorimetry?
Use of a standard of known molar enthalpy of combustion, usually benzoic acid
94
Equation to calculate dH in bomb calorimetry (assuming we have already calculated dU)
dcH=dcU+d(PV)
95
What is another name of the constant pressure calorimeter?
Coffee-cup calorimeter
96
What type of enthalpy reactions are typically studied in constant pressure calorimetry?
Solvation
97
List the name of all phase changes.
1. Melting: s - l
2. Freezing: l - s
3. Vaporization: l - g
4. Condensation: g - l
5. Sublimation: s - g
6. Deposition: g - s
7. Ionization: g - p
8. Recombination: p - g
98
How is the enthalpy of sublimation related to the other enthalpies of phase changes?
dsubH=dmeltH+dvapH
99
What variable represents the isobaric volumetric thermal expansion coefficient and what is it equal to?
alpha, a=(1/V)(dV/dT)
100
What is the name of the variable kappa_T and what is the equation?
Isothermal compressibility,
kappa_T=(-1/V)(dV/dP)
101
Relation of partial differentials to exact differentials
Let b represent the symbol for a partial differential.
df=(bf/bx)dx+(bf/by)dy
102
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
103
Relation of heat capacity at constant volume
dU/dT=Cv
104
What is the name of the relation defined by:
dU/dV=T(dP/dT)-P
Internal Pressure
105
Joule Experiment
Attempted to measure dU/dV for an ideal gas.
106
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.
107
Joule-Thomson experiment
Seeks to measure dH/dV, far more accurate than the Joule experiment
108
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.
109
What is the name of a process occurring at constant enthalpy?
Isenthalpic
110
What is u_J-T?
Joule-Thomson coefficient
Limiting ratio of dT and dP
111
What dominates at positive u_J-T?
Attraction
112
What dominates at negative u_J-T?
Repulsions
113
What is the temperature at which the Joule-Thomson coefficient is 0?
Inversion Temperature
114
What approximation can be made for U and H for solids and liquids?
They can be considered a function of T alone
115
What is the direction of evolution of a system known as?
Spontaneous direction
116
What are the 2 formulations of the 2nd law?
1. It is impossible for a system to undergo a cyclic process that turns all heat completely into work done on the surroundings.
2. 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.
117
Classical definition of entropy
Entropy is the amount of work not available to do work
118
What is the entropy for a cyclic process that is entirely reversible, and is this feasible?
dS=0, not feasible
119
Equation definition of entropy
dS=dqrev/T
120
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.
121
Is expansion of compression spontaneous?
Expansion
122
What is the equation representation of entropy for phase changes?
dvapS=dvapH/Tvap
123
Statistical definition of entropy
Measure of the degree to which energy is dispersed into the available E levels associated with random molecular motion.
124
Point
E spreads out more easily when the energy gap between adjacent levels is small.
125
Single particle microstate
Any particular E state of a single molecule; quantized unit combined trans, rot, and vib E states
126
N-particle microstate
Any quantized state of a whole system of molecules. Collection of single particle microstates.
127
What are the 5 rules for entropy and the number of N-particle microstates?
1. At any given instant in time, total E of the system is dispersed throughout one N-particle microstate.
2. In the next instant in time, total E is dispersed throughout a different N-particle microstate of equal energy
3. Each accessible equal E N-particle microstate is equally possible
4. Number of single particle microstates is large, the number of N-particle microstates is enormous
5. 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
128
What is the Ludwig Boltzmann entropy equation?
S=kBln(omega)
129
If dS is positive, the system has changed from:
smaller number of N-particle microstates to larger number of N-particle microstates
130
As T increases, molecules have more energy and can populate higher E levels, causing:
Increase number of accessible N-particle microstates
131
What is the condition for entropy decrease in a system?
dStotal>0
132
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
133
3rd Law of Thermodynamics
The entropy of a pure, perfectly crystalline substance is 0 at 0K.
134
What is the number of microstates in a perfectly crystalline substance?
1
135
Residual entropy
Entropy at 0K for crystals that are not perfectly crystalline
136
What is the significance of entropy changes in chemical reactions?
They are important in determining equilibrium concentrations in a reaction.
137
How do absolute entropies differ from enthalpies?
Entropies of pure substances are not zero in their reference state.
138
What is the cyclic process in heat engines? (4 steps)
1. Fuel intake
2. Ignition and expansion
3. Exhaust
4. Compression
139
Can heat or work be entirely converted to the other?
Work
140
Does compression or expansion determine the max work for a reversible process?
Expansion
141
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.
142
What is the efficiency of a Carnot cycle?
Ratio of work output to the heat withdrawn from the reservoir.
e=-wcycle/qab
143
What is the work for each segment of the Carnot cycle (ideal gas)
Expansions: w<0
Compressions: w>0
144
The Clausius Inequality
TdS>=dq (reversible)
dS>dq/T (irreversible)
145
Hemholtz Energy
A=(U-TS)
Total exapansive and non-expansive work (total max work)
146
What is the formula for change in Hemholtz E?
dA=dU-TdS
147
Gibb's Energy
Total maximum non-expansive work possible.
148
When is a system at equilibrium?
dA=0
149
When is GIbb's E spontaneous?
dG<=0
150
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.
151
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
152
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
153
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)
154
Maxwell relations (briefly explain)
State how U, H, A, and G vary with their natural state variables.
155
Does G increase or decrease with increase in T and P?
Decreases with increase in T, increase with increase in P
156
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.
157
What is the Gibbs E of mixing?
Gfinal-Ginitial
158
What is the entropy of mixing?
dmixS=-dmixG/dT
159
What is the enthalpy of mixing?
dmixH=dmixG+TdmixS
160
What is the extent of reaction?
The number of moles the reaction is allowed to proceed to the right
161
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
162
In a simple reaction, what are the two contributions to Gibbs E?
1. Unmixed substances
2. Mixing
163
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
164
Relation of Gibbs E and equilibrium constant
drG=-RTlnQp
165
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
166
Chemical Kinetics
Study of the rates and mechanisms of chemical reactions
167
Reaction Rate
Change in the extent of reaction with time
168
Rate of Reaction
in respect to the change in the number of moles of a given species with time
169
What must be assumed to discuss rate laws?
The reaction is homogeneous
170
True or False: the reaction order is related to stoichiometric coefficients.
False
171
How must all rate laws be determined?
Experimentally
172
Rate constant, k
Proportionality constant between the concentrations of reactants and the reaction rate.
173
General formula for the units of a rate constant in relation to the overall order, n
M^(1-n)s-1
174
What are the 2 methods for determining reaction orders? Briefly describe each.
1. Isolation method: all reagents are provided in excess but one. The order with respect to that reagent can be determined.
2. Method of Initial Rates: the concentration of a single reagent is changed while all others are held constant and initial rate is determined.
175
How do we measure the rate of a reaction? (2 categories)
1. Chemical methods: chemical rxn initiated and periodically samples are taken out of rxn mixture and manipulated to terminate the rxn.
2. Physical methods: a physical property of the system is measured/monitored as the rxn proceeds.
176
Reaction mechanism
Collection of individual kinetic processes or elementary steps involved in the transformation of reactants to products.
177
Elementary reaction steps
Single steps and a pathway/mechanism may contain one or more of these
178
Molecularity
Stoichiometric quantity of reactants involved (i.e. unimolecular has 1 reactant, bimolecular has 2, etc.)
179
When are the order and molecularity equivalent?
For elementary reaction steps
180
Integrated rate law expressions
Provide a predicted temporal evolution of the reactant/product concentrations that can be used in lieu of known rate expressions.
181
How can a first order rate law be expressed? (Choose linearly convenient form)
ln[A]=ln[A]0-kt
182
Half-Life
time for reactant concentration to decrease to half its initial value.
183
Half-life for first order equation?
t1/2=ln2/k
184
What is half life independent of?
Initial concentration
185
Second Order Type 1 Reaction
A reaction that is second order with respect to 1 reactant.
186
Second Order Type 2 Reaction
A reaction with 2 reactants that is 2nd order overall but first order with respect to each reactant.
187
What is the rate law for second order type 1?
1/[A]=1/[A]0+kefft
188
What is the effective rate constant?
keff=2k. Used for Second order type 1 reactions.
189
Half-life for second order type 1
t1/2=1/keff[A]0
190
Why are second order reactions dependent on [A]0?
Bimolecular reactions are dependent on the number of successful collisions taking place.
191
Rate law for second order type 2
1/[B]0-[A]0*ln([B]/[B]0/[A]/[A]0)=kt
192
What is the half life for second order type 2 reactions?
Concept of half-life does not exist.
193
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
194
Intermediate
A product of one sequential step that is consumed in another
195
Maximum Intermediate species concentration eqn
tmax=(1/KA-kI)*ln(kA/kI)
196
Rate determining step
If one step is significantly slower than the other, it determines the rate of reaction
197
Euler's Method in the Steady State Approximation
Determines the concentrations numerically as a function of time
198
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.
199
When is the steady state approximation valid?
When the intermediate decay rate is greater than the rate of production
200
Yield (Kinetics)
Probability that a given product will be formed by the decay of the reactant
201
Arrhenius Expression
k=Ae^-Ea/RT
202
Graphical form of Arrhenius equation
ln(k)=ln(A)-Ea/RT
203
Apparent rate constant eqn
kapp=kA+kB
204
