Thermodynamics (Topics 1-5) Flashcards
K (equilibrium constant) =
Concentration of products at equilibrium/concentration of reactants at equilibrium
Molar change in Gibbs free energy (Jmol^-1) =
-RTln(K) = Molar Gibbs energy of reactants-products (Jmol^-1)
Fundamental units for heat
kg m^2 s^-2 (J)
Boltzmann constant
1.381 x 10^-23 J K^-1
Gas constant
8.314 J K^-1 mol^-1
Avogadro Constant
6.022 x 10^23 mol^-1
Atomic mass unit
1.661 x 10^-27 kg
Pascal SI units
kg m^-1 s^-2
(N m^-2)
Newton SI units
kg m s^-2
Kinetic energy (J)
1/2 mass (kg) x velocity^2 (m s^-1)^2
Potential energy (J) =
Mass (kg) x gravity (9.81 m s^-2 on earth) x heights (m)
g on earth
9.81 m s^-2
Joule in SI units
kg m^2 s^-2
Work (J) =
Force (N) x distance (m)
-p delta V
Ideal gas law
p(Pa) x V(m^3) = n(mol) x R(8.314 J K^-1 mol^-1) x T(K)
Equation linking gas constant and Boltzmann constant
R = NA x kB
Real Gas Law
(p+an^2 / V^2 )(V-nb) = nRT
Force acting on the piston (N or kg m s^-2) =
External pressure (Pa or kg m^-1 s^-2) x Area (m^2)
Area = pi r^2
dw = (2 equations)
Integrated form also
-p(ext) pi r^2 (dx) = -p(ext) dV
w = equations above integrated with limits Vf and Vi
Internal energy (J) =
Kinetic energy (J) + potential energy (J)
Intensive properties are
Name 3
Independent of the size of the system
Temperature
Density
Concentration
Extensive properties are
Name 3
A sum of that property for each component subsystem
Entropy
Mass
Volume
Internal energy for monatomic gas = (2 equations)
3 kB T / 2 per molecule
3 R T / 2 per mole
Enthalpy change is equal to
Heat change
H (J) =
U (J) + pV (J)
Change in internal energy (J) =
Heat transferred (J) + work done (J)
=0 in an isothermal process
q(rev) (J) + w(rev) (J) = 0
Change in entropy (J K^-1)
4 equations
delta S surr = q sys (J) / T (K) = c p,m lnT2 / T1
c integral between Tf and Ti 1/T dT = Cv or Cp ln(Tf/Ti)
-nR {XA ln XA + XB ln XB} where XA / XB = molar fraction of A/B
nR ln (Vf/Vi)
Gibbs Free Energy Change (J)
3 equations
Delta G = delta H - T delta S
Delta G = nRT {XA ln XA + XB ln XB} where XA / XB = molar fraction of A/B
Delta G = -nRTlnK
Clausius inequality
0 > change in enthalpy - Temperature x change in entropy of system
Change in entropy of system > q / T
For a spontaneous reaction, Gibbs Free Energy Change is
Less than 0
State functions
Name 3
Depend on the energy of the system
Defines present state and is independent on how that state was reached
Gibbs free energy
Internal energy
Enthalpy
Entropy
(Not heat or work)
Gibbs free energy change and enthalpy change calculations
(Involving standards of formation)
Gibbs free energy change = sum of (stoichiometrically weighted Gibbs free energy of formation of products - reactants)
Enthalpy change = sum of (stoichiometrically weighted enthalpy change of formation of products - reactants)
First Law of Thermodynamics
For an isolated system, the change in internal energy is the sum of the heat transferred and the work dome
Delta U = q + w
Second Law of Thermodynamics
The driving force for a process if entropy
Key to what drives chemical reactions, to predict weather processes will go and what determines the position of equilibrium
The total entropy of an isolated system increases
Delta S > 0
Third Law of Thermodynamics
The entropy of a system approaches a constant value as the temperature approaches absolute 0
No motion of any type at absolute 0
Hess’s Law
The total enthalpy change for a reaction is independent of the path by which it occurs
Kirchhoff’s Law
Integral of dH = integral between T1 and T2 Cp dT
Delta H = H(T2) - H(T1) = Cp(T2 - T1)
Pressure exerted by a mixture of gases (Pa) =
Sum of the pressure exerted by each gas (partial pressure)
Partial pressure (Pa) =
Molar fraction x total pressure (Pa)
Molar fraction =
mol of a gas / total gas moles
Total volume (m^3) =
nA VA + nB VB
Moles A x vol A + moles B x vol B
Gibbs free energy (J) =
2 equations
nA GA + nB GB
nA uA + nB uB
u = mu = chemical potential
van’t Hoff equation
Integrated form
Indefinite integrated form
dlnK/dT = delta H/RT^2
lnK(T2) - lnK(T1) = -delta H/R (1/T2 - 1/T1)
lnK(T) means K at that temp, don’t multiply by temp
lnK = -delta H/R 1/T + delta S/R
How would you plot van’t Hoff plot
What does gradient and intercept means
Plot: lnK v 1/T
Gradient: -delta H/R
Intercept: delta S/R
q(rev) (J) =
-w(rev) = nRT ln(Vf/Vi)
Heat capacity of a system (c) (JK^-1) =
q(rev) (J) / delta T (K)
Cv / Cp
Heat capacity at constant volume/pressure (J K^-1)
d q(rev) =
3 answers
Cp dT = TdS = dU + P dV
Change in heat capacity at constant pressure (J K^-1)
Sum of (stoichiometric weight of products - reactants)
dG =
2 lines
dH - TdS - SdT
VdP - SdT
Rearrange equation dG = VdP - SdT when at constant pressure and temperature
-delta S = (d delta G/dT)P
V = (dG/dP)T = nRT/P
P and T outside brackets are subscript
Integrated form of V = (dG/dP)T = nRT/P
T subscript
Integrated between G1 and G2 dG = nRT integrated between P2 and P1 1/P dP
Delta G = G2-G1 = nRT ln(P2/P1)
PV is constant so can interchange P with V
For an exothermic process, the entropy of surroundings … and in an endothermic process, the entropy of surroundings
Increases
Decreases
1 atmosphere in pascals
101325
What does the slope gradient represent on the lnk vs 1/T graph
-Ea/R
Enthalpy is
The heat content of a compound at constant pressure
Energy can be transferred as
Heat or work
Maximum work for a system via reversible expansion is achieved by
External pressure at maximum
External pressure less than pressure in system
External pressure infinitesimally less than pressure of gas in system
Open system
Can exchange energy and matter with surroundings
Closed system
Can exchange energy but not matter with surroundings
Isolated system
Can’t change energy or matter with surroundings
Entropy of the system
Measure of randomness
Larger disorder = larger entropy
Spontaneous change is driven by
The tendency of energy and matter to become disordered.
An increase in entropy in the universe
Change in entropy of universe =
Change in entropy of surroundings + system
Position of equilibrium depends on
The relative molar energies of reactants and products
Chemical potential
Partial molar Gibbs energy
When is a system in equilibrium
When at constant pressure and temperature the chemical potential of the reactants equals that of the products
A real gas will approach ideal gas behaviour under which of the following conditions?
High temp
Low pressure
In a plot of pressure vs volume for a real gas at the critical temperature, the critical point is
a point of inflexion
1 m^3 in litres
1000
A process will be spontaneous if the entropy
of the system and surroundings increase
2 path functions
heat and work
(not state)
A positive slope would indicate that the reaction is … in a Van’t Hoff plot
exothermic
Pressure in irreversible expansion work
The value of the external pressure changes
The value of the internal pressure within the
system changes
External pressure must be smaller than the internal pressure within the system
Explain how you would determine experimentally the activation energy
(Ea) and pre-exponential factor (A) for a reaction.
Measure the rate constant (k) at different temperatures.
Plot lnk versus 1/T
Determine the slope (m) and y-intercept (c) of the linear fit.
Calculate Ea from the slope:
Ea = −mR.
Calculate A from the intercept: A=e^c
delta H =
delta U + delta n (g) RT
