CHEM 351: ACS Midterm

thermodynamics

the study of work and heat in chemistry

system

the part of the universe that’s of interest, described using macroscopic variables

macroscopic variables

pressure, volume, temperature, amount of matter

surroundings

region outside the system, sometimes where we make our measurements

universe

the system, the surroundings, and the boundary in between

extensive parameters

obtained by summing together the contributions from all the molecules in a system

• N (number of particles in a system), V (total space occupied by a system), E (sum of translational, rotational, vibrational, and electronic energies)

intensive parameters

obtained by averaging the contributions from the molecules in a system

• P, density, T

zeroth law of thermodynamics

if two systems are in thermal equilibrium with each other and a third system is in thermal equilibrium with one of them, then it is in thermal equilibrium with the other also

first law of thermodynamics

the total energy of an isolated system remains constant

second law of thermodynamics

when two systems are brought into thermal contact, heat flows spontaneously from the one at a higher temperature to the one at a lower temperature

third law of thermodynamics

all perfect materials have the same entropy (S) at T=0, and this value may be taken to be S = 0. At higher temperatures, S is always positive

open system

energy and matter can be exchanged between the system and its surroundings

closed system

only energy can be transferred, either as work or by heat transfer. matter cannot be exchanged

isolated system

neither energy nor matter can be exchanged

adiabatic

the system is insulated well enough, heat will not be able to get into or leave the system (work can be performed on or by the system)

• q=0

diathermic 

heat transfer is possible

exothermic process

a process that released energy as heat

• H < 0

• q < 0

endothermic process

absorbs energy as heat

• H > 0

• q > 0

reversible process

one which is carried out in infinitesimally small incremental steps, the system essentially remains at equilibrium at all stages during the process

irreversible process

cannot be reversed by an infinitesimal perturbation, occurs spontaneously

temperature

measures how much kinetic energy a system has, NOT a form of energy (can be used to compare energy levels → more energy = higher temperature)

heat

the energy transferred between systems caused by temperature differences

equations of state

a mathematical equation into which we can substitute two of the variables and calculate what the remaining variable must be 

• Boyle’s law, Charles’ law, Avogadro’s principle

limiting laws

laws that hold true within certain limits (ex: Boyle’s and Charles’ laws hold true when P approaches zero)

ideal gas law!

PV = nRT

compressibility factor, Z

at low temperatures and high pressures, gases will deviate from the ideal gas law

• Z = PV/RT

• the further away Z is from 1, the less ideally the gas will behave

virial equation

the equation of state for nonideal gases

• Z = 1 + B/V + C/V² + …

where B, C.. are correction factors, and B has the largest correction 

Boyle temperature

Z = 1, nonideal gases start to act like an ideal gas

• T_B = a/bR

considerations for an ideal gas

1. there are no repulsive or attractive forces between the gas particles

2. the particles are so small, their volumes are negligible

3. there are no interactions between particles

van der Waals equation

where a represents the pressure correction related to the magnitude of the interactions between particles, and b is the volume correction related to the size of the particle

translation energy for a gas (equipartition principle)

E = 3/2kT

rotational energy for a non linear molecule (equipartition principle)

E = 3/2kT

rotational energy for a linear molecule (equipartition principle)

E = kT

vibrations of a non-linear molecule

3N - 6

vibrations of a linear molecule

3N - 5

work

done when an object moves some distance, s, due to applying a force, F; a way to transfer energy

negative work

indicates the work done results in a decrease in the system’s energy

positive work

indicates the work done results in an increase in the system’s energy

free expansion

w = 0, expansion is done against no opposing force

reversible expansion

change that can be reversed by an infinitesimal modification of a variable, let the system respond to a change before continuing

irreversible expansion

the change occurs irreversibly, suddenly changing the initial pressure to the final pressure 

a system does maximum work when…

the process is carried out reversibly: w_exp < w_irr

heat capacity, C

an extensive property that includes amount of material

what is the difference between work and heat?

work is ordered energy transfer while heat is disordered energy transfer

internal energy

enthalpy

state function

if heat capacity is independent of temperature over the range of temperatures of interest…

derivative for internal pressure

joule-thompson coefficient

molar heat capacity at constant volume

C_V = 3/2R = 12.471

molar heat capacity at constant pressure

C_P = C_V + R = 5/2R = 20.785

gamma for monoatomic perfect gas

5/3

gamma for linear polyatomic molecule

7/5

gamma for non-linear polyatomic molecule

4/3

phase transition

a spontaneous change of one phase into another, occurs at a specific temperature for a given pressure

hess law

standard enthalpies of individual reactions can be combined to determine the enthalpy of another reaction

kirchhoff’s law

relates the heat of a reaction at different temperatures through heat capacity

engines

have a hot source and a cold sink, some energy is lost to the cold sink as heat and not converted into work

what does heat stimulate?

random motion in the surroundings

what does work stimulate?

uniform motion of atoms in the surroundings, doesn’t change entropy

carnot cycle

1. reversible isothermal expansion from A to B at T_hot

2. reversible adiabatic expansion from B to C (temperature falls from T_hot to T_cold)

3. reversible isothermal compression from C to D at T_cold

4. reversible adiabatic compression from D to A (temperature rises from T_cold to T_hot)

efficiency

carnot efficiency

clausius inequality

more work is done when a change is reversible than irreversible (for expansion)

dS > 0 (isolated system)

the process is spontaneous

dS = 0 (isolated system)

the process is in equilibrium

dS < 0 (isolated system)

not allowed for a process in an isolated system

reversible change in a non-isolated system

S_sur = -S_sys, so S_tot = 0

irreversible change in a non-isolated system

S_sur > -S_sys, so S_tot > 0

mole fraction

ratio of the number of moles of a given gas and the total number of moles of gas

exothermic phase transitions

freezing or condensing → change in entropy of the system is negative

endothermic phase transition

melting or vaporization → change in entropy of the system is positive

trouton’s rule

empirical observation that a wide range of liquids gives approximately the same standard entropy of vaporization (about 85 J/molK)

• implies that a comparable change in volume occurs when any liquid evaporates to become a gas

Boltzmann’s molecular interpretation

“an atom or a molecule can possess only certain energy values, called its ‘energy levels’.”

microstate

the ways in which the molecules of a system can be arranged while keeping the total energy constant

Helmholtz energy, A

Gibbs energy, G

G < 0

the process is spontaneous

G = 0

the system is in equilibrium

G > 0

the process is non-spontaneous

maximum expansion work

the change in Helmholtz function (A) is equal to the maximum amount of work that a process can do at constant temperature

maximum non-expansion work

at constant temperature and pressure, the maximum non-expansion work is given by the change of the Gibbs energy (G)

from U (maxwell relationships)

from H (maxwell relationships)

from A (maxwell relationship)

from G (maxwell relationship)

in which phase is the Gibbs energy most sensitive to changes in temperature?

gas phase

Gibbs-Helmholtz equation

thermodynamic square mnemonic

good physicists have studied under very ambitious teachers

chemical potential

extent of reaction

extent of reaction > 0

chemical process moves to the right (reactants)

extent of reaction < 0

chemical process moves to the left (products)

the forward reaction is spontaneous

the reverse reaction is spontaneous

G < 0

the forward reaction is spontaneous, the reaction is exergonic

G > 0

the forward reaction is non-spontaneous, the reaction is endergonic

G = 0

the reaction is in equilibrium

reaction quotient, Q

activities of products/activities of reactants

fugacity