Thermodynamics

Question 1

What is an ideal gas?

Answer 1

A gas that obeys the ideal gas equation at all pressures.

Question 2

Ideal gas equations of state

Answer 2

pV = nRT

Question 3

What is a real gas?

Answer 3

A gas that behaves more like an ideal gas as its pressure is reduced towards zero.

Question 4

What are the three sets of experimental observations summarised by the ideal gas law?

Answer 4

1. Boyle’s law: at constant temperature, p is inversely proportional to V
2. Charles’ law: at constant pressure, V is directly proportional to T
3. Avogadro’s principle: at constant temp. and pressure, V is directly proportional to n (number of moles)

Question 5

Dalton’s law for ideal gases

Answer 5

p = p(A) + p(B) + …

Pressure exerted by mixture of ideal gases is sum of pressures each gas would exert if alone in container at same temp.

By definition (for ideal and real gas): p(J) = x(J)p where x(J) = mole fraction of gas

Question 6

Critical isotherm

Answer 6

The isotherm at the critical temperature

Question 7

Critical point

Answer 7

In critical isotherm, volumes at each end of horizontal part of isotherm merged to single point, critical point of gas.

Question 8

Critical pressure, p(c)

Answer 8

Pressure at critical point

Question 9

Critical volume, v(c)

Answer 9

Molar volume at critical point

Question 10

Supercritical fluid, SCF

Answer 10

Dense fluid obtained by compressing gas when its temp. is higher than its critical temp.
Not a true liquid
Has density similar to that of liquid but never possesses surface that separates it from vapour phase.
Not like gas as it is so dense

Question 11

What is a vapour?

Answer 11

Gaseous phase of substance below its critical temp. which can be liquefied by compression

Question 12

What is a gas?

Answer 12

Gaseous phase of substance above its critical temp. that cannot be liquefied by compression alone.

Question 13

Compression factor Z

Answer 13

Z = V(m) / V(m) standard where V(m) is molar volume of gas
For ideal gas, Z = 1
Z = pV(m) / RT
If Z < 1, molar volume smaller than that of ideal gas, attractive interactions dominant
If Z > 1, molar volume greater than that of ideal gas, repulsive forces dominant

Question 14

Virial equation of state

Answer 14

Z = 1 + B/V(m) + C/V(m)^2 + …, B, C are called virial coefficients
Viral coefficients vary depending on gas and temp.
V(m) = V/n
Virial equation of state: pV(m)/RT = 1 + B/Vm + C/Vm^2 + …

Question 15

Van der Waals equation of state (for repulsions)

Answer 15

Shows how intermolecular interactions contribute to deviations of a gas from ideal gas law
Repulsive interaction between 2 molecules implies they can’t come closer than a certain distance
So actual volume V in which molecules can travel reduced to V - nb
p = nRT / V - nb
When V&raquo_space; nb, nb can be ignored

Question 16

Van der Waals equation of state (repulsions and attractions)

Answer 16

Attractive interactions between molecules reduces pressure that gas exerts as attractions slow molecules down.
Molecules strike walls less frequently and with weaker impact
Attractive interactions proportional to conc. n/V
Reduction in pressure = a x (n/V)^2 where a is constant of proportionality
Equation of state: p = nRT/(V - nb) - a(n/V)^2

Question 17

Difference between an extensive and intensive property? /

Answer 17

Extensive property depends on amount of substance in sample, intensive is independent.

Question 18

Difference between open and closed system?

Answer 18

Open can exchange both energy and matter with surroundings, closed can only exchange energy. Isolated can exchange neither.

Question 19

First law of thermodynamics

Answer 19

Internal energy of isolated system is constant
Delta U = w + q

Question 20

What is expansion work?

Answer 20

Work done when system expands against opposing pressure.
F = p(ex)A
w = delta d x p(ex)A = p(ex) x delta dA = p(ex) delta V
work done when system expands through volume delta V against constant external pressure p(ex): w = -p(ex) delta V

Question 21

Reversible isothermal expansion of ideal gas

Answer 21

w = -nRT ln(Vf/Vi)
q = -w
Therefore q = nRT ln(Vf/Vi)

Question 22

Heat capacity equations

Answer 22

C = dq/dT by definition where C is heat capacity (JK-1), q is transferred heat (J) and dT is temp. change
Specific heat capacity: C(s) = C/m where m is mass of sample in g.
Molar heat capacity: C(m) = C/n
Cp is heat capacity at constant pressure and Cv is at constant volume
When heat capacity at constant volume independent of temperature: C(V) = dU/dT
When heat capacity at constant pressure independent of temperature: C(p) = delta H/delta T
Cp,m - Cv,m = R

Question 23

Enthalpy

Answer 23

Change in internal energy of system that is free to expand or contract. Not equal to energy supplied as heat.

delta H = delta U + delta(pV)
For ideal gas: delta H(m) = delta U(m) + R delta T
At constant pressure: delta H = delta U + p delta V
At constant pressure (no nonexpansion work): delta H = q(p)
At constant volume (no nonexpansion work): delta U = q(v)

Question 24

Difference between spontaneous and non-spontaneous change

Answer 24

Spontaneous is a change with a tendency to occur without work having to be done to bring it about, whereas non-spontaneous can only be brought about by doing work

Question 25

Second law of thermodynamics

Answer 25

Entropy of an isolated system tends to increase

Question 26

Change of entropy at constant temp. by definition (equation)

Answer 26

dS = dq(rev)/T --> delta S = q(rev)/T

Question 27

Dependence of entropy accompanying expansion

Answer 27

For isothermal, reversible expansion of ideal gas: q(rev) = nRT ln(Vf/Vi) delta S = q(rev)/T = nRT ln(Vf/Vi)/T Therefore for isothermal expansion of ideal gas: delta S = nR ln(Vf/Vi)

Question 28

Entropy change accompanying heating

Answer 28

dS = q(rev)/T C = q(rev)/dT --> dS = C dT/T delta S is area under graph of C/T against T so between Ti and Tf: delta S = integration (between Tf and Ti) of C dT/T If heat capacity is constant: delta S = C ln(Tf/Ti)

Question 29

Entropy change accompanying phase transition

Answer 29

At melting temp. and constant p: delta fusion S = delta fusion H(Tf)/Tf where Tf is melting temp. At boiling temp. and constant p: delta vap. S = delta vap. H(Tb)/Tb where Tb is boiling temp.

Question 30

Trouton's rule

Answer 30

- Entropy of vaporisation (S vap.) per 1 mole at boiling temp. is the same for all liquids except when hydrogen bonding or another kind of specific molecular interaction is present - Therefore these liquids have approx. same entropy of vap. at their boiling points

Question 31

Third law of thermodynamics

Answer 31

Entropies of all perfectly crystalline substances are the same at T = 0.

Question 32

Standard reaction entropy definition and equation

Answer 32

Difference in molar entropy between products and reactants in their standard states. delta S standard = sum of standard molar entropies of products - sum of standard molar entropies of reactants

Question 33

Entropy changes in suroundings

Answer 33

delta S sur = q sur, rev/T Surroundings so extensive they remain at constant p so: q sur, rev = delta H sur Entropy is state function so change in its value is independent of path. So its value remains the same regardless of how heat is transferred: q sur = -q so delta S sur = -q/T At constant p: delta S sur = - delta H/T

Question 34

(Molar) Gibbs energy

Answer 34

G(m) = G/n where G(m) is molar Gibbs energy Molar Gibbs energy depends on phase of substance delta G = nGm (phase 2) - nGm (phase 1) Change of Gibbs energy with p and T: dG = V dp - S dT Change of Gibbs energy with p at constant T: delta Gm = Vm delta p where Vm is constant in pressure range of interest Change of Gibbs energy with T: delta Gm = Sm delta T (when entropy of substance is unchanged over range of T, becomes negative) For ideal gas at constant T: delta Gm = RT ln(p final/p initial)

Question 35

Location of phase boundaries (Clapeyron equation - GIVEN)

Answer 35

Relationship between change in T and p needed to maintain eqm. given by Clapeyron equation: dp = (delta H trs/T delta V trs) x dT This equation applies to small variations in p and T where delta H trs and delta V trs can be treated as constant

Question 36

Clausius-Clapeyron equation (GIVEN in a different form)

Answer 36

We suppose vapour behaves as ideal gas then relation between delta p and delta T can be given by Clausius-Clapeyron equation: lnp' = lnp + (delta H vap/R)(1/T -1/T')

Question 37

The phase rule

Answer 37

For a system at equilibrium: F = C - P + 2 where F = number of degrees of freedom C = number of components P = number of phases When only 1 phase present, F = 2 and p and T can be varied When 2 phases present, F = 1 (if T changed, p must be changed by specific amount) When 3 phases present, F = 0 (no freedom to change either variable) 4 phases cannot coexist in mutual eqm.

Question 38

Partial molar property

Answer 38

Contribution per mole that a substance makes to an overall property of a mixture

Question 39

Chemical potential

Answer 39

Partial molar Gibbs energy which is indication of potential of substance to be active chemically. G = n(A)G(A) + n(B)G(B) Total energy of mixture: G = n(A)mu(A) + n(B)mu(B) where mu is partial molar Gibbs energy/ chemical potential molar Gibbs energy of pure substance is same in all phases at eqm. System at eqm. when chemical potential of each substance has same value in every phase in which it occurs

Question 40

Real solutions (GIVEN)

Answer 40

No actual solutions ideal, solution deviates from ideal-dilute behaviour by increasing conc. of solute Activity of substance ,a(J), is a kind of effective conc. At all concs. for both solvent and solute by definition: mu J = mu J standard + RT ln a(J)

Question 41

Ideal solutions

Answer 41

Consist of a pair or more of liquids that obey Raoult's law through composition range Raoult's law: partial vapour pressure of substance in liquid mixture proportional to its mole fraction in mixture and vapour pressure when pure p(J) = x(J)p(J)* where p(J)* is vapour pressure of pure substance, J is substance in general, a is solvent and b is solute

Question 42

Ideal gas in a mixture

Answer 42

mu(J) = mu(J) standard + RT ln(pJ/p standard) where mu(J) standard is standard chemical potential of pure gas J at 1 bar and p(J) is partial pressure of gas Equation shows that the higher the partial pressure of gas, the higher its chemical potential

Question 43

Equation for ideal solution

Answer 43

Chemical potential of pure A: mu A = mu A standard + RT ln x(A) xA < 1 so lnxA < 0 and chemical potential of solvent is lower in solution than when pure (where xA = 1)

Question 44

Ideal-dilute solutions and Henry's Law

Answer 44

Solutions dilute enough for solute to obey Henry's law Henry's law: vapour pressure of volatile solute B proportional to its mole fraction in solution p(B) = x(B)K(H) or p(B) = K(H)[J] where K(H) is Henry's law constant (constant is characteristic of solute)

Question 45

Spontaneous mixing of ideal gases (1 equation given)

Answer 45

Spontaneous mixing of ideal gases at constant T and p: delta G = nRT {xA ln xA + xB ln xB} (GIVEN) delta S = -nR {xA ln xA + xB ln xB} No interactions between molecules in mixture of ideal gases so no change in enthalpy when 2 ideal gases mix Increase in entropy as mixed gas more disordered than unmixed gases

Question 46

Spontaneous mixing of ideal solution

Answer 46

For mixing to form ideal solution: same equations as mixing of ideal gases delta H = 0 value of delta H indicates that although there are interactions between molecules in ideal solution, average intermolecular interactions are the same. Intermolecular interactions in ideal gas are 0.

Question 47

Statistical entropy

Answer 47

Boltzmann equation calculates entropy using number of configurations. Configuration = each arrangement of molecules over available energy levels in sample. Boltzmann equation: S = k ln W where k = Boltzmann's constant = 1.381x10^-23 JK-1 = R/N(A) W = number of configurations (weight) N(A) = Avogadro's constant E.g. 19 arrangments of 4 molecules A, B, C, D in system with 3 energ levels and total energy of 4 epsilon so W = 19

Question 48

Boltzmann distribution and partition function (given similar equations)

Answer 48

Partition function (q) contains all thermodynamic information about the system N(i) = Ne^(Ei/kT)/q R = N(A)k where Ni = number of molecules in state of energy Ei N = total number of molecules q = the sum of e^(-E0/kT) = e^-E0/kT + e^-E1/kT + ... N2/N1 = e^- delta E/kT

Question 49

Boltzmann distribution's application to populations of states

Answer 49

In some cases different states have same energy e.g. rotating molecules Some levels are degenerate If degeneracy of energy level (number of states of that energy) is g, we use factor of g to use Boltzmann distribution to get populational of level: N(L) = (Ng(L)e^-E(L)/kT)/q q = sum of g(L)e^-E(L)/kT where N(L) is total number of molecules in level L (sum of populations of all states of that level) g(L) is its degeneracy E(L) is its energy

Question 50

Interpretation of partition function

Answer 50

q = sum over states, not levels q = 1 + e^-E1/kT + e^-E2/kT + ... All energies measured relative to ground state, ground state energy set equal to 0. First term is 1 as E0 = 0