Cheatsheet Kimia Fisika

changein p
dp #of particles
particle
N 1
dp 2mu f (u ) Aududt nMc 2 nRT
V 3
r1 M2

1/ 2
N 3RT
dp 2mu 2 f (u ) Adudt c
V r2 M1 M
Cheatsheet Kimia Fisika
Molecules in Motion Basic Kinetic Theory

* Kinetic model of gases Based on 3 assumptions: 1. Molecules are in ceaseless
random motion
2. Size of molecules is
negligible
3. Molecules do not
interact
nMc 2
p
3V
1
pV nMc 2
3

* Relative rates of effusion
* Rate of Effusion 1/M
Pressure and Molecular Speed

* Bernoullis Derivation
- Kinematics
1. In time dt, only molecules striking wall are those with positive velocity (u>0)
between u and u+du
Assumes initial distance udt
2. # of Molecules striking wall during dt are those within volume V=Audt at t= 0
with right velocity N/V(f(u)du)) is N/Vf(u) Audt du
3. Momentum change with each collision is Dp= mu - (-mu) = 2mu. Incremental
momentum change is:
v2
f (v1 v2 ) f (v)dv
v1
Distribution of Speeds, f(u)du

- Evaluating Maxwell distribution
1. Over narrow range, Dv,evaluate f(v) Dv
2. Over wide range, numerically integrate
Molecular Speed Relationships
* Root mean speed, c, c = (3RT/M)0.5
* Mean speed, c , c = (8RT/M)0.5
* Most probable speed, c*
- Maximum of Maxwell distribution, i.e, df(v)/d(v) = 0
c* = (2RT/M) 0.5
0.5
- Most probable speed = (/4) x mean speed = 0.886 c
* Relative mean speed, crel ,speed one molecule approaches another

- Range of approaches, but typical approach is from side
c rel 2 c
0.5
8kT
c rel

R
k Boltzmann ' scons tan t
NA
m A mB
reduced mass
m A mB
0.5
m 8 RT
If m A m B , and c rel c
2 M
Collisions
- Collision diameter, d - distance > which no collision occurs, i.e., no change in p of
either molecule
- Not necessarily molecular diameter, except for hard spheres
ex N2, d = 0.43 nm
- Collision frequency, z - number of collisions made by molecule per unit time
z = s x crel x N
s = collision cross section = d
N = # molecules per unit

volume = N/V
crel = relative mean speed
For ideal gas, in terms of pressure ,

z = (s crel p)/kT
-- As T increases, z increases because the rel. mean speed a T 1/2
-- As p increases, z increases because the # of collisions a density of gas a N/V
N2 at 1 atm and 25C, z = 5 x 109 s-1
Theoretical Models for Chemical Kinetics

Activation Energy is: The minimum energy above the average kinetic energy that
molecules must bring to their collisions for a chemical reaction to occur.
* For a reaction to occur there must be a redistribution of energy sufficient to break
certain bonds in the reacting molecule(s).
Effect of Temperature on Reaction Rates
- Svante Arrhenius demonstrated that many rate constants vary with temperature
k = Ae-Ea/RT
according to the equation:
-Ea
lnR1T
k=
Arrhenius
lnkk1 -Ea=1 1 Equation
RT T
-
2 2 1
+
ln
Phases, Components, and
A Degrees of Freedom
* Phase
A consistent, physically distinct segment of a system that is separated from other
segments of the system by binding surfaces.
- Phase
Signifies a form of matter that is uniform throughout, not only in chemical
composition but also in physical state.
- Number of phases is denoted by P
P = 1 for gas, gaseous mixture, crystal, two miscible liquids, ice
P = 2 for slurry of ice and water, immiscible metal alloys
* Degrees of Freedom
Intensive variables that must be known to describe the system completely. Ex.
temperature, concentration, pressure, density, etc.
In a single-component, single-phase system (C=1, P=1) the pressure and
temperature may be changed independently without disturbing the number of
phases in equilibrium:
F = 2, system is bivariant, or has two degrees of freedom
If two phases are in equilibrium in a single-component system (C=1, P=2)
(e.g., a liquid and its vapour), the temperature (or pressure) can be changed, but
there must be an accompanying change in pressure (or temperature) to preserve
the phases in equilibrium
F = 1, system has one degree of freedom
* Components or Chemical Entities

Constituents by which the composition or make-up of each phase in the system
can be expressed. Usually the chemical formula or chemical equation is used.
- When no reaction takes place, Constituents = Components
- When a reaction can occur, the number of components is the minimum number
of species which specifies the composition of all of the phases
PHASE RULE
F = C P +2 where F : The number of degrees of freedom

C : The number of components
P : The number of phases at
equilibrium
SISTEM CAMPURAN
* Hukum Raoult
Pada larutan yang terdiri dari solute dan solvent yang volatil, ditemukan bahwa
tekanan uap jenuh pelarut di atas permukaan suatu larutan, selalu lebih kecil dari
tekanan uap pelarut tersebut dalam keadaan murni.
PA = tekanan uap jenuh pelarut di atas larutan

PA x A PAo PA = tekanan uap jenuh pelarut murni
*Peningkatan titik didih & penurunan titik beku

Peningkatan titik didih: Tb = Kb . m Penurunan titik beku : Tf =
Kf . m
Kb = konstanta kenaikan titik didih molal
Kf = konstanta penurunan titik beku mola
* Tekanan Osmotik (cont.)
Osmosis: pergerakan pelarut melalui membran semipermeabel ke arah larutan
dengan konsentrasi solut lebih besar.
Rumus Tekanan Osmotik
Tekanan osmosis (): tekanan yang dibutuhkan untuk menghentikan osmosis dari
pelarut murni ke larutan
=(n/V) RT=M.RT
Keterangan: = tekanan osmotik n = mol zat terlarut
V = volume(dalam liter) larutan R = tetapan gas (0,00821
L atm/mol.K)
2
RTe a / RTVm nRT n RT a n2a
p p a 2 p (V nB) nRT
Vm b V nb V Vm b Vm TV 2
Compression
Factor, Z
- Compression factor, Z, is ratio of the actual molar volume of a gas to the molar
volume of an ideal gas at the same T & P
Z = Vm/ Vm, where Vm = V/n
- Using ideal gas law, p Vm = RTZ
- The compression factor of a gas is a measure of its deviation from ideality
Depends on pressure (influence of repulsive or attractive forces)
z = 1, ideal behavior
z < 1 attractive forces dominate, moderate pressures
z > 1 repulsive forces dominate, high pressures
Real Gases - Other Equations of State
Virial equation is phenomenolgical
Other equations of state based on models for real gases as well as cumulative data
on gases
- Berthelot (1898)
1. Better than van der Waals at pressures not much above 1 atm
2. a is a constant
- van der Waals (1873)
- Dieterici (1899)
Features of Van der Waals equation

Can derive (by setting 1st and 2nd derivatives of equation to zero) expression for
critical constants
Vc = 3b, pc = a/27b2, Tc =8a/27Rb
Can derive expression for the Boyle Temperature
TB = a/Rb

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Cheatsheet Kimia Fisika

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changein p

Molecules in Motion Basic Kinetic Theory

Pressure and Molecular Speed

Distribution of Speeds, f(u)du

* Relative mean speed, crel ,speed one molecule approaches another

N = # molecules per unit

For ideal gas, in terms of pressure ,

Theoretical Models for Chemical Kinetics

* Components or Chemical Entities

F = C P +2 where F : The number of degrees of freedom

PA = tekanan uap jenuh pelarut di atas larutan

*Peningkatan titik didih & penurunan titik beku

Features of Van der Waals equation

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