The StokesEinstein equation for the diffusion coefficient of a spherical particle is given
as
D=
kT
6 r
As can be seen, the diffusion coefficient depends on the inverse of the viscosity of the
fluid ( ) , as well as the inverse of the particle radius ( r
Brownian motion is the seemingly random motion of a large particle due to diffusion
through a medium. The motion is driven by the force of particles from the medium
colliding with the large particle.
The viscosity of a liquid or gas is measured by the flow rate of the substance, or the time
it takes for a specified volume of the substance to pass through a column under specified
pressure.
4982-17-7Q
=
AID: 1112 | 29/01/2013
1 CV , m
ave N
3 NA
we see that the thermal conductivity depends on the product of the number density and
the mean free path. For an ideal gas, the mean free path is dependent on the inverse of
the pressure, while the
The thermal conductivity, , is defined as
=
1 CV , m
ave N
3 NA
where CV , m is the molar volume independent heat capacity, and ave and are the
average speed and the mean free path, respectively.
The number density of particles that diffuse from a fixed plane is given by the solution to
Fick's Second Law of Diffusion,
N=
N0
2 A ( Dt )
12
x2
exp
4 Dt
where N 0 is the number of particles initially confined to the plane, D is the diffusion
coeff
The diffusion coefficient, D , is defined as
1
D = vave
3
Where vave is the average speed and is the mean free path of a gas particle, both as
defined by the kinetic gas theory. The vave term is inversely proportional to the square
root of the molar mass
The spatial gradient of a property is a continuous difference in a physical property such
as pressure, temperature, or molecular distribution. The flux of the property is a change
that occurs due to the spatial gradient, defined as the amount of a given p
a) The conductivity of a weak electrolyte is given as
m =
m
The autoionization constant of water is given by the following equation:
K w = H + OH
H + OH
=
1M 1M
And it can be rearranged as
Kw =
2
2
( 1M )
1
= ( 1M ) K w 2
And m is given as
= ( H
The conductivity is defined as
=
l
K
=
R. A R
The equation for cell constant is derived from above equation is shown below:
K =R
Here, = Conductivity
K = Cell constant
R = Resistance
We have, = 1.06296 106 S m 1
R = 4.2156
a) The cell constant is calcula
The equation for diffusion coefficient is shown below:
d N ( x)
J x = D
dx
Here, J x = Flux
D = Diffusion coefficient
N = Number density
dx = Thickness of foil
We have,
P = 1 atm
R = 8.21102 L atm mol1 K 1
T = 298 K
V = 15.2 cm3
A = 0.750 cm 2
T = 24 h
The equation for probability is shown below:
P=
W=
W
2
!
+x
+ x
!
!
2
2
!
+x
+ x
!
!
2
2
P=
2
Here, P = Probability
= Tot number of steps
x = Number of steps
We have,
= 10
x=6
The probability is calculated by following equation:
!
+x
+ x
!
!
2
For a weak electrolyte like a weak acid, the following equilibrium exists in aqueous
solution:
HA+H 2 O
A +H3O +
And the equilibrium constant, K a , is equal to
H 3O A
Ka =
HA
The dissociation of the acid can be defined relative to the degree of ion
c
( assuming co = 1 M ) should yield a
co
straight line. The corresponding plot is shown below:
If the electrolyte is strong, a plot of m versus
The linearity of the plot demonstrates that sodium acetate is a strong electrolyte. Best by
a straight line yi
According to Kohlrauschs law, a plot of conductivity versus
c
should yield a straight
co
line for a long electrolyte:
c
co
m = o K
m
Using a reference concentration of 1 M , the following plot is obtained:
0.0122
0.012
0.0118
0.0116
m
0.0114
0.0112
0.011
The species given in question are strong electrolytes, and the molar conductivity can be
related to individual ionic conductivities as follows:
( KCl ) = K + Cl
m
( NaCl ) = Na + Cl
m
( KNO3 ) = K + NO3
m
( a)
( b)
( c)
Subtracting (b) from (a) yields:
The equation for amount of charge is shown below:
Q = It
Here, Q = Amount of charge
I = Current
t = Time
We have,
I = 2.00 A
t = 30 s
The amount of charge is calculated by following equation:
Q = It
= 2.00 A 30 s
Q = 60 C
Coulombs of charge can be convert
xb
versus t can be constructed, the
xb,t =0
a) Using the data from the table, a plot of ln
slope of which is equal to 2 s :
The slope from the best fit to the line is 0.0107 hr 1 . Using this slope, the sedimentation
coefficient is determined as follo
The equation of molecular weight is shown below:
M=
(
RT s
D 1V
)
Here, M = Molecular weight
R = Gas constant
= Density
V = Specific volume
s = Sedimentation coefficient
T = Temperature
We have, for catalase
R = 8.314 J mol 1 K 1
= 0.998 g cm 3
V = 0.7
The equation for size of myoglobin is:
r=
kT
6 D
Here, r = Radius
k = Thermal conductivity
T = Temperature
D = Diffusion coefficient
= Viscosity
We have,
k = 1.38 1023 J K 1
( By Assuming from thermodynamic data )
T = 293 K
D = 1.13 1010 m 2 s 1
= 1.002
a) The equation given in question is shown below:
( T ) = Ae E RT
Taking the natural log of both sides of the above empirical equation:
( T ) = Ae E RT
We get:
ln = ln ( A ) +
E
RT
So, a graph of the natural log of the viscosity versus T 1 should yield
a) The thermal conductivity equation is
1 Cv , m
ave N
3 NA
=
And the equation for viscosity is
1
= ave Nm
3
From above both of equation, we get
1
C
= ave N v ,m
3
NA
C
C
= v , m = v ,m
mN A
M
=
Cv , m
M
b) The equation for thermal conductivity in te
a) The diffusion coefficient equation is
1
D = ave
3
And viscosity equation is
1
= ave N m
3
1
= ave Nm
3
(
)
= DNm
1
Q D = ave
3
= DNm
b) The equation for diffusion coefficient is shown below:
D=
Nm
Above equation can be rearranged as
kT RT RT
=
=
The equation of flow rate is shown below:
V r 4 P2 P
1
=
t
8 x2 x1
Here, V = Volume of fluid
t = Time taken by fluid
r = Radius of tube
= Viscosity of fluid
P = Exit pressure
1
P2 = Entrance pressure
x2 x1 = Length of tube
We have, for H 2
V = 200 ml =
The equation for viscosity is shown below:
= At
Here, = viscosity
A = Viscometer constant
= Density
t = Time
We have, = 1.0015 cP
= 0.998 g mL1
t = 15 s
The Viscometer constant is calculated by
A=
t
0.1 kg m 1 s 1 1 m3
=
1000 L
1P
0.998 kg L1 15 s
The equation for viscosity is shown below:
12
1 8 RT
=
3 M
1M
2 N A
Taking the ratio of viscosities for two species (denoted as 1 and 2) yields
2
M 2 1
=
1
M1 2
Assuming that the collisional cross sections for the species are the same, the ratio of
v
The equation for maximum average velocity is shown below:
Vx =
Re
d
Here, Re = 2000 , then
Vx =
2000
d
Here, Vx =
= Viscosity
d = Diameter
= Density
We have,
= 313 P
d = 2 mm
= It is calculated by data for an ideal gas by following equation:
=
=
PM
RT
The equation for flow rate is shown below:
V r 4 P2 P
1
=
t
8 x2 x1
Here, V = Volume of fluid
t = Time taken by fluid
r = Radius of tube
= Viscosity of fluid
P = Exit pressure
1
P2 = Entrance pressure
x2 x1 = Length of tube
We have, for O2
r = 2 mm = 2
The equation of collisional cross section in terms of viscosity and thermal conductivity in
terms of collisional cross section is shown below:
1
1 8 RT 2 1 M
=
3 M
2 N A
1
1 3 R 8RT 2 1
And =
3 2 NA M
2
Here, = Collisional cross section
= Thermal con