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 (
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
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 in
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 inve
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 t
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
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, = 1.0629
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
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 probabilit
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 o
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 acet
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 obt
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
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
=
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 slop
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
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 thermo
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 th
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
=
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
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 pressu
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=
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 cros
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
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 press
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 N