Equations

Question 1

Equations for Osmosis
- The equation for pressure of an ideal gas
- osmotic pressure (ideal solution)

Answer 1

Equation for pressure:

P = (n/V)RT

where

n: number of molecules (6.022*10^23 avogadros tal pr mol af et stof)
V: Volumen
R: gas konstant (0.0821)
T: Temperatur i Kelvin

Equation for Osmotic Pressure of Ideal Solution:

Phi = icR*T

where

i: van der Walls constant
c: Concentration
R&T: same as before

Question 2

Diffusion (Ficks Law)

Answer 2

Is the change in concentration field

Equation
j = -D (dc/dx)

Question 3

Diffusion (Stokes-Einstein equation)
Be able to say how the different components of the equation affects the diffusion coefficient

Answer 3

Calculation of diffusion coefficient:

D = KbT / 6pinR

Kb is a constant
T is the temperature
n is the number of particles
R is the radius of the particles

Question 4

Diffused Distance

Answer 4

Sqrt(x^2) = sqrt( 2Dt)

where x is the distance
D is the diffusion coeffecient (Stokes-Einstein)
t is the time

Question 5

Capillarity (Height of water column h)

Answer 5

Height of water column, h is given by:

h = 2ycos(THETA) / rhogR0

where

y is the surface tension
THETA is the contact angle of the water and the capillary
rho is the mass density
g is the gravitational acceleration constant
R0 is the radius

Question 6

Flow Rate (Through tube)

Answer 6

Q = pidPd^4 / 128nl

where

dP is the difference in pressure
d is the diameter
n is the viscosity of the liquid
l is the length of the tube

Question 7

Entropic Elasticity (Force)

Answer 7

F = -KbT3R / Nl^2

where
Kb is a constant
T is the temperature
R is the end-to-end distance
N is the number of segments in the protein
l is the length of each N segments in protein (kuhn length)

Question 8

Kuhn Length, Force to extende Stiff and flexible proteins

Answer 8

If you pull a polymer apart, you decrease its entropy. hence you need to add force.

The amount of force needed to stretch a polymer with a short persistance length (felixible polymer) is larger than the force needed to stretch a polymer with a longer persistance length (Stiff polymer)

The proportional difference in force can be calculated given to persistence lengths of f.ex. 50nm and 10nm

50/10 = 5

i.e. you would need to use 50 times the amount of force to stretch the polymer with 10nm persistance length to the same end-to-end distance.