10. Diffusion

Question 1

What is diffusion?

Answer 1

spreading of particles of a substance due to thermal motion.

Question 2

How do we define a flux?

Answer 2

By defining the flow density of particles per second that gives the amount of chemical material that passes through a unit area in unit time. Its unit is mol /(m2∙s).

Question 3

What is Fick’s first law?

Answer 3

the flow of particles per unit time across a unit area (flux) is proportional to the concentration drop

Where the coefficient D is the diffusion coefficient.

Question 4

What is the concentration drop (concentration gradient)

Answer 4

where 􏵺∆c/∆􏵺x is the concentration change along a unit distance (along the x axis)

Question 5

What is the relationship between the flow density of particles per second and the concentration drop?

Answer 5

the flow density of particles per second is proportional to the concentration drop

Question 6

What is diffusion coefficient (D)

Answer 6

gives the amount of material diffused across a unit area in a unit time, driven by a unit concentration drop. The unit of the diffusion coefficient is m2/s.

Question 7

What does the diffusion coefficient depend on?

Answer 7

• the size and shape of the diffusing particle
• the viscosity and temperature of the medium

Question 8

For spherical particles, how to calculate diffusion coefficient?

Answer 8

the diffusion coefficient can be calculated from the Einstein-Stokes formula as….

where r is the radius of the particle, 􏶐n is the viscosity and T is the temperature of the medium.

Question 9

What doesn’t the Fick’s 1st law take into account?

Answer 9

the possibility of temporal changes in concentration

Question 10

What does Fick 2nd law state?

Answer 10

describes the spatial and temporal changes of the concentration as

If the spatial distribution of the concentration is known at a given time [c(x,t)], it gives the distribution at a later time t+􏵺t.

Question 11

Determination of the diffusion coefficient

We will apply Fick’s second law to determine the diffusion coefficients of K+ and Cl– ions (together with their hydration shells, which are roughly the same).

What are the 3 things we need to suppose

Answer 11

1. an outward diffusion process happens in a cylinder-shaped gel and in the surrounding water → the conditions are identical inside and outside the gel from the point of view of diffusion
2. The concentration is c₀ everywhere inside the gel → the area of the end faces is negligible compared to the cylinder jacket
3. the concentration outside the cylinder body is always zero.

Question 12

Determination of the diffusion coefficient

We will apply Fick’s second law to determine the diffusion coefficients of K+ and Cl– ions (together with their hydration shells, which are roughly the same).

initially, the concentration is c0 everywhere inside the gel, and the area of the end faces is negligible compared to the cylinder jacket

→ What does this imply?

Answer 12

this implies diffusion in the radial direction, with cylindrical symmetry

Question 13

Determination of the diffusion coefficient

We can see from the lin-log graph (Fig. 4) that, after a sufficiently long time after the beginning of the process, the change of the amount of the material as a function of time becomes ___.

Answer 13

exponential

Question 14

Determination of the diffusion coefficient

We can see from the lin-log graph (Fig. 4) that, after a sufficiently long time after the beginning of the process, the change of the amount of the material as a function of time becomes exponential.

→ When does this transition to exponential behavior occur?

Answer 14

when the shape of the concentration distribution inside the gel stabilizes

→ the transport process occurs not only at the edges (near the cylinder jacket), but inside the gel (near the axis) as well

Question 15

Determination of the diffusion coefficient

The gel contains KCl solution, and is surrounded by distilled water. During the diffusion process, K+ and Cl– ions move outward into the water, and make it a ___

Answer 15

conductor (electrolyte)

Question 16

What is time constant of diffusion?

Answer 16

depends on the diffusion coefficient and on the radius of the gel

Question 17

Name the parameters influencing the value of diffusion coefficient.

Answer 17

Size and shape of the particle as well as the temperature and viscosity of the medium

Question 18

What diffuses faster: a potassium ion or a virus particle?

Answer 18

K+ ion due to smaller diffusion coefficient (smaller size)

Question 19

Determination if diffusion-coefficient by image analysis

Answer 19

From the lin-log graph (Fig. 4) that,

• after a sufficiently long time after the beginning of the process → the change of the amount of the material as a function of time becomes exponential.
• We determine the t half-life (T = ln2∙ half-life􏱐)
• We get the diffusion coefficient

Question 20

The electrical resistance of a wire can be determined by the following formula ___

Answer 20

Question 21

What is conductance?

Answer 21

The reciprocal of the resistance (G = 1/R)

Question 22

The relationship between Conductivity of a dilute solution and the concentration of the solution.

Characteristics of The proportionality constant

Answer 22

Conductivity of a dilute solution is directly proportional to the concentration of the solution.

Question 23

The proportionality constant is characteristic to the solute and characterizes the mobility of the ions in the solution. Thus, a___can be prepared (see Fig. 6), or the slope of the linear function can be given, and the concentrations corresponding to the measured conductivity values, or the amount of material in the given volume can be calculated.

Answer 23

calibration graph

Question 24

It is possible to measure the amount of material inside the gel?

Answer 24

It is not possible to measure the amount of material inside the gel

→ but the amount of the material that has diffused out can be measured.

→ Thus, the amount that remained inside the gel can be determined.

Question 25

How to measure the amount of material inside the gel?

Answer 25

It is not possible to measure the amount of material inside the gel

→ but the amount of the material that has diffused out can be measured.

→ Thus, the amount that remained inside the gel can be determined.

Question 26

What is random walk model?

Answer 26

Brownian motion is a phenomenon where particles have “random walk” (which itself exists in many other fields as well).

Brownian motion: the random motion of particles due to collisions with the surrounding molecules.

Question 27

How to make a home-made macroscopic model of random-walk model?

Answer 27

vibrated poppy seads = solvent particles, plastic ball on top = suspended particle