Calculating Diffusion Constant Equations: Homework

In summary, the problem involves counting ants at concentric 5cm circles on a smooth table. The number of ants at each ring starting from the origin are 3, 5, 15, 19, 37, 23, 11, 1, 0, 0, and 2 respectively. The average displacement is 39.18, the root-mean-squared displacement is 6.94, and the diffusion constant is unknown.
  • #1
3=MCsq
4
0

Homework Statement


Ants are release from the center point of a smooth table and after 1 minute a snapshot is taken and the ants are counted at concentric 5cm circles. There are 10 outer circles ( The most outer circle being 50cm from origin). The number of ants at each ring starting from origin: 3, 5, 15, 19, 37, 23, 11, 1, 0, 0, 2, respectively.

What are the average displacement, root-mean-squared displacement, and diffusion constant?

Homework Equations


Average displacement is sum of the squared value of each counted # of ants at each ring,, divided by the number of rings? == [(x1)^2 + (x2)^2 + ... + (xn)^2]/11 ? I'm not sure about this, it seems to easy, and I'm not confident that I understand exactly what is being asked for.

Root-mean-squared displacement: √[(1/11)*(x1)^2+(x2)^2+ ... + (xn)^2].
This seems straight forward, but then again, I'm not sure that I started out on the right path.

Diffusion constant: This is where I'm very lost, I have t = (x^2)/2D but my teacher hinted that the solution was the Gaussian distribution and I have no idea how to derive or arrive at that conclusion. Thanks guys
 
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  • #2
.The Attempt at a Solution Average displacement: [(3)^2 + (5)^2 + (15)^2 + (19)^2 + (37)^2 + (23)^2 + (11)^2 + (1)^2 + (0)^2 + (0)^2 + (2)^2]/11 = 39.18Root-mean-squared displacement: √[(1/11)*(3)^2 + (5)^2 + (15)^2 + (19)^2 + (37)^2 + (23)^2 + (11)^2 + (1)^2 + (0)^2 + (0)^2 + (2)^2] = 6.94Diffusion constant: I have no idea what to do here.
 

1. What is the diffusion constant equation?

The diffusion constant equation is a mathematical formula that relates the rate of diffusion of a substance to its properties, such as temperature, concentration, and molecular weight. It is often denoted by D in scientific literature and can vary depending on the type of diffusion being observed (e.g. Fickian diffusion or non-Fickian diffusion).

2. How do I calculate the diffusion constant?

The diffusion constant can be calculated using the following equation: D = (MRT)/(6πrη), where M is the molecular weight of the diffusing substance, R is the gas constant, T is the temperature, r is the radius of the diffusing particles, and η is the viscosity of the medium in which diffusion is occurring. These values can be obtained from experimental data or from known physical properties of the substances involved.

3. What units are used for the diffusion constant?

The units for the diffusion constant depend on the units used for the other variables in the equation. In the SI system, the diffusion constant is typically expressed in m^2/s, while in the CGS system, it is expressed in cm^2/s. It is important to ensure that all units are consistent when using the equation to calculate the diffusion constant.

4. Can the diffusion constant be used for all types of diffusion?

No, the diffusion constant equation is most commonly used for Fickian diffusion, which involves the movement of particles from an area of high concentration to an area of low concentration. However, it may also be applicable to other types of diffusion, such as non-Fickian diffusion, depending on the specific conditions and substances involved.

5. What are some factors that can affect the accuracy of the diffusion constant equation?

The diffusion constant equation assumes ideal conditions and does not take into account factors such as external forces (e.g. gravity), non-uniformity of the medium, and interactions between particles. Additionally, experimental errors and variations in the physical properties of the substances being studied can also affect the accuracy of the calculated diffusion constant.

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