Find the Diffusion coefficient

In summary, a student 3.0 m away in a chemistry lab creates an odour that takes a while to reach you. After moving 2.0 m further away, the odour catches up with you in 60 seconds. Using the equation t = R^2 / 6D, with the hint that the root mean square distance and time must be measured from the source of the diffusing molecule, the attempt at a solution involves finding the time from 0-3m and using the ratio between the two distances. However, the resulting equation is unclear and does not match the textbook's answer of 0.044 for the diffusion coefficient. Further clarification and assistance is needed to solve the problem correctly.
  • #1
HelpaSista
1
0

Homework Statement



A student working 3.0 m away from you in the chemistry lab creates a bad odour. The odour takes a while to get to you (assume that air currents are negligible). You then move 2.0 m further away, but the odour catches up with you in another 60 seconds. What is the diffusion coefficient of the molecules you smell?

hint: the root mean square distancee and the time must be measured from the source of the diffusing molecule.


Homework Equations



t= R^2 / 6D


The Attempt at a Solution



I first tried to find time from 0-3m by using the ratio between the two distances

2^2 / 6*s X 6T/^3 = 1 (1 since D is the same)

I found that t = 135s

I then added 135 to 60 seconds and used that as my total time and 5 as my total R and solved for D

D = R^2 / 6*T

= 25 / 6*195

=0.02136


However, my textbook says the answer is 0.044 and I don't see what I am doing wrong. :(

Any help will be much appreciated, thank you!
 
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  • #2
Welcome to Physics Forums.
HelpaSista said:

Homework Statement



A student working 3.0 m away from you in the chemistry lab creates a bad odour. The odour takes a while to get to you (assume that air currents are negligible). You then move 2.0 m further away, but the odour catches up with you in another 60 seconds. What is the diffusion coefficient of the molecules you smell?

hint: the root mean square distancee and the time must be measured from the source of the diffusing molecule.


Homework Equations



t= R^2 / 6D


The Attempt at a Solution



I first tried to find time from 0-3m by using the ratio between the two distances

2^2 / 6*s X 6T/^3 = 1 (1 since D is the same)
It is not at all clear how you got this equation. What does it have to do with the ratio of the two distances? What is the "T/^3" supposed to mean, that combination of symbols makes no sense?

I found that t = 135s

I then added 135 to 60 seconds and used that as my total time and 5 as my total R and solved for D

D = R^2 / 6*T

= 25 / 6*195

=0.02136


However, my textbook says the answer is 0.044 and I don't see what I am doing wrong. :(

Any help will be much appreciated, thank you!
 

1. What is diffusion coefficient?

Diffusion coefficient is a measure of how quickly a substance moves through a medium by random molecular motion. It is also known as the diffusion constant, and is typically denoted by the symbol D.

2. How is diffusion coefficient calculated?

Diffusion coefficient is calculated by dividing the diffusion rate by the concentration gradient. It can also be determined experimentally by measuring the rate of diffusion of a substance over a known distance and time period.

3. What factors affect diffusion coefficient?

The diffusion coefficient is affected by several factors, including temperature, molecular size, and the nature of the medium. Higher temperatures and smaller molecules generally lead to higher diffusion coefficients, while a denser medium can slow down diffusion.

4. What is the unit of diffusion coefficient?

The unit of diffusion coefficient depends on the system of measurement being used. In the SI system, it is measured in square meters per second (m^2/s), while in the CGS system it is measured in square centimeters per second (cm^2/s).

5. How is diffusion coefficient used in scientific research?

Diffusion coefficient is a crucial parameter in many scientific fields, including chemistry, biology, and materials science. It is used to study the movement of molecules in different environments, as well as to understand the properties and behavior of various substances. It is also used in practical applications such as drug delivery systems and industrial processes.

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