Simulating a Random Walk

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Lab Partners:

When entering numeric data, use exponentials: ie., 1.6 * 10^-19 = 1.6E-19.

Procedure

1. Record the average distance "walked" over 10 trials by a molecule of 2 - Furylmethanethiol (C₅ H₆ OS, which is one of the ingredients in the aroma of coffee) in 10^-8 s at room temperature:

   x1 = m		y1 = m		d1 = m
   x2 = m		y2 = m		d2 = m
   x3 = m		y3 = m		d3 = m
   x4 = m		y4 = m		d4 = m
   x5 = m		y5 = m		d5 = m
   x6 = m		y6 = m		d6 = m
   x7 = m		y7 = m		d7 = m
   x8 = m		y8 = m		d8 = m
   x9 = m		y9 = m		d9 = m
   x10 = m		y10 = m		d10 = m

   d₂₉₃ = m

2. Repeat step 1 for four more temperatures (0 F, the boiling point of Nitrogen, the boiling point of water and the boiling point of Sulfur):

   x1 = m		y1 = m		d1 = m
   x2 = m		y2 = m		d2 = m
   x3 = m		y3 = m		d3 = m
   x4 = m		y4 = m		d4 = m
   x5 = m		y5 = m		d5 = m
   x6 = m		y6 = m		d6 = m
   x7 = m		y7 = m		d7 = m
   x8 = m		y8 = m		d8 = m
   x9 = m		y9 = m		d9 = m
   x10 = m		y10 = m		d10 = m

   d₂₅₅ = m

   x1 = m		y1 = m		d1 = m
   x2 = m		y2 = m		d2 = m
   x3 = m		y3 = m		d3 = m
   x4 = m		y4 = m		d4 = m
   x5 = m		y5 = m		d5 = m
   x6 = m		y6 = m		d6 = m
   x7 = m		y7 = m		d7 = m
   x8 = m		y8 = m		d8 = m
   x9 = m		y9 = m		d9 = m
   x10 = m		y10 = m		d10 = m

   d₇₇ = m

   x1 = m		y1 = m		d1 = m
   x2 = m		y2 = m		d2 = m
   x3 = m		y3 = m		d3 = m
   x4 = m		y4 = m		d4 = m
   x5 = m		y5 = m		d5 = m
   x6 = m		y6 = m		d6 = m
   x7 = m		y7 = m		d7 = m
   x8 = m		y8 = m		d8 = m
   x9 = m		y9 = m		d9 = m
   x10 = m		y10 = m		d10 = m

   d₃₇₃ = m

   x1 = m		y1 = m		d1 = m
   x2 = m		y2 = m		d2 = m
   x3 = m		y3 = m		d3 = m
   x4 = m		y4 = m		d4 = m
   x5 = m		y5 = m		d5 = m
   x6 = m		y6 = m		d6 = m
   x7 = m		y7 = m		d7 = m
   x8 = m		y8 = m		d8 = m
   x9 = m		y9 = m		d9 = m
   x10 = m		y10 = m		d10 = m

   d₇₁₈ = m

Analysis

1. Compute the diffusion constant for each temperature using the equation

   average distance = Sqrt(6 D t),

   where D is the diffusion constant:

   D293 = m2 / s

   D255 = m2 / s

   D77 = m2 / s

   D373 = m2 / s

   D718 = m2 / s

2. Graph the diffusion constant as a function of temperature.
3. Compute the diffusion constant for each temperature using

   3 k T / 2 = m v² / 2

   and

   D = v l / 3

   where k is the Boltzmann constant, m = 1.89306 x 10^-25 kg (the mass of a molecule of 2 - Furylmethanethiol), v is the molecular velocity, and l is the mean free path (3.34 x 10^-9 m):

   D293 = m2 / s

   D255 = m2 / s

   D77 = m2 / s

   D373 = m2 / s

   D718 = m2 / s

4. Graph the diffusion constant as a function of temperature for the results of the last step. Which graph is more accurate?