R = 8.315 J/(mol K) (Universal Gas Constant) T = temperature of suspension in Ke

Question

R = 8.315 J/(mol K) (Universal Gas Constant)

T = temperature of suspension in Kelvin

= viscosity of the fluid

a = radius of the particle in the suspension

In order to determine Avogadros number we need to determine themean square displacement of the particles as a function of time andthen plot <r2> versus time. The slope of this plotshould then equal the expression between the square brackets in Eq.1. Knowing R, T, , a and n, we can determine NA. Asimplified, yet less accurate, version - instead of plotting<r2> versus time - is to determine<r2> for one specific time t and plugging thosetwo numbers into the equation.

Explanation / Answer

Question 1: The equation looks complicated - the way to tackle it is to firstsingle out the constants. For this question, d, R, a,NA and t are all constant. Theonly parameters we need concern ourselves with are viscosity and T.From the equation, increasing T will increase the numerator of theequation, resulting in an increased . Justfrom this we can answer the first part of the question and say thatwe expect to change. What about the effect ofviscosity on ? Generally, as temperature (T)increases, viscosity decreases (i.e. 'runnier'). So decreasingviscosity = smaller denominator = larger again. So we expect to increase withincreasing temperature. Question 2: (A) 'a' is the radius of the particle, so increasing the particle'size' means 'a' changes. (B) This time we assume the other constants - d, R, T, viscosity(?), NA, t - are all constant. Thus, increasing 'a' =larger denominator = smaller . (C) As particle size increases, the particles are heavier andtherefore harder to move - just like how a big boulder is harder toroll than a small pebble. This means the distance that they travelduring their 'random walk' is, on average, less than for a smallparticle. Question 3:Assuming we do not change any ofthe other parameters, as t increases willincrease. ('number' x short time < 'number' x long time). Thisalso makes sense, since the longer we observe the particle thefurther (distance, not displacement) we will see it travel.

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