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McKay, Donald. "Front matter" Multimedia Environmental Models ...

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iomagnification is more significant for these animals, rendering them more vulnerable<br />

to toxic effects of persistent chemicals.<br />

Worked Example 8.2<br />

Calculate the fugacity of a fish at steady-state when exposed to uptake of a<br />

hydrophobic chemical from water and food. Deduce the fluxes and determine if<br />

biomagnification occurs. What would be the implication it the metabolic rate constant<br />

increases by a factor of 8?<br />

Input data<br />

f W = 10 –6<br />

f A<br />

= 2 ¥ 10 –6 (slight biomagnification in food)<br />

D V = 10 –4<br />

D A = 10 –3<br />

D M = 10 –4<br />

Q = 4<br />

f F<br />

= (D V f W + D A f A)/(D V + D M + D A /Q) = (10 –10 + 2 ¥ 10 –9 )/(4.5 ¥ 10 –4 )<br />

= 4.67 ¥ 10 –6 Pa<br />

There is food to fish biomagnification by a factor of 2.33.<br />

If D M is increased to 8 ¥ 10 –4 , the fugacity in the fish drops to 1.83 ¥ 10 –6 Pa,<br />

which eliminates biomagnification entirely. The fluxes in the two cases are (in units<br />

of 10 –9 mol/h or n mol/h) as follows.<br />

Input from water 0.1<br />

Input from food 2.0 (total input is 2.1)<br />

Loss to water 0.467 (slow metabolism), 0.183 (fast metabolism)<br />

Loss by egestion 1.168 (slow metabolism), 0.457 (fast metabolism)<br />

Loss by metabolism 0.467 (slow metabolism), 1.460 (fast metabolism)<br />

Total loss 2.1 (slow metabolism), 2.1 (fast metabolism)<br />

In both cases, because fugacity in the fish exceeds that of the water, there is net loss<br />

by respiration. The presence of biomagnification depends on whether the fish can<br />

clear the chemical fast enough to maintain a fugacity less than that of the food. In<br />

this case, if the metabolic rate was zero, the fish would reach a fugacity of 6 ¥<br />

10 –6 Pa, 3 times that of the food, losing 0.6 to water and 1.5 by egestion.<br />

©2001 CRC Press LLC

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