Question

Introduction: A mixing equation for any property X that is formed from two sources has the general form: X = fAXA + fBXB where fA is the fraction from source A having property XA and fB is the fraction from source B having property XB. Since X is only formed from two sources fA + fB = 1, i.e. the fractions add up to 1. For example, any property X of DOM in lake water is a mixture of that property of DOM specific to terrestrial sources (XA) and aquatic sources (XB). The first two questions of this assignment use this principle. 1. (20%) You are studying the properties of a lake and need to determine the amount of allochthonous (terrestrial) versus autochthonous (aquatic) dissolved organic matter (DOM) found in the water. Laboratory analysis for the elemental analysis of the DOM shows that terrestrial DOM has an N/C ratio = 1:125 whereas for the aquatic DOM the N/C ratio = 1:40. A sample of the lake water has a C/N = 55. Calculate: (a) the fraction of terrestrial organic matter in the sample water; (b) the fraction of aquatic organic matter in water sample.

Answer 1

For terrestrial DOM, C/N ratio = 125:1 = 125

Xa = 125

For aquatic DOM, C/N ratio = 40:1 = 40

Xb = 40

Lake water, C/N ratio = 55

X = 55

Fa * Xa + Fb * Xb = X

Fa + Fb = 1

Or Fa = 1 – Fb

Substituting in eqn (1) we get,

(1 – Fb) * Xa + Fb * Xb = X

Fb * (Xb – Xa) = X – Xa

Fb = X – Xa / (Xb – Xa)

= (55 – 125) / (40 – 125)

= 0.82

Fa = 1 – Fb = 1 – 0.82

= 0.18

a)

The fraction of terrestrial organic matter in the sample water, Fa = 0.18

b)

The fraction of aquatic organic matter in water sample, Fb = 0.82