Ocean 520
Marine Chemistry
Autumn 2008
Problem Set 2 solutions
1.a. Find the volume of the lake:
Surface Area = 1 km2 = (1000 m/km)2 = 1 * 106 m2
Volume = SA * Depth = (1 * 106 m2) * (20 m) = 2 * 107 m3
Use the residence time equation:
τ = V/f
= (2 * 107 m3) / (50 m3 s-1) = 400000 s
400000 s * (1 m / 60 s) * (1 h / 60 m) * (1 d / 24 h) = 4.6 days
b. Use equation in Appendix 2.2:
C – Cin = (Co – Cin)exp-(f*t/V)
Where Cin = 10 µM L-1
f = 50 m3 s-1
t = 5 days (convert to seconds) = 5 * 60 * 60 * 24 = 432000 s
V = 2 * 107 m3
Solve for C:
C = (10 µM L-1) – (10 µM L-1) * (0.339596) = 6.6 µM L-1
c. Use same equation as above except now:
Co = 6.6 µM L-1
Cin = 1 µM L-1
t = still 5 days (from end of spill to 10 days after spill began) = 432000 s
Solve for C:
C = (6.6 µM L-1 – 1 µM L-1) * (0.339596)) + 1 µM L-1 = 2.9 µM L-1
