Question

If the amount of mercury in a polluted lake is 0.40 ug/mL, what is the total mass of mercury in the lake? (The lake has a surface area of 100 mi squared and an average depth of 25 ft).

Answer 1

You're given the area (100 mi^2) and the thickness (25ft). A few things to keep in mind:

Volume = area * thickness
1mL = 1 cm^3
Density = mass/volume

Thus, you have the volume and the density of mercury in the lake (which is .40 ug/mL). Inconveniently, you were given garbled units for the volume, so you must convert them. I'm going to convert them to cm.

100mi^2 * (1.6km/mi)^2 * (1000m/km)^2 * (100cm/m)^2 = 25600cm^2

25ft * 12in/ft * 2.54cm/in = 762 cm

Now plug them in the equation for volume:

thickness * area = Volume
762cm * 25600cm^2 = 19507200cm^3

You are trying to find the total mass of Hg (mercury) in the lake, so switch the density formula around for mass and plug in the numbers:

density * volume = mass
.40 ug/mL * 19507200mL = 7802880ug of mercury.