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Mercury (Hg) poisoning is a debilitating disease that is often fatal. In the human body, mercury reacts with essential enzymes leading to irreversible inactivity of these enzymes. If the amount of mercury in a polluted lake is 0.4 \muμg Hg/mL, what is the total mass in kilograms of mercury in the lake? (The lake has a surface area of 100 mi2 and an average depth of 20 ft.) (1 mile = 5280 ft; 1 ft = 12 in; 2.54 cm = 1 in) (Use scientific notation)

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Answer:

6 x 10⁵ kg Hg

Explanation:

The mass of mercury in the entire lake is found by multiplying the concentration of the mercury by the volume of the lake.

The volume of the lake is calculated in cubic feet:

V = (SA)x(depth) = (100mi²)(5280ft/mi)² x (20ft) = 5.57568 x 10¹⁰ ft³

Cubic feet are then converted to mL (1cm³=1mL)

(5.57568 x 10¹⁰ ft³) x (12in/ft)³ x (2.54cm/in)³ = 1.578856752 x 10¹⁵ mL

The mass of mercury is then found:

m = CV = (0.4μg/mL)(1g/10⁶μg)(1kg/1000g) x (1.578856752 x 10¹⁵ mL) = 6 x 10⁵ kg Hg

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