Mercury 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 mg Hg/mL, what is the total mass in kilograms of mercury in the lake? ( the lake has a surface area of 100 mi^2 and an average depth of 20 ft. )
To find the total mass of mercury in the lake, we need to calculate the volume of the lake and then multiply it by the concentration of mercury.
1. Start by converting the surface area of the lake from square miles to square feet:
100 mi^2 * 5280 ft/mi * 5280 ft/mi = 27,878,400,000 ft^2 (square feet).
2. Calculate the volume of the lake by multiplying the surface area by the average depth:
27,878,400,000 ft^2 * 20 ft = 557,568,000,000 ft^3 (cubic feet).
3. Convert the volume from cubic feet to milliliters (ml):
557,568,000,000 ft^3 * 28,316.8466 ml/ft^3 = 15,783,498,280,000 ml.
4. Finally, multiply the volume in milliliters by the concentration of mercury to get the total mass of mercury in the lake:
15,783,498,280,000 ml * 0.4 mg Hg/mL = 6,313,399,312,000 mg Hg.
To convert the mass from milligrams (mg) to kilograms (kg), divide the mass by 1,000:
6,313,399,312,000 mg Hg / 1,000,000 = 6,313,399,312 kg Hg.
Therefore, the total mass of mercury in the lake is approximately 6,313,399,312 kilograms.
To find the total mass of mercury in the lake, we need to calculate the volume of the lake first. We can then multiply the volume by the concentration of the mercury to find the mass.
Step 1: Convert the surface area from square miles to square meters.
1 square mile = 2.59 square kilometers (km²)
1 square kilometer = 1,000,000 square meters (m²)
100 mi² * 2.59 km²/mi² * 1,000,000 m²/km² = 259,000,000 m²
So, the surface area of the lake is 259,000,000 m².
Step 2: Convert the average depth from feet to meters.
1 foot = 0.3048 meters (m)
20 ft * 0.3048 m/ft = 6.096 m
So, the average depth of the lake is 6.096 m.
Step 3: Calculate the volume of the lake.
Volume = surface area * average depth
Volume = 259,000,000 m² * 6.096 m = 1,577,464,000 m³
Step 4: Convert the concentration from milligrams per milliliter (mg/mL) to kilograms per cubic meter (kg/m³).
1 mg/mL = 1 kg/m³
So, the concentration of mercury is 0.4 kg/m³.
Step 5: Calculate the mass of mercury in the lake.
Mass = volume * concentration
Mass = 1,577,464,000 m³ * 0.4 kg/m³ = 630,985,600 kg
Therefore, the total mass of mercury in the lake is 630,985,600 kilograms.
I would convert 100 square miles to cm^2, then multiply 20 feet (converted to cm) to find the volume in cc(mL). I'm assuming it is a rectangular shaped lake. It is some other shape you must use the appropriate formula to convert to volume.
Then 0.4 mg x volume in cc will give you the total Hg in mg. Convert mg to kg. The number I get is rather large.