Mercury concentration in a polluted lake is 0.0125 micrograms/L. What is the total mass in kilograms of mercury in the lake if the lake is approximately circular witha diameter of 10 miles and an average depth of 50 ft.?

Convert 5 mi radius to cm and 50 ft depth to cm, then pi*r^2*h will give you the volume in cc. Then convert cc to L and multiply by 0.0125 to give micrograms Hg in the lake. Convert to kg. Post your work if you get stuck.

2.2345x10^-2kg

To find the total mass of mercury in the lake, we first need to calculate the volume of the lake.

1. Convert the diameter of the lake from miles to feet:
10 miles = 10 * 5280 feet = 52,800 feet

2. Calculate the radius of the lake by dividing the diameter by 2:
Radius = 52,800 feet / 2 = 26,400 feet

3. Calculate the area of the lake using the formula for the area of a circle:
Area = π * Radius^2
Area = 3.14 * (26,400 feet)^2

4. Calculate the volume of the lake by multiplying the area by the average depth:
Volume = Area * Depth
Note: The average depth needs to be converted from feet to liters.
1 liter = 1000 cm³
1 cm = 0.0328 feet
Average depth in feet = 50 feet
Average depth in cm = 50 feet / 0.0328 = 1524 cm
Average depth in liters = 1524 cm * (1 liter / 1000 cm³) = 1.524 liters
Volume = (3.14 * (26,400 feet)^2) * 1.524 liters

5. Convert the volume from liters to cubic meters:
1 cubic meter = 1000 liters
Volume in cubic meters = Volume in liters / 1000

6. Calculate the mass of mercury in the lake using the concentration:
Mass = Volume in cubic meters * Mercury concentration in micrograms / (1,000,000 micrograms/gram)

Let's calculate the total mass of mercury in the lake step-by-step.

Step 1: Convert the diameter to feet
10 miles = 10 * 5280 feet = 52,800 feet

Step 2: Calculate the radius
Radius = 52,800 feet / 2 = 26,400 feet

Step 3: Calculate the area
Area = 3.14 * (26,400 feet)^2

Step 4: Calculate the volume
Average depth in feet = 50 feet
Average depth in liters = 1524 cm * (1 liter / 1000 cm³) = 1.524 liters
Volume = (3.14 * (26,400 feet)^2) * 1.524 liters

Step 5: Convert the volume to cubic meters
Volume in cubic meters = Volume in liters / 1000

Step 6: Calculate the mass
Mass = Volume in cubic meters * Mercury concentration in micrograms / (1,000,000 micrograms/gram)

To calculate the total mass of mercury in the lake, we need to know the volume of the lake and then multiply it by the concentration of mercury.

First, let's convert the measurements to a consistent unit system.

The diameter of the lake is given as 10 miles. To simplify calculations, we need to convert this distance to a smaller unit such as feet. Since 1 mile is approximately equal to 5280 feet, we can multiply the diameter by 5280 to obtain the diameter in feet:

10 miles * 5280 feet/mile = 52,800 feet

Next, we need to calculate the volume of the lake. Assuming the lake is a perfect cylinder shape, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

where π is a mathematical constant (approximately 3.14159), r is the radius of the lake, and h is the height or depth of the lake.

Since the lake is circular, the radius is half the diameter. Therefore, the radius is:

52,800 feet / 2 = 26,400 feet

The average depth of the lake is given as 50 feet.

Now we can substitute the values into the volume formula:

Volume = 3.14159 * (26,400 feet)^2 * 50 feet

Calculating this equation gives us the volume of the lake in cubic feet.

Finally, we need to convert the volume to liters since the concentration of mercury is provided in micrograms per liter. To convert cubic feet to liters, we can use the conversion factor: 1 cubic foot = 28.3168466 liters.

After calculating the volume in liters, we can multiply it by the concentration of mercury to find the total mass of mercury in the lake.

Let's go ahead and calculate the total mass of mercury in the lake:

1. Calculate the radius of the lake:
r = 26,400 feet

2. Calculate the volume of the lake:
Volume = 3.14159 * (r^2) * h = 3.14159 * (26,400 feet)^2 * 50 feet

3. Convert the volume to liters:
Volume (liters) = Volume (cubic feet) * 28.3168466 liters/cubic foot

4. Calculate the total mass of mercury:
Mass = Volume (liters) * 0.0125 micrograms/L

This will give us the total mass of mercury in the lake in micrograms. To convert it to kilograms, we need to divide by 1,000,000 since there are 1,000,000 micrograms in a kilogram.

Now you have all the steps to calculate the total mass of mercury in the lake. Plug in the values and follow the steps to find the answer.