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).

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.

Well, before we dive into calculating the total mass of mercury in the lake, let's take a moment to appreciate the fact that the lake didn't turn into Freddie Mercury from all that pollution! Phew!

Now, to calculate the total mass of mercury, we'll need to consider the lake's volume. First, we need to convert the surface area from square miles to square feet, which gives us 100 mi² * 5,280 ft/mi * 5,280 ft/mi = a whopping 27,878,400 ft².

Next, let's convert the average depth from feet to miles. We have 25 ft * 1 mi/5,280 ft = approximately 0.0047 mi.

To find the volume of the lake, we multiply the surface area by the average depth, resulting in 27,878,400 ft² * 0.0047 mi = 130,785 ft³.

Finally, we need to convert the volume from cubic feet to milliliters. Since 1 ft³ is approximately 28,316.8466 mL, we have 130,785 ft³ * 28,316.8466 mL/ft³ = 3,699,166,370 mL.

Now, if the concentration of mercury is 0.40 μg/mL, we can multiply the concentration by the volume to find the total mass of mercury in the lake: 0.40 μg/mL * 3,699,166,370 mL = approximately 1,479,666,548 μg.

So, the total mass of mercury in the lake is around 1,479,666,548 micrograms. That's a whole lot of heavy metal, but don't worry, the Clown Bot is here to bring some lightness to the situation!

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

The surface area of the lake is given as 100 mi², which is equivalent to 2.59 x 10^14 mm² (since 1 mi² = 2.59 x 10^12 mm²).
The average depth of the lake is 25 ft, which is equivalent to 7.62 m (since 1 ft = 0.3048 m).

To find the volume of the lake, we can multiply the surface area by the average depth:

Volume = Surface Area x Average Depth
Volume = 2.59 x 10^14 mm² x 7.62 m
Volume = 1.97 x 10^15 mm³.

Now, we know the concentration of mercury in the lake is 0.40 ug/mL. We'll use this information to calculate the total mass of mercury in the lake.

To do this, we'll need to convert the volume of the lake from mm³ to mL, since the concentration is given in ug/mL.

1 mL = 1 cm³.

So, we have:
Volume = 1.97 x 10^15 mm³
Volume = 1.97 x 10^15 cm³ (since 1 mm³ = 1 cm³).

Now, let's calculate the total mass of mercury:

Total Mass = Volume x Concentration
Total Mass = 1.97 x 10^15 cm³ x 0.40 ug/mL.

Multiplying these values:

Total Mass = 7.88 x 10^14 ug.

Therefore, the total mass of mercury in the lake is 7.88 x 10^14 ug.

To find 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. Let's calculate it step by step.

Step 1: Convert the lake's surface area to the corresponding volume. The surface area is given as 100 mi², but we need to convert it to cubic feet since the average depth is given in feet. Since 1 mile = 5280 feet, we have:

Volume = Surface Area x Depth = 100 mi² x 5280 ft/mi x 25 ft
Volume = 100 x 5280 x 25 ft³

Step 2: Convert the volume from cubic feet to milliliters. Since 1 ft³ = 28,316.8 mL, the volume in milliliters is:

Volume = 100 x 5280 x 25 ft³ x 28,316.8 mL/ft³

Step 3: Calculate the total mass of mercury. The concentration of mercury is given as 0.40 ug/mL:

Mass of Mercury = Volume x Concentration
Mass of Mercury = (100 x 5280 x 25) x 28,316.8 x 0.40 ug

By performing the calculations, you can find the mass of mercury in the lake.