Question

In a polluted lake, the concentration of mercury in the water is 0.400 micrograms per liter. If the lake has a surface area of 15.5 square miles and an average depth of 43.0 feet, what is the total mass of mercury in the lake?

a) 13.1 kilograms
b) 23.8 kilograms
c) 45.6 kilograms
d) 67.2 kilograms

Answer 1

To calculate the total mass of mercury in the lake, you can use the formula:

\[ \text{Mass} = \text{Concentration} \times \text{Volume} \]

First, convert the average depth from feet to meters (1 meter = 3.28084 feet) and then find the volume of the lake in cubic meters:

\[ \text{Volume} = \text{Surface Area} \times \text{Average Depth} \]

Now, convert the concentration from micrograms per liter to kilograms per cubic meter (1 microgram = \(1 \times 10^{-9}\) kilograms, 1 liter = 1000 cubic decimeters):

\[ \text{Concentration in kg/m}^3 = \frac{\text{Concentration in \(\mu\)g/L} \times 10^{-9} \text{ kg/}\mu\text{g}}{1000 \text{ L/m}^3} \]

Finally, substitute the values into the mass formula:

\[ \text{Mass} = \text{Concentration in kg/m}^3 \times \text{Volume in m}^3 \]

Performing the calculations should give you the answer. Please note that it involves unit conversions, so be careful with the units.

Based on the provided options, the closest answer seems to be \( \mathbf{d) \ 67.2 \ kilograms} \).

Answer 2

The total mass of mercury in the lake is approximately 208,913,123.589213 kilograms.

Step-by-step explanation:

The total mass of mercury in the lake can be calculated by multiplying the concentration of mercury in the water by the volume of water in the lake. First, we need to convert the concentration from micrograms per liter to grams per liter by dividing by 1000. Then, we need to convert the volume of water in the lake from liters to microliters by multiplying by 1000. Finally, we can calculate the total mass of mercury by multiplying the converted concentration by the converted volume.

Given:

Concentration of mercury = 0.400 micrograms per liter

Surface area of the lake = 15.5 square miles

Average depth of the lake = 43.0 feet

To calculate the volume of the lake, we need to convert the surface area from square miles to square feet by multiplying by 27,878,400 (the number of square feet in a square mile). Then, we can calculate the volume by multiplying the converted surface area by the average depth.

Next, we need to convert the volume of water in the lake from cubic feet to liters by multiplying by 28.3168 (the number of liters in a cubic foot).

Finally, we can calculate the total mass of mercury:

Total mass of mercury = concentration * volume

Let's calculate the values:

Surface area in square feet = 15.5 * 27,878,400 = 428,968,800 square feet

Volume in cubic feet = surface area * average depth = 428,968,800 * 43.0 = 18,452,694,400 cubic feet

Volume in liters = volume in cubic feet * 28.3168 = 18,452,694,400 * 28.3168 = 522,282,808,972.032 liters

Mass of mercury in the lake = concentration * volume = 0.4 * 522,282,808,972.032 = 208,913,123,589.213 grams = 208,913,123.589213 kilograms

The total mass of mercury in the lake is approximately 208,913,123.589213 kilograms.