If the amount of mercury in a polluted lake is 0.4 µg Hg/mL, what is the total mass in kilograms of mercury in the lake? (The lake has a surface area of 100mi^2 and an average depth of 20 ft.)
I'll probably be able to solve this once I know what it's going on about. Is this micrograms per hectogram per milliliter? I'm just not sure what it means by "0.4 µg Hg/mL".
Never mind, Hg is mercury. Someone helped me offsite.
Change the surface of area from 100 mi^2 to cm^2 and the 20 ft to cm. Then surface area x depth = volume in cm^3 = mL. Then you have 0.4 x 10^-6 grams Hg/mL. Post your work if you get stuck.
The notation "0.4 µg Hg/mL" means that there is 0.4 micrograms of mercury (Hg) per milliliter (mL) of water.
To find the total mass of mercury in the lake, we need to consider the volume of water in the lake.
First, we need to convert the surface area of the lake from square miles to square meters. Since 1 mile is approximately equal to 1609 meters, we multiply the surface area by (1609 m/mile)^2 to convert it to square meters.
Surface area of the lake = 100 mi^2 * (1609 m/mile)^2
Next, we need to convert the average depth of the lake from feet to meters. Since 1 foot is approximately equal to 0.3048 meters, we multiply the depth by 0.3048 to convert it to meters.
Average depth of the lake = 20 ft * 0.3048 m/ft
Now, we can calculate the volume of water in the lake by multiplying the surface area by the average depth.
Volume of water in the lake = Surface area of the lake * Average depth of the lake
Next, we need to convert the volume from cubic meters to milliliters. Since 1 cubic meter is equal to 1,000,000 milliliters, we multiply the volume by 1,000,000 to convert it to milliliters.
Volume of water in the lake = Volume of water in the lake * 1,000,000 mL/m^3
Finally, we can calculate the total mass of mercury in the lake by multiplying the volume of water in the lake by the concentration of mercury.
Total mass of mercury in the lake = Concentration of mercury * Volume of water in the lake
Note: The final answer will be in micrograms (µg). If you want to convert it to kilograms, you would divide the final answer by 1,000,000.
Let me know if you would like me to perform the calculations for you or if you have any further questions!
The notation "0.4 µg Hg/mL" represents a concentration of mercury in the polluted lake. It means that there are 0.4 micrograms (µg) of mercury per milliliter (mL) of water in the lake. The "Hg" stands for mercury, which is the chemical symbol for this element.
To find the total mass of mercury in the lake, you need to know the volume of the lake. The volume can be calculated by multiplying the surface area of the lake by its average depth.
Given:
Surface area of the lake = 100 mi²
Average depth of the lake = 20 ft
Before we proceed with the calculations, we will need to convert the given values to a consistent unit system. Let's convert them to metric units:
Surface Area:
1 mi² = 2.59 km² (conversion factor: 1 mi² = 2.59 km²)
100 mi² ≈ 259 km²
Average Depth:
1 ft = 0.3048 m (conversion factor: 1 ft = 0.3048 m)
20 ft ≈ 6.096 m
Now that we have the surface area and average depth in metric units, we can calculate the volume of the lake:
Volume of the lake = Surface Area × Average Depth
Volume of the lake = 259 km² × 6.096 m
To perform the calculation, convert the given value of surface area in square kilometers into square meters:
1 km² = 1,000,000 m² (conversion factor: 1 km² = 1,000,000 m²)
259 km² ≈ 259,000,000 m²
Now substitute the values into the equation:
Volume of the lake = 259,000,000 m² × 6.096 m
= 1,579,664,000 m³
So, the volume of the lake is approximately 1,579,664,000 cubic meters (m³).
Now that we know the volume of the lake, we can calculate the mass of mercury using the concentration provided:
Concentration of mercury = 0.4 µg Hg/mL
To find the mass of mercury in the lake, we need to multiply the concentration by the volume:
Mass of mercury = Concentration × Volume
Mass of mercury = 0.4 µg Hg/mL × 1,579,664,000 m³
To perform this calculation, we will need to convert µg to kg:
1 µg = 0.000001 kg (conversion factor: 1 µg = 0.000001 kg)
0.4 µg ≈ 0.0000004 kg
Substitute the values into the equation:
Mass of mercury = 0.0000004 kg/mL × 1,579,664,000 m³
= 631.8656 kg
Therefore, the total mass of mercury in the lake is approximately 631.8656 kilograms (kg).