# Question #539ce

##### 1 Answer

#### Answer:

#### Explanation:

Start by converting the surface area of the lake to *square meters*. This will then allow you to calculate the **volume** of the lake in *cubic meters*.

Use the fact that

#"1 km"^2 = "1 km" * "1 km"#

to get

#100 color(red)(cancel(color(black)("km"))) * color(red)(cancel(color(black)("km"))) * (10^3color(white)(.)"m")/(1color(red)(cancel(color(black)("km")))) * (10^3color(white)(.)"m")/(1color(red)(cancel(color(black)("km")))) = 1 * 10^8# #"m"^2#

Now, you can calculate the volume of the lake by multiplying its surface area by its average depth.

In your case, you will have

#1 * 10^8color(white)(.)"m"^2 * "20 m" = 2 * 10^9# #"m"^3#

Now, in order to be able to use the known concentration of arsenic, you must convert the volume to *cubic decimeters*.

#2 * 10^9 color(red)(cancel(color(black)("m"))) * color(red)(cancel(color(black)("m"))) * color(red)(cancel(color(black)("m"))) * "10 dm"/(1color(red)(cancel(color(black)("m")))) * "10 dm"/(1color(red)(cancel(color(black)("m")))) * "10 dm"/(1color(red)(cancel(color(black)("m")))) = 2 * 10^12# #"dm"^3#

Next, use the fact that

#"1 dm"^3 = "1 L"#

and

#"1 L" = 10^3# #"mL"#

to convert the volume to *milliliters*

#2 * 10^(12) color(red)(cancel(color(black)("dm"^3))) * (1color(red)(cancel(color(black)("L"))))/(1color(red)(cancel(color(black)("dm"^3)))) * (10^3color(white)(.)"mL")/(1color(red)(cancel(color(black)("L")))) = 2 * 10^(15)# #"mL"#

Next, calculate the mass of arsenic in *micrograms*

#2 * 10^15 color(red)(cancel(color(black)("mL"))) * (0.4color(white)(.)mu"g")/(1color(red)(cancel(color(black)("mL")))) = 8 * 10^(14)# #mu"g"#

Finally, use the fact that

#"1 g" = 10^6# #mu"g"#

and

#"1 kg" = 10^3# #"g"#

to convert the mass to *kilograms*

#8 * 10^(14) color(red)(cancel(color(black)(mu"g"))) * (1color(red)(cancel(color(black)("g"))))/(10^6color(red)(cancel(color(black)(mu"g")))) * "1 kg"/(10^3color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)(8 * 10^5color(white)(.)"kg")))#

The answer is rounded to one **significant figure**.