Question

The bromine content of the ocean is about 65 g of bromine per million g of sea water. How many cubic meters of ocean must be processed to recover 500 mg of bromine, if the density of sea water is 1.0x 103 kg/m3?

Answer 1

To recover 500 mg of bromine from the ocean, one must process approximately 7.69231 liters or 7.69231 x 10^-3 cubic meters of sea water, considering the bromine content and the density of sea water.

Step-by-step explanation:

The student asked how many cubic meters of ocean must be processed to recover 500 mg of bromine, given that the ocean contains about 65 g of bromine per million g of sea water and the density of sea water is 1.0x 103 kg/m3.

To find the volume of ocean water needed to extract 500 mg (0.5 g) of bromine, we use the proportion:

• 65 g bromine/1,000,000 g sea water = 0.5 g bromine/x g sea water

Solving for x gives us:

• x = (0.5 g bromine * 1,000,000 g sea water) / 65 g bromine
• x ≈ 7692.31 g of sea water

To convert grams of sea water to cubic meters, we use the density of sea water:

• density = mass/volume, which rearranges to volume = mass/density
• volume = 7692.31 g sea water / (1.0 x 103 kg/m3)
• Since 1 kg = 1000 g, we have volume ≈ 7692.31 g / (1.0 x 106 g/m3)
• volume ≈ 7.69231 x 10-3 m3 or 7.69231 liters

Therefore, to recover 500 mg of bromine, approximately 7.69231 liters or 7.69231 x 10-3 cubic meters of ocean water would need to be processed.

Answer 2

7.69 X 10^-6 cubic meters of sea water must be processed to recover 500 mg of bromine.

Step-by-step explanation:

First of all We need to work with consistent units, so let's convert mg of bromine to grams:

500 mg of bromine (divided by 1000) = 0,5g of bromine

So, to find the right answer to this problem we have to apply a direct rule of three:

If there are 65 g of bromine in 1,000,000 grams of sea water, How many grams of sea water is needed to recover 0,5 grams

65g (bromine) _____________ 1,000,000 g (sea water)

0,5g (bromine) ______________ X

X = (0,5 * 1,000,000)/(65)

X = 7.69 g of sea water

But now we need to convert these 7.69 g of sea water to cubic meters.

Sea water density is 1.0 x 10^3 kg/m3 = 1,000 kg/m3

If we multiply this by 1000 to convert kg to grams, We will find that

the equivalent sea water density is: 1.0 x 10^6 g/m3

It means that each cubic meter of sea water weights 1,000,000 g.

So, If one cubic meter of sea water equals to 1,000,000 g of sea water

We need to apply another rule of three to find the final answer:

1,000,000 g __________ 1 m3

7.69g __________ X

X= (7.69* 1)/ 1,000,000

X= 7,69 x 10^-6 m3