Question

A 2.3−mL volume of seawater contains about 4.0 × 10−10 g of gold. The total volume of ocean water is about 1.5 × 1021 L. Calculate the total worth of all the gold in the world's oceans if the price of gold is $21.66 per gram.

Answer 1

About $5.65x10^15 or $5,650,000,000,000,000

Step-by-step explanation:

Given:

Volume of seawater: 2.3 mL

Grams of gold: 4.0 x 10^-10

Total volume of the ocean: 1.5 x 10^21

Price of gold: $21.66/g

Need:

1000 mL = 1 L

Find:

Dollar worth of all the gold in the world's oceans

Steps:

1. We know that there is 4.0 x 10^10 g of gold in 2.3 mL of seawater, therefore we can write it like this:

`(4.0 * 10^(-10)g)/(2.3 mL)`

2. In order to find the amount of gold in the entire ocean we need to cancel out the 2.3 mL of seawater on the bottom. To do this we will use the volume of the entire ocean (1.5 x 10^21 L). Before we plug it into the equation, we have to match the units of the mL and the L. We will use the 1000mL = 1 L to accomplish this. The formula should now look like this:

`(4.0*10^(-10)g )/(2.3mL) (1000mL)/(1L) (1.5*10^(21)L)/(1)`

3. Solve the equation to find the amount of gold in all the oceans:

`(4.0*10^(-10)g )/(2.3mL) (1000mL)/(1L) (1.5*10^(21)L)/(1) = 2.61 x 10^(14) g`

4. Now since we found the amount of gold in all the oceans we can use this to find the total worth of all of it. We can do this by multiplying all the grams of the gold by the price of gold per gram. It can be represented like this:

`(21.66 dollars)/(1 gram) (2.61*10^(14)g )/(1)`

5. Get the answer:

`(21.66 dollars)/(1 gram) (2.61*10^(14)g )/(1) = 5.65 x 10 ^ {15}dollars`

There ya go!