Respuesta :
Answer:
a) Mass of gold in ocean = 8.1*10¹² g
b) Volume of gold = 4.2*10¹¹ cm³
c) Value of gold = $ 4.1*10¹³
Explanation:
a) Depth of ocean = 3800 m
Surface area of ocean = 3.63*10⁸ km²
Now, 10⁶ m² = 1 km²
Therefore, the area in units of m² = 3.63*10¹⁴ m²
[tex]Volume\ of\ ocean = Depth*Area = 3800m*3.63*10^{14} m2=1.4*10^{18} m3[/tex]
Average concentration of gold in ocean = 5.8*10⁻⁹ g/L
Now, 1 g/L = 1000 g/m³
Therefore, concentration of gold in g/m³ = 5.8*10⁻⁶ g/m³
[tex]Mass\ of\ gold =1.4*10^{18} m^{3} *5.8*10^{-6} g/m3 = 8.1*10^{12} g[/tex]
b) Mass of gold present = 8.1*10¹² g
Density of gold = 19.3 g/cm³
[tex]Volume\ of\ gold = \frac{Mass}{density} =\frac{8.1*10^{12} }{19.3} =4.2*10^{11} cm^{3}[/tex]
c) Price of gold = $1595/troy oz
Unit conversion
1 troy oz = 311 g
Therefore, 8.1*10¹² g of gold is equivalent to:
[tex]\frac{8.1*10^{12} g* 1\ troy\ oz}{311g} =2.6*10^{10} \ troy\ oz[/tex]
The value of gold in the ocean is:
[tex]\frac{2.6*10^{10} troy\ oz*1595\ dollars}{1\ troy\ oz} =4.1*10^{13} \ dollars[/tex]
