Question

What is the difference in mass between 3.01×10^24 atoms of gold and a gold bar with the dimensions 6.00 cm X 4.25 cm X 2.00 cm

Answer 1

The difference in mass between 3.01×10^24 atoms of gold and a gold bar with the dimensions 6.00 cm X 4.25 cm X 2.00 cm is :

Difference in mass = 985.32 - 984.5 = 0.82 g

Step-by-step explanation:

Part I :

`n =(3.01* 10^(24))/(6.022* 10^(23))`

n = 4.9983

n = 4.99 moles

(Note : You can also take n = 5 mole )

Molar mass of gold = 196.96 g/mole

This means, 1 mole of gold(Au) contain = 196.96 grams

So, 4.99 moles of gold contain =
`5* 196.96` g

4.99 moles of gold contain = 984.8 g

Mass of
`{3.01* 10^(24)}` atoms of gold = 984.5 g

Part II :

Density of Gold =
`19.32 g/cm^(3)`

Volume of the cuboid =
`length* breadth* height`

Volume of the gold bar =
`6.00* 4.25* 2.00`

Volume of the gold bar = 51
`cm^(3)`

Using formula,

`Density = (mass)/(Volume)`

`Mass = Density* Volume`

`Mass = 19.32 * 51`

Mass = 985.32 g

So, A gold bar with the dimensions 6.00 cm X 4.25 cm X 2.00 cm has mass of 985.32 g

Difference in mass = 985.32 - 984.5 = 0.82 g