Question

A penny has a thickness of approximately 1.0 mm. If you stacked Avogadro's number of pennies one on top of the other on Earth's surface, how far would the stack extend (in km)?

Answer 1

A stack of Avogadro's number of pennies would reach a height that is comparable to the diameter of the Milky Way, showcasing the enormous quantity that a mole represents in chemistry and physics.

Step-by-step explanation:

Avogadro's number, which is approximately 6.022 x 1023, represents a mole and is a way to quantify the number of particles in a substance. When it comes to the physical scale of a mole, it is incredibly vast because individual particles like atoms and molecules are so small. A penny has a thickness of approximately 1.0 mm. If Avogadro's number of pennies were stacked one on top of the other, we can calculate the height of the stack.

To find out the height of such a stack in km, we use the following calculation:
Height = (1.0 mm x 6.022 x 1023) pennies

Since 1 km = 1,000,000 mm, we convert the height in mm to km:

Height in km = (1.0 mm/penny x 6.022 x 1023 pennies) / 1,000,000 mm/km

After performing the calculation, we get a height that is astronomical, reaching a distance comparable to the diameter of our galaxy, the Milky Way. This demonstrates the immensity of a mole and how it relates to everyday objects. It's an abstract concept that helps in understanding the scale of chemical quantities in chemistry and physics.

Answer 2

The height of the stack will be
`6.022* 10^(17)` km.

Step-by-step explanation:

Thickness of the single penny ,t= 1.0 mm

Avogadro number =
`N_A=6.022* 10^(23)`

If we stack Avogadro numbers of pennies one top of the other on Earth surface, the height of the pennies can be said to be h.

`t\time N_A=h`

`1.0 mm* 6.022* 10^(23) =6.022* 10^(23) mm`

`1 m = 10^(-6) km`

`h=6.022* 10^(23) mm=6.022* 10^(23) * 10^(-6) km`

`h=6.022* 10^(17) km`

The height of the stack will be
`6.022* 10^(17)` km.