Question

A newspaper story describing the local celebration of Mole Day on October 23 (selected for Avogadro's number, 6.02 X 10^ 23 ) attempting to give the reader a sense of the size of the number by stating that a mole of M&Ms would be equal to 18 tractor trailers full. Assuming that an M&M occupies the volume of about 0.5 cm ^ 3 calculate the dimensions of a cube required to hold one mole of M&Ms. Would 18 tractor trailers be sufficient?

Answer 1

A mole is a unit in chemistry representing Avogadro's number of items. To hold a mole of M&Ms, given each occupies 0.5 cm³, would require a cube with sides much larger than the capacity of 18 tractor trailers.

Step-by-step explanation:

Calculating the Volume of a Mole of M&Ms

To calculate the dimensions of a cube required to hold one mole of M&Ms, we must first understand what a mole is in chemistry. A mole contains Avogadro's number, which is 6.02 × 1023 representative particles of a substance. This means a mole of M&Ms would have that many candies. If each M&M occupies approximately 0.5 cm3, the total volume would be:

Volume of one mole of M&Ms = 0.5 cm3 × 6.02 × 1023 = 3.01 × 1023 cm3

To find the dimensions of a cube that could hold this volume, we take the cube root:

Cube side length = ∛(3.01 × 1023) cm3

We would then compare this calculated volume to the total volume that could be held by 18 tractor trailers. Given that a standard trailer has a volume of about 60-100 m3, 18 trailers would have a combined volume of 1080-1800 m3. To compare, we need to convert cubic centimeters to cubic meters by dividing by 1,000,000.

From the calculation, it's clear that a cube large enough to contain a mole of M&Ms would be far larger than 18 tractor trailers could hold.