Question

What is the volume (in (m³)) of Avogadro’s number of sand grains if each grain is a cube and has sides that are 1.0 mm long?

a) (1.67 X 10⁻11 m³)
b) (1.00 X 10⁻12 m³)
c) (6.02 X 10²3 m³)
d) (6.02 X 10⁻7 m³)

Answer 1

The calculated volume of Avogadro's number of sand grains with 1.0 mm long sides, when each grain is a cube, is 6.022 x 10¹⁴ m³, which does not match any of the provided choices.

Step-by-step explanation:

The question is asking for the volume occupied by Avogadro's number of sand grains, where each grain is a cube with sides that are 1.0 mm long. Firstly, we need to calculate the volume of a single sand grain, which is a cube, so the volume (V) is side³, which in this case equates to (1.0 x 10⁻⁳ m)³ = 1.0 x 10⁻⁹ m³. Next, we multiply the volume of a single grain by Avogadro's number to get the total volume for 6.022 x 10²³ grains: 6.022 x 10²³ x 1.0 x 10⁻⁹ m³ = 6.022 x 10¹⁴ m³. This result is equivalent to option c) 6.02 x 10²³ m³. However, we must recognize that the choices provided do not align with our calculation; hence, either the question or the provided options contain an error, as none of the options reflect the calculated volume.