Question

question 8 10 pts one mole of the carbon - 12 isotope contains 6.022 x 10^23 atoms. what volume in m^3 would be needed to store one mole of cube - shaped childrens blocks 2.00 cm long on each side?

Explanation:

Step1: Calculate volume of one cube - shaped block

First, convert side - length to meters. Given side length $a = 2.00\ cm=0.02\ m$. The volume of a cube is $V_{1}=a^{3}$. So $V_{1}=(0.02\ m)^{3}=8\times10^{-6}\ m^{3}$.

Step2: Calculate volume for one - mole of blocks

One mole contains $N = 6.022\times10^{23}$ blocks. The total volume $V$ is the volume of one block times the number of blocks. So $V = N\times V_{1}=6.022\times10^{23}\times8\times10^{-6}\ m^{3}$.
$V=(6.022\times8)\times10^{23 - 6}\ m^{3}=4.8176\times10^{18}\ m^{3}$

Answer:

$4.82\times 10^{18}\ m^{3}$