Question

How much time would it take to distribute one Avogadro number of wheat grains, if ${10}^{10}$ grains are distributed each second?

Answer 1

Avogadro number:

• Avogadro's number is defined as the number of units in a mole of any substance that is equal to $6.02\mathrm{x}{10}^{23}$units, in which the units can be referred to as any molecule, electron, or ion depending on the nature of the substance.
• Hence, in numerical value, Avogadro number = $6.02\mathrm{x}{10}^{23}$
• As given,${10}^{10}$ grains are distributed = in 1 second
• Therefore, time would take to distribute Avogadro's number of grains;

$$\begin{gathered} =(6.02\mathrm{x}{10}^{23})/{10}^{10}\mathrm{s} \\ =6.02\mathrm{x}{10}^{13}\mathrm{s} \\ =(6.02\mathrm{x}{10}^{13})/(60\mathrm{x}60\mathrm{x}24\mathrm{x}365)\mathrm{years} \\ =1.909\mathrm{x}{10}^6\mathrm{years} \end{gathered}$$

Hence, the time taken would be$1.909\mathrm{x}{10}^6\mathrm{years}$to distribute one Avogadro number of wheat grains.