Question

What ­if you discovered Avogadro’s number was not $\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}$at a rate of one number each second? Determine your hourly wage. Would you do it? Could you do it?

Short answer

As the mass of carbon- 12 thenthe hourly wage is 6 g.

Step-by-step solution

Definition of mole

A mole is a sample of a natural element with a mass equal to the element's atomic mass expressed in grams and contains 1 mole of atoms. This number of atoms is called Avogadro's number.

Calculation of Avogadro’s number

If the Avogadro's numberis $3.01\times {10}^{23}$, mass of $3.01\times {10}^{23}$atoms of carbon-12 (atomic mass of 12 u) willbe 12g.

$$\begin{gathered} \left(3.01\times {10}^{23}atoms\right)\left(\frac{12u}{atoms}\right)=12g \\ 3.01\times {10}^{23}u=1g \end{gathered}$$

As carbon 12 is taken as standard value for reference, the relative masses of all the elements also remain the same.So, relative masses given in periodic table remain same.

Calculation of Avogadro’s number

If the Avogadro’s number is $3.01\times {10}^{23}$, it is not considered on the basic on the mole, mass of $3.01\times {10}^{23}$atoms of carbon-12 (atomic mass of 12 u) can be calculated as shown below:

$$\begin{gathered} \left(6.02\times {10}^{23}atoms\right)\left(\frac{12u}{atom}\right)=12g \\ massof3.01\times {10}^{23}atoms=\left(\frac{12g}{\left(6.02\times {10}^{23}atoms\right)}\right)\left(3.01\times {10}^{23}\right) \end{gathered}$$

$massof3.01\times {10}^{23}atoms=6g$

Conclusion

As the mass of carbon- 12 is 6g,the hourly wage is 6 g.