Question

Find the number of molecules in 60.0g of N2O?

Answer 1

To find the number of molecules, we first need to find the number of moles.

To do that, we need the molar mass of N₂O, which we can calculate using the molas masses of the elements in it:

`\begin{gathered} M_(N_2O)=2\cdot M_N+1\cdot M_O \\ M_(N_2O)\approx2\cdot14g\/mol+1\cdot16g\/mol \\ M_(N_2O)\approx28.0g\/mol+16.0g\/mol \\ M_(N_2O)\approx44.0g\/mol \end{gathered}`

To convert from mass, m, to number of moles, n, we will use the following:

`\begin{gathered} M_{N_(2)O}=\frac{m_(N_2O)}{n_{N_(2)O}} \\ n_{N_(2)O}=\frac{m_(N_2O)}{M_{N_(2)O}} \\ n_{N_(2)O}=(60.0g)/(44.0g\/mol) \\ n_(N_2O)=1.3636\ldots mol \end{gathered}`

And to convert from number of moles to number of molecules, we use the Avogadro's number:

`N_A\approx6.02*10^(23)mol^(-1)`

So:

`\begin{gathered} N_{N_(2)O}=n_(N_2O)* N_A \\ N_(N_2O)=1.3636\ldots mol\cdot6.02*10^(23)mol^(-1) \\ N_(N_2O)=8.20909\ldots*20^(23) \\ N_(N_2O)\approx8.21*20^(23) \end{gathered}`

So, the number of molecules in 60.0 g of N₂O is approximately 8.21 x 10²³.