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:

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

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

$N_A\approx6.02\times10^{23}mol^{-1}$

So:

$\begin{gathered} N_{N_{2}O}=n_{N_2O}\times N_A \\ N_{N_2O}=1.3636\ldots mol\cdot6.02\times10^{23}mol^{-1} \\ N_{N_2O}=8.20909\ldots\times20^{23} \\ N_{N_2O}\approx8.21\times20^{23} \end{gathered}$

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