Question

Calculate the following:
Number of molecules of ${\mathrm{CH}}_4$ in 80.0 g of it.

Answer 1

From the given data,

The amount of Methane (${\mathrm{CH}}_4$) is 80.0 g.

$$\begin{gathered} \mathrm{Molar}\mathrm{mass}\mathrm{of}{\mathrm{CH}}_4=12+4\left(1\right) \\ =16\mathrm{g}/\mathrm{mol} \end{gathered}$$

By Avagadro's law,

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{in}80.0\mathrm{g}\mathrm{of}{\mathrm{CH}}_4=\frac{\mathrm{Given}\mathrm{mass}\mathrm{of}{\mathrm{CH}}_4}{\mathrm{Molar}\mathrm{mass}\mathrm{of}{\mathrm{CH}}_4}\times \mathrm{Avagadro}\mathrm{number} \\ =\frac{80}{16}\times 6.022\times {10}^{23} \\ =5\times 6.022\times {10}^{23} \\ =30.11\times {10}^{23}\mathrm{molecules} \end{gathered}$$

Hence, the number of molecules of ${\mathrm{CH}}_4$ in 80.0 g of it is $30.11\times {10}^{23}\mathrm{molecules}$.