# Is the largest number of molecules in 36 g of water or 54 g of dinitrogen pentaoxide?

Recently my teacher asked us which of the following has the largest number of molecules? He gave us two options:

1. $$\pu{36 g}$$ of $$\ce{H2O}$$
2. $$\pu{54 g}$$ of $$\ce{N2O5}$$

I'm stuck, because both of them are having two moles of each of the respective molecules. And technically, the number of molecules equals the amount of substance multiplied by Avogadro's number.

So shouldn't $$\pu{2 mol} \times N_\mathrm{A} = N(\text{molecules})$$ be the same number of molecules for both of them?

But yet, the teacher said that water is the correct answer.

And I'm still not able to figure out why?

## 1 Answer

I'm stuck, because both of them are having two moles of each of the respective molecules.

Are you sure?

\begin{align} M(\ce{H2O}) &= \pu{18 g mol^-1} & \implies \pu{36 g} &\mathop{\hat{=}} \pu{2 mol} \\ M(\ce{N2O5}) &= \pu{108 g mol^-1} & \implies \pu{54 g} &\mathop{\hat{=}} \pu{0.5 mol} \\ \end{align}