Answer to Question #94944 in Physical Chemistry for mya

Question

how many total atoms are in .220g of P2O5?

Answer 1

At the first let's find the molar mass of ${P_2}{O_5}$ - it can be calculated as the sum of atomic weights taking into account the number of atoms of each type in the molecule

$${M_{{P_2}{O_5}}} = 2{M_P} + 5{M_O} \approx 2 \cdot 16[\frac{{\rm{g}}}{{{\rm{mol}}}}] + 5 \cdot 30.97[\frac{{\rm{g}}}{{{\rm{mol}}}}] = 141.94[\frac{{\rm{g}}}{{{\rm{mol}}}}]$$

(atomic weights of atoms $P$ and $O$ can be found in periodic table and respectively equal to $30.97[\frac{{\rm{g}}}{{{\rm{mol}}}}]$ and $16[\frac{{\rm{g}}}{{{\rm{mol}}}}]$)

The number of moles in $0.220[{\rm{g}}]$ of ${P_2}{O_5}$ can be found as

$$\nu = \frac{m}{{{M_{{P_2}{O_5}}}}} = \frac{{0.220[{\rm{g}}]}}{{141.94[\frac{{\rm{g}}}{{{\rm{mol}}}}]}} \approx 1.55 \cdot {10^{ - 3}}[{\rm{mol}}]$$

Now let's use that there are ${N_A} \approx 6.022 \cdot {10^{23}}[\frac{1}{{{\rm{mol}}}}]$ (particles per 1 mole). In our case it will be the number of molecules. But to find the total number of atoms we can notice that there are $7$ atoms in $1$ molecule of ${P_2}{O_5}$ (2 atoms of $P$ and 5 atoms of $O$). Thus the total number of atoms is

$$N = 7\nu {N_A} = 7 \cdot 1.55 \cdot {10^{ - 3}}[{\rm{mol}}] \cdot 6.022 \cdot {10^{23}}[\frac{1}{{{\rm{mol}}}}] \approx 6.53 \cdot {10^{21}}$$