Question

calculate the mass of diphosphorus pentoxide (p₂o₅) that contains a million (1.00×10⁶) oxygen atoms. be sure your answer has a unit symbol if necessary, and round it to 3 significant digits.

Explanation:

Step1: Calculate moles of oxygen atoms

Use Avogadro's number ($N_A = 6.022\times 10^{23}\text{ atoms/mol}$). The number of moles of oxygen atoms ($n_O$) is given by $n_O=\frac{N_O}{N_A}$, where $N_O = 1.00\times 10^{6}$ oxygen atoms. So $n_O=\frac{1.00\times 10^{6}\text{ atoms}}{6.022\times 10^{23}\text{ atoms/mol}}=\frac{1.00\times 10^{6}}{6.022\times 10^{23}}\text{ mol}\approx1.66\times 10^{-18}\text{ mol}$.

Step2: Relate moles of oxygen to moles of $P_2O_5$

In one - molecule of $P_2O_5$, there are 5 oxygen atoms. So the number of moles of $P_2O_5$ ($n_{P_2O_5}$) is $n_{P_2O_5}=\frac{n_O}{5}$. Then $n_{P_2O_5}=\frac{1.66\times 10^{-18}\text{ mol}}{5}= 3.32\times 10^{-19}\text{ mol}$.

Step3: Calculate the molar mass of $P_2O_5$

The molar mass of $P$ is $M_P = 30.97\text{ g/mol}$ and the molar mass of $O$ is $M_O=16.00\text{ g/mol}$. The molar mass of $P_2O_5$ ($M_{P_2O_5}$) is $M_{P_2O_5}=2\times30.97\text{ g/mol}+5\times16.00\text{ g/mol}=61.94\text{ g/mol}+80.00\text{ g/mol}=141.94\text{ g/mol}$.

Step4: Calculate the mass of $P_2O_5$

Use the formula $m = n\times M$. So the mass of $P_2O_5$ ($m_{P_2O_5}$) is $m_{P_2O_5}=n_{P_2O_5}\times M_{P_2O_5}=3.32\times 10^{-19}\text{ mol}\times141.94\text{ g/mol}\approx4.71\times 10^{-17}\text{ g}$.

Answer:

$4.71\times 10^{-17}\text{ g}$