Question

practice: mixed mole conversions (2-step)
what is the mass of 8.07 x 10²⁴ molecules of o₂ ?

1 mol o₂ 1.93 x 10²⁵ molecules o₂ 2.58 x 10²⁶ molecules o₂ 6.02 x 10²³ molecules o₂
8.07 x 10²⁴ molecules o₂ 31.998 g o₂ 151.32 g o₂ 214.47 g o₂ 428.94 g o₂ 857.88 g o₂

Explanation:

Step1: Convert molecules to moles

To convert the number of molecules to moles, we use Avogadro's number ($6.02\times 10^{23}$ molecules/mol). The formula is:
$$\text{Moles of } O_2=\frac{\text{Number of molecules of } O_2}{\text{Avogadro's number}}$$
Substituting the given number of molecules ($8.07\times 10^{24}$ molecules) and Avogadro's number ($6.02\times 10^{23}$ molecules/mol):
$$\text{Moles of } O_2=\frac{8.07\times 10^{24}\text{ molecules}}{6.02\times 10^{23}\text{ molecules/mol}}\approx 13.405\text{ mol}$$

Step2: Convert moles to mass

The molar mass of $O_2$ is calculated as follows: the atomic mass of $O$ is approximately $15.999$ g/mol, so for $O_2$, the molar mass ($M$) is $2\times15.999 = 31.998$ g/mol. The formula to convert moles to mass is:
$$\text{Mass of } O_2=\text{Moles of } O_2\times\text{Molar mass of } O_2$$
Substituting the moles we found in Step 1 ($13.405$ mol) and the molar mass ($31.998$ g/mol):
$$\text{Mass of } O_2 = 13.405\text{ mol}\times31.998\text{ g/mol}\approx 428.94\text{ g}$$

Answer:

The mass of $8.07\times 10^{24}$ molecules of $O_2$ is $\boldsymbol{428.94\ \text{g}}$ (or we can also see from the given options, the calculation matches with $428.94\ \text{g}\ O_2$).