Answer:
227 grams
Step-by-step explanation:
First, we can convert molecules to moles using Avogadro's number:
[tex]N_A = 6.022 \times10^{23} \ \dfrac{\text{molecules}}{1 \text{ mole}}[/tex]
↓↓↓
[tex]\dfrac{2.13 \times 10^{24} \text{ molecules}}{1} \times \dfrac{1 \text{ mole}}{6.022\times 10^{23}\text{ molecules}} = 3.54 \text{ moles SO}_2[/tex]
Next, we can multiply the number of moles by SO₂'s molar mass:
From the periodic table, we get:
Putting these into the equation for molar mass:
[tex]M_{SO2} = \dfrac{(32.07 + 2(16.00))\text{ g}}{1 \text{ mole}} = \dfrac{64.07\text{ g}}{1\text{ mole}}[/tex]
↓↓↓
[tex]\dfrac{3.54\text{ moles}}{1} \times\dfrac{64.07\text{ g}}{1\text{ mole}} = \boxed{226.6 \text{ g}}[/tex]
So, the mass of 2.13 × 10²⁴ molecules of sulfur dioxide is approximately 226.6 grams. If we want to use the amount of significant figures for the given data (3), we can round to:
227 grams
