ANSWER
[tex]\text{ 5.5567 }\times\text{ 10}^{24}\text{ particles}[/tex]
EXPLANATION
Given that:
The mass of oxygen is 492.3 grams
Follow the steps below to find the number of particles of CO2
Step 1; Write the balanced equation of the reaction
[tex]\text{ C}_3H_{8(g)}\text{ + 5O}_{2(g)}\text{ }\rightarrow\text{ 3CO}_{2(g)}\text{ + 4H}_2O_{(g)}[/tex]
Step 2; Find the number of moles of oxygen using the formula below
[tex]\text{ mole = }\frac{\text{ mass}}{\text{ molar mass}}[/tex]
Recall, that the molar mass of oxygen is 32 g/mol
[tex]\begin{gathered} \text{ mole = }\frac{\text{ 492.3}}{\text{ 32}} \\ \text{ mole = 15.384 moles} \end{gathered}[/tex]
Step 3; Find the number of moles of CO2 using a stoichiometry ratio
5 moles O2 give 3 moles CO2
Let moles of CO2 be x
[tex]\begin{gathered} \text{ 5 moles O}_2\text{ }\rightarrow\text{ 3 moles CO}_2 \\ \text{ 15.384 moles O}_2\text{ }\rightarrow\text{ x moles CO}_2 \\ \text{ Cross multiply} \\ \text{ 5 moles O}_2\text{ }\times\text{ x moles CO}_2\text{ = 3 moles CO}_2\times15.384\text{ moles O}_2 \\ \text{ Isolate x} \\ \text{ x = }\frac{\text{ 3moles CO}_2\times15.384moles\cancel{O_2}}{5moles\cancel{O_2}} \\ \text{ x = }\frac{\text{ 3 }\times\text{ 15.384}}{5} \\ \text{ x =}\frac{46.152}{5} \\ \text{ x = 9.2304 moles} \\ \text{ Therefore, the number of moles of CO}_2\text{ IS 9.2304 moles} \end{gathered}[/tex]
Step 4; Find the number of particles of CO2 using the formula below
[tex]\begin{gathered} \text{ mole = }\frac{\text{ number of particles}}{\text{ Avogadro's number}} \\ \text{ } \end{gathered}[/tex]
Recall, that the Avogadro's constant is 6.02 x 10^23
[tex]\begin{gathered} \text{ 9.2304 = }\frac{\text{ number of particles}}{\text{ 6.02 }\times\text{ 10}^{23}} \\ \text{ cross multiply} \\ \text{ Number of particles = 9.2304 }\times\text{ 6.02 }\times\text{ 10}^{23} \\ \text{ Number of particles = 55.567 }\times\text{ 10}^{23} \\ \text{ Number of particles = 5.5567 }\times\text{ 10}^{24}\text{ particles} \\ \text{ Therefore, the number of particles of CO}_2\text{ is 5.5567 }\times\text{ 10}^{24}\text{ particles} \end{gathered}[/tex]