Let's solve the problem step-by-step:
1. Identify the given data:
- Mass of propane ([tex]\(C_3H_8\)[/tex]): [tex]\(12.5 \, \text{g}\)[/tex]
- Chemical reaction: [tex]\[
C_3H_8(g) + 5 O_2(g) \longrightarrow 3 CO_2(g) + 4 H_2O(g)
\][/tex]
2. Calculate the molar mass of propane ([tex]\(C_3H_8\)[/tex]):
- Carbon (C) has an atomic mass of approximately [tex]\(12.01 \, \text{g/mol}\)[/tex]
- Hydrogen (H) has an atomic mass of approximately [tex]\(1.01 \, \text{g/mol}\)[/tex]
- Molar mass of propane:
[tex]\[
(\text{3 atoms of C}) \times (12.01 \, \text{g/mol}) + (\text{8 atoms of H}) \times (1.01 \, \text{g/mol}) = 44.11 \, \text{g/mol}
\][/tex]
3. Calculate the number of moles of propane:
[tex]\[
\text{Number of moles of propane} = \frac{\text{mass of propane}}{\text{molar mass of propane}} = \frac{12.5 \, \text{g}}{44.11 \, \text{g/mol}} \approx 0.283 \, \text{mol}
\][/tex]
4. Determine the stoichiometry of the reaction:
- From the balanced chemical equation, [tex]\(1 \, \text{mol}\)[/tex] of [tex]\(C_3H_8\)[/tex] produces [tex]\(3 \, \text{mol}\)[/tex] of [tex]\(CO_2\)[/tex].
5. Calculate the moles of carbon dioxide ([tex]\(CO_2\)[/tex]) produced:
[tex]\[
\text{Moles of } CO_2 = (\text{moles of } C_3H_8) \times 3 = 0.283 \, \text{mol} \times 3 \approx 0.850 \, \text{mol}
\][/tex]
6. Calculate the molar mass of carbon dioxide ([tex]\(CO_2\)[/tex]):
- Carbon (C) has an atomic mass of approximately [tex]\(12.01 \, \text{g/mol}\)[/tex]
- Oxygen (O) has an atomic mass of approximately [tex]\(16.00 \, \text{g/mol}\)[/tex]
- Molar mass of carbon dioxide:
[tex]\[
(12.01 \, \text{g/mol}) + (\text{2 atoms of O}) \times (16.00 \, \text{g/mol}) = 44.01 \, \text{g/mol}
\][/tex]
7. Calculate the mass of carbon dioxide produced:
[tex]\[
\text{Mass of } CO_2 = (\text{moles of } CO_2) \times (\text{molar mass of } CO_2) = 0.850 \, \text{mol} \times 44.01 \, \text{g/mol} \approx 37.415 \, \text{g}
\][/tex]
Therefore, the mass of carbon dioxide produced when 12.5 g of propane undergoes complete combustion is approximately [tex]\(37.415 \, \text{g}\)[/tex].
