Final answer:
To determine the volume of CO2 produced from the combustion of propane, we need to use stoichiometry and the ideal gas law. First, convert the mass of propane to moles. Then, use the stoichiometric ratio to determine the moles of CO2 produced. Finally, use the ideal gas law to calculate the volume of CO2 produced.
Step-by-step explanation:
To answer this question, we need to use the stoichiometry of the given balanced chemical equation to determine the amount of CO₂ produced. From the balanced equation, we can see that for every 1 mole of propane (C₃H₈), 8 moles of CO₂ are produced. First, we need to convert the mass of propane (13.4 g) to moles by dividing it by the molar mass of propane (44.10 g/mol). This gives us 0.304 moles of propane.
Next, we use the stoichiometric ratio of the balanced equation to determine the moles of CO₂ produced. Since the ratio is 8 moles of CO₂ to 1 mole of propane, we can multiply the moles of propane by this ratio. 0.304 mol of propane * 8 mol of CO₂ / 1 mol of propane = 2.43 mol of CO₂.
Finally, we can use the ideal gas law to calculate the volume of CO₂ produced. We can use the equation V = nRT/P, where V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L∙atm/mol∙K), T is the temperature in Kelvin, and P is the pressure in atmospheres. Since the volume is given in liters, the temperature is in Celsius and needs to be converted to Kelvin by adding 273.15. Plugging in the values, we get:
V = (2.43 mol)(0.0821 L∙atm/mol∙K)(54 + 273.15 K) / 1 atm = 58.97 L.