Answer:
0.779
Step-by-step explanation:
Determine the molecular weight of the hydrocarbon. We know that its vapor density is 29, which means that one mole of the hydrocarbon has a mass of 29 grams. Therefore, the molecular weight of the hydrocarbon is 29 g/mol.
Calculate the number of moles of the hydrocarbon. We can use the formula:
moles = mass / molecular weight
Substituting the values, we get:
moles = 29 g / 29 g/mol = 1 mol
Therefore, we have one mole of the hydrocarbon.
Write the balanced chemical equation for the combustion of the hydrocarbon in oxygen. The general equation is:
hydrocarbon + oxygen → carbon dioxide + water
For one mole of the hydrocarbon, we need one mole of oxygen to completely burn it. The balanced equation is:
CnHm + (n+m/4) O2 → n CO2 + m/2 H2O
Calculate the volume of carbon dioxide produced. We know that 1 mole of any gas at STP occupies 22.4 L. Therefore, one mole of carbon dioxide occupies 22.4 L. The volume of 448 ml of carbon dioxide at STP can be converted to liters:
448 ml = 0.448 L
The number of moles of carbon dioxide produced can be calculated using the ideal gas law:
PV = nRT
where P is the pressure (1 atm), V is the volume (0.448 L), n is the number of moles, R is the gas constant (0.0821 L atm/mol K), and T is the temperature (273 K). Substituting the values, we get:
n = PV/RT = (1 atm x 0.448 L) / (0.0821 L atm/mol K x 273 K) = 0.0177 mol
Therefore, 0.0177 moles of carbon dioxide are produced.
Calculate the mass of carbon dioxide produced. We can use the formula:
mass = moles x molecular weight
The molecular weight of carbon dioxide is 44 g/mol. Substituting the values, we get:
mass = 0.0177 mol x 44 g/mol = 0.779 g
Therefore, the mass of carbon dioxide produced is 0.779 grams.