Ethanol, C2H5OH or C2H6O, is mixed with gasoline and sold as gasohol. Given the following thermo-chemical reaction, calculate the kilograms (kg) of CO2 produced when enough ethanol is combusted to provide (or give off) 369 kJ of heat:
C2H5OH (l) + 3 O2 (g) --> 2 CO2 (g) +3 H2O (l);
delta-H rxn = -1235 kJ
1 mole C2H5OH has a mass of 46 grams and will produce 2*44 = 88 g CO2 in producing 1235 kJ of energy. Therefore, how much CO2 is produced when only 369 kJ of heat are produced. That will be
88 x (369 kJ/1235 kJ) = ??
To calculate the kilograms of CO2 produced when enough ethanol is combusted to provide 369 kJ of heat, we need to use the given delta-H value and convert it to the heat produced by one mole of ethanol. Then, we can use stoichiometry to calculate the amount of CO2 produced.
Step 1: Calculate the heat produced by one mole of ethanol
Given: delta-H rxn = -1235 kJ
We need to find the heat produced by one mole of ethanol.
From the balanced equation, we see that the reaction produces 2 moles of CO2 for every mole of ethanol.
Therefore, the heat produced by one mole of ethanol is:
Heat_per_mole_ethanol = delta-H rxn / (2 moles of CO2) = -1235 kJ / 2 = -617.5 kJ/mol
Step 2: Convert kJ to J
We need to convert the heat from kilojoules to joules since the heat per mole calculation is in kJ/mol.
Heat_per_mole_ethanol_J = Heat_per_mole_ethanol * 1000 = -617500 J/mol
Step 3: Calculate the moles of ethanol that will produce 369 kJ of heat
We have the heat produced by one mole of ethanol, and we need to find the moles of ethanol that will produce 369 kJ of heat.
Moles_of_ethanol = Heat_required / Heat_per_mole_ethanol_J = 369 kJ/ -617500 J/mol
Step 4: Calculate the moles of CO2 produced
According to the balanced equation, for every mole of ethanol, 2 moles of CO2 are produced.
Therefore, Moles_of_CO2 = Moles_of_ethanol * 2
Step 5: Convert moles of CO2 to kilograms
To calculate the kilograms of CO2, we need to convert moles to grams, and then to kilograms.
Molar_mass_CO2 = 44.01 g/mol (molar mass of CO2)
Mass_of_CO2 = Moles_of_CO2 * Molar_mass_CO2 in grams
Mass_of_CO2_kg = Mass_of_CO2 / 1000 in kilograms
Now, let's substitute the values and calculate the kilograms of CO2 produced:
Heat_per_mole_ethanol_J = -617500 J/mol
Heat_required = 369 kJ
Molar_mass_CO2 = 44.01 g/mol
First, calculate the moles of ethanol:
Moles_of_ethanol = 369 kJ / -617500 J/mol
Moles_of_ethanol = -0.00059819 mol (rounded)
Next, calculate the moles of CO2 produced:
Moles_of_CO2 = Moles_of_ethanol * 2
Moles_of_CO2 = -0.00119638 mol (rounded)
Finally, calculate the mass of CO2 in kilograms:
Mass_of_CO2 = Moles_of_CO2 * Molar_mass_CO2
Mass_of_CO2 = (-0.00119638 mol) * (44.01 g/mol)
Mass_of_CO2 = -0.0527 g (rounded)
Since mass cannot be negative, it means that the reaction did not produce any CO2 when 369 kJ of heat was produced.
To calculate the kilograms of CO2 produced when combusting ethanol, we can use the given thermo-chemical reaction and the heat released during the reaction.
First, let's calculate the moles of heat released during the combustion reaction using the given energy change:
delta-H rxn = -1235 kJ
We need to convert this to joules since the SI unit is joules:
delta-H rxn = -1235 kJ = -1235000 J
Next, we need to find the moles of ethanol that produce this amount of heat. According to the thermo-chemical equation, 1 mole of ethanol produces -1235000 J of heat.
Since the molecular weight of ethanol (C2H5OH) is 46.07 g/mol, we can calculate the moles as follows:
moles of ethanol = (369 kJ / -1235 kJ/mol) = 0.299 mol
Now, let's find the moles of carbon dioxide (CO2) produced during the combustion reaction. According to the balanced equation, we know that for every 2 moles of CO2 produced, we need 1 mole of ethanol.
moles of CO2 = 0.299 mol × (2 mol CO2 / 1 mol ethanol) = 0.598 mol
To find the mass of CO2 produced, we need to know the molar mass of CO2, which is 44.01 g/mol. We can now calculate the mass of CO2 produced as follows:
mass of CO2 = moles of CO2 × molar mass of CO2
= 0.598 mol × 44.01 g/mol
= 26.35 g
Finally, we can convert grams to kilograms by dividing by 1000:
mass of CO2 = 26.35 g / 1000
= 0.02635 kg
Therefore, when enough ethanol is combusted to provide 369 kJ of heat, approximately 0.02635 kg of CO2 is produced.