Calculate enthalpy change of reaction for the combustion of gaseous ethanol.
C2H5OH + 3O2 >> CO2 + 3H2O.
Using standard molar enthalpies of formation.
C2H5OH -235.3 ( it's negative sign)
CO2 -393.5
H2O -241.8
(1) Calculate the enthalpy change of reaction per mole of ethanol
(2) Calculate enthalpy change of reaction when 1000 g of ethanol are burned with enough oxygen.
(1) To calculate the enthalpy change of reaction per mole of ethanol, we need to use the standard molar enthalpies of formation.
The stoichiometric coefficients in the balanced chemical equation indicate that 1 mole of ethanol is burned, producing 1 mole of CO2 and 3 moles of H2O.
The enthalpy change of reaction per mole of ethanol is given by:
ΔH = Σ(n * ΔHf(products)) - Σ(n * ΔHf(reactants))
Where:
ΔH = Enthalpy change of reaction
n = Stoichiometric coefficient
ΔHf = Standard molar enthalpy of formation
Plugging in the values:
ΔH = (1 * ΔHf(CO2) + 3 * ΔHf(H2O)) - (1 * ΔHf(C2H5OH) + 3 * ΔHf(O2))
ΔH = (1 * -393.5 kJ/mol + 3 * -241.8 kJ/mol) - (1 * -235.3 kJ/mol + 3 * 0 kJ/mol)
ΔH = (-1180.9 kJ/mol) - (-235.3 kJ/mol)
ΔH = -945.6 kJ/mol
Therefore, the enthalpy change of reaction per mole of ethanol is -945.6 kJ/mol.
(2) To calculate the enthalpy change of reaction when 1000 g of ethanol are burned, we need to convert the mass to moles using the molar mass of ethanol.
The molar mass of ethanol (C2H5OH) is calculated as follows:
2 * Atomic mass of carbon (C) + 6 * Atomic mass of hydrogen (H) + 1 * Atomic mass of oxygen (O)
= (2 * 12.01 g/mol) + (6 * 1.01 g/mol) + (1 * 16.00 g/mol)
= 46.07 g/mol
Now, we can calculate the number of moles of ethanol in 1000 g:
Number of moles = Mass / Molar mass
= 1000 g / 46.07 g/mol
= 21.70 mol
The enthalpy change of reaction when 1000 g of ethanol are burned can be calculated by multiplying the enthalpy change per mole of ethanol by the number of moles:
Enthalpy change = ΔH * Number of moles
= -945.6 kJ/mol * 21.70 mol
= -20516.92 kJ
Therefore, the enthalpy change of reaction when 1000 g of ethanol are burned is approximately -20516.92 kJ.
To calculate the enthalpy change of the combustion reaction using the standard molar enthalpies of formation, you need to apply the following steps:
(1) Calculate the enthalpy change of reaction per mole of ethanol:
Step 1: Write out the balanced equation for the combustion reaction:
C2H5OH + 3O2 → CO2 + 3H2O
Step 2: Identify the stoichiometric coefficients for the reactants and products:
Reactants: C2H5OH = 1, O2 = 3
Products: CO2 = 1, H2O = 3
Step 3: Determine the enthalpy change for each compound by multiplying the stoichiometric coefficient with its standard molar enthalpy of formation:
ΔH = (1 × ΔHf[CO2] + 3 × ΔHf[H2O]) - (ΔHf[C2H5OH] + 3 × ΔHf[O2])
ΔH = (1 × -393.5 kJ/mol + 3 × -241.8 kJ/mol) - (-235.3 kJ/mol + 3 × 0 kJ/mol)
ΔH = -1,274.3 kJ/mol - (-235.3 kJ/mol)
ΔH = -1,274.3 kJ/mol + 235.3 kJ/mol
ΔH = -1,039 kJ/mol
Therefore, the enthalpy change of the reaction per mole of ethanol is -1,039 kJ/mol.
(2) Calculate the enthalpy change of reaction when 1000 g of ethanol are burned with enough oxygen:
Step 1: Convert grams of ethanol to moles using the molar mass of ethanol.
Molar mass of ethanol (C2H5OH) = 2 × 12.01 g/mol + 6 × 1.01 g/mol + 16.00 g/mol + 1.01 g/mol = 46.07 g/mol
Moles of ethanol = 1000 g ÷ 46.07 g/mol
Moles of ethanol = 21.69 mol
Step 2: Multiply the moles of ethanol by the enthalpy change of reaction per mole of ethanol calculated in step 1:
Enthalpy change = 21.69 mol × (-1,039 kJ/mol)
Enthalpy change = -22,553.91 kJ
Therefore, the enthalpy change of the reaction when 1000 g of ethanol are burned with enough oxygen is approximately -22,554 kJ (rounded to three significant figures).