(b) When a sample of C2H5OH was combusted, the volume of CO2(g) produced was 18.0 L when measured at
21.7°C and 1.03 atm.
(i) Determine the number of moles of CO2(g) that was produced.
(ii) Determine the volume of C2H5OH(1), in mL, that was combusted to produce the volume of CO2(g)
collected. (The density of C2H5OH() is 0.79 g/mL.)
(iii) Determine the amount of heat, in KJ, that was released by the combustion reaction.

i) The number of moles of CO₂ (g) produced from the reaction = 0.07663 mole

ii) The volume of C₂H₅OH (l), in mL, that was combusted to produce the volume of CO₂ (g)

collected = 2.234 mL

iii) The amount of heat, in KJ, that was released by the combustion reaction = 52.4 kJ

Explanation:

The balanced chemical reaction when ethanol is combusted is given as

C₂H₅OH (l) + 3O₂ (g) → 2CO₂ (g) + 3H₂O (g)

The volume of CO₂(g) produced was 18.0 L when measured at 21.7°C and 1.03 atm.

i) Number of moles of CO₂ (g) produced by the reaction

With the correct and logical assumption that CO₂ is an ideal gas, the ideal gas equation has the relation

PV = nRT

P = pressure = 1.03 atm = 1.03 × 101325 Pa = 10,435.96 Pa

V = Volume of the gas = 18.0 L = 0.018 m³

n = number of moles = ?

R = molar gas constant = 8.314 J/mol.K

T = absolute temperature in Kelvin = 21.7 + 273.15 = 294.85 K

(10,435.96 × 0.018) = n × 8.314 × 294.85

n = 0.076629106 = 0.07663 mole

ii) The volume of C₂H₅OH (l), in mL, that was combusted to produce the volume of CO₂(g)

collected.

Recall the stoichiometric balance of the reaction

C₂H₅OH (l) + 3O₂ (g) → 2CO₂ (g) + 3H₂O (g)

2 moles of CO₂ is obtained from 1 mole of C₂H₅OH

0.07663 mole of CO₂ will be obtained from (0.07663×1/2) mole of C₂H₅OH; that is, 0.03831 mole of C₂H₅OH.

But we can convert this number of moles used up to mass of C₂H₅OH produced

Mass = (Number of moles) × (Molar Mass)

Molar mass of C₂H₅OH = 46.07 g/mol

Mass of C₂H₅OH combusted from the reaction

= 0.03831 × 46.07 = 1.765 g

But density of C₂H₅OH = 0.79 g/mL

Density = (Mass)/(Volume)

Volume = (Mass)/(Density) = (1.765/0.79)

= 2.234 mL

iii) The amount of heat, in KJ, that was released by the combustion reaction.

The heat of combustion of C₂H₅OH at the temperature of the reaction = -1367.6 kJ/mol. (From literature)

1 mole of C₂H₅OH combusts to give 1367.6 kJ of heat

0.03831 mole of C₂H₅OH will give (0.03831×1367.6) = 52.39 kJ = 52.4 kJ

Hope this Helps