In an experiment, a 0.3621 g sample of 1,8-octanediol (C₈H₁₈O₂) is burned completely in a bomb calorimeter. The calorimeter is surrounded by 1.005 × 10³ g of water. During the combustion, the temperature increases from 23.22 to 25.58 °C. The heat capacity of water is 4.184 J·g⁻¹·°C⁻¹.
The heat capacity of the calorimeter was determined in a previous experiment to be 930.9 J·°C⁻¹.
Assuming that no energy is lost to the surroundings, calculate the molar heat of combustion of 1,8-octanediol based on these data.
C₈H₁₈O₂(s) + (23/2)O₂(g) → 9H₂O(l) + 8CO₂(g) + Energy
Molar Heat of Combustion = ______ kJ/mol
Answer (1)
To calculate the molar heat of combustion of 1,8-octanediol (C₈H₁₈O₂), we first need to determine the total energy change during the combustion and then relate it to the moles of 1,8-octanediol combusted.
Step 1: Calculate the total heat absorbed by the system
The temperature change observed in the water and the calorimeter is from 23.22 °C to 25.58 °C, a difference of:
Δ T = 25.58 − 23.22 = 2.36 °C
Heat absorbed by water:
Using the formula q = m ⋅ c ⋅ Δ T , where m is the mass, c is the specific heat capacity, and Δ T is the temperature change:
q water = 1005 g × 4.184 J/g°C × 2.36 °C = 9940.968 J
Heat absorbed by calorimeter:
Using q = C ⋅ Δ T where C is the calorimeter's heat capacity:
q calorimeter = 930.9 J/°C × 2.36 °C = 2195.924 J
Total heat absorbed:
q total = q water + q calorimeter = 9940.968 J + 2195.924 J = 12136.892 J
Step 2: Calculate the molar heat of combustion
Convert the total heat absorbed to kilojoules:
q total = 12.136892 kJ
Determine the moles of 1,8-octanediol combusted:
The molar mass of C₈H₁₈O₂:
( 8 × 12.01 ) + ( 18 × 1.01 ) + ( 2 × 16.00 ) = 146.23 g/mol
Moles of 1,8-octanediol:
Moles = 146.23 g/mol 0.3621 g = 0.002476 mol
Calculate the molar heat of combustion:
Molar heat of combustion = 0.002476 mol 12.136892 kJ = 4901.98 kJ/mol
Therefore, the molar heat of combustion of 1,8-octanediol is approximately 4902 kJ/mol .
