How Do You Find the Experimental Molar Heat of Combustion?

The experimental molar heat of combustion is determined by measuring the heat released when one mole of a substance is completely burned in a calorimeter. Here's a step-by-step breakdown of the process:

1. Understanding Molar Heat of Combustion

Molar heat of combustion is the amount of heat released (or absorbed, though combustion is typically exothermic) when one mole of a substance undergoes complete combustion under standard conditions. It's usually expressed in kJ/mol (kilojoules per mole).

2. The Calorimetry Process

The key to experimentally determining the molar heat of combustion is calorimetry, the science of measuring heat flow. A calorimeter is a device used to measure the heat involved in a chemical reaction or physical change.

Types of Calorimeters

• Bomb Calorimeter (Constant Volume): This is commonly used for combustion reactions. It involves burning a known mass of the substance in a sealed vessel (the "bomb") surrounded by a known mass of water.

• Coffee Cup Calorimeter (Constant Pressure): While less accurate for combustion, it can be used. It is an insulated container, such as a coffee cup, where the reaction takes place in solution.

3. Experimental Procedure (using a Bomb Calorimeter as an example)

1. Prepare the Calorimeter:

   • A known mass of the substance to be combusted is carefully weighed and placed inside the bomb calorimeter.
   • The bomb is then filled with oxygen gas under pressure to ensure complete combustion.
   • The bomb is immersed in a known mass of water inside the calorimeter.
   • The initial temperature of the water is recorded.

2. Initiate Combustion:

   • An electrical ignition system inside the bomb is used to ignite the substance.

3. Measure Temperature Change:

   • The combustion reaction releases heat, which is absorbed by the water surrounding the bomb.
   • The temperature of the water increases. The maximum temperature reached by the water is carefully recorded.

4. Calculations

The following steps are used to calculate the experimental molar heat of combustion:

a. Calculate the Heat Absorbed by the Water (q_water)

Use the following formula:

q<sub>water</sub> = m<sub>water</sub> * c<sub>water</sub> * ΔT

Where:

• q<sub>water</sub> = Heat absorbed by the water (in joules or kilojoules)
• m<sub>water</sub> = Mass of the water (in grams or kilograms)
• c<sub>water</sub> = Specific heat capacity of water (4.184 J/g°C or 4.184 kJ/kg°C)
• ΔT = Change in temperature of the water (°C or K) (Final temperature - Initial temperature)

b. Account for Calorimeter Heat Capacity (If Applicable)

For more accurate results, particularly with bomb calorimeters, you also need to consider the heat absorbed by the calorimeter itself. This is expressed as the calorimeter's heat capacity (C_cal), usually given in J/°C or kJ/°C.

q<sub>calorimeter</sub> = C<sub>calorimeter</sub> * ΔT

c. Calculate the Total Heat Released (q_combustion)

The total heat released by the combustion is equal to the negative of the sum of the heat absorbed by the water and the calorimeter:

q<sub>combustion</sub> = -(q<sub>water</sub> + q<sub>calorimeter</sub>)

If the calorimeter heat capacity isn't considered:

q<sub>combustion</sub> = -q<sub>water</sub>

Note: The negative sign indicates that the heat is released during combustion (an exothermic process).

d. Calculate the Number of Moles Combusted (n)

Determine the number of moles of the substance that was combusted:

n = mass of substance / molar mass of substance

e. Calculate the Molar Heat of Combustion (ΔH_comb)

Finally, calculate the molar heat of combustion:

ΔH<sub>comb</sub> = q<sub>combustion</sub> / n

This value will be in joules/mole (J/mol) or kilojoules/mole (kJ/mol).

5. Example

Let's say you burn 1.00 g of glucose (C₆H₁₂O₆, molar mass = 180.16 g/mol) in a bomb calorimeter. The water (2.00 kg) temperature rises from 25.0 °C to 28.5 °C. The calorimeter's heat capacity is 837 J/°C.

1. q_water = (2.00 kg) (4.184 kJ/kg°C) (28.5 °C - 25.0 °C) = 29.29 kJ
2. *q_calorimeter = (837 J/°C) (3.5 °C) = 2929.5 J = 2.93 kJ**
3. q_combustion = -(29.29 kJ + 2.93 kJ) = -32.22 kJ
4. n = 1.00 g / 180.16 g/mol = 0.00555 mol
5. ΔH_comb = -32.22 kJ / 0.00555 mol = -5805 kJ/mol

Therefore, the experimental molar heat of combustion of glucose in this example is approximately -5805 kJ/mol.

6. Important Considerations

• Complete Combustion: Ensuring complete combustion is critical. Incomplete combustion produces less heat and leads to inaccurate results.
• Heat Loss: Ideal calorimeters are perfectly insulated. However, in reality, some heat loss to the surroundings may occur, leading to inaccuracies. Proper insulation minimizes this.
• Accuracy of Measurements: The accuracy of the mass and temperature measurements directly impacts the accuracy of the final result. Use precise instruments.
• Standard Conditions: The molar heat of combustion is often reported under standard conditions (298 K and 1 atm pressure). Corrections may be needed if the experiment is performed under non-standard conditions, though the temperature correction is usually negligible.