Calorimetry

Heat of Combustion of Methane

Concepts

The combustion reaction for methane is

CH₄ (g) + 2 O₂ (g)

CO₂ (g) + 2 H₂O (l)

The enthalpy change for this reaction is measured by pressurizing a strong metal reaction vessel (called a bomb) with a mixture of methane and oxygen gas. The bomb is immersed in a calorimeter filled with water. An electrical current is passed through ignition wire (a fine iron wire), which ignites the wire and the gas mixture.

The heat balance for this calorimetry experiment is:

0 = q_cal + q_wire + q_comb

The heat flow for the calorimeter, q_cal, is determined from the heat capacity of the calorimeter and the temperature change for the calorimetry experiment. Typically the amount of water in the calorimeter is always the same; therefore C_cal includes the heat capacities of the calorimeter, the water, and the bomb itself.

The burning of the ignition wire releases heat, q_wire, and this heat must be included in the calculations. (This heat is treated separately, because the amount of ignition wire used varies from one measurement to the next.)

The heat released by the combustion reaction is q_comb, which is related to the molar internal energy of combustion by

ΔE_comb =

q_comb

n_methane

Combustion experiments are general conducted with a large excess of oxygen, so that the fuel (methane in this case) is the limiting reactant. In this experiment, unlike previous experiments in this sequence, the reaction occurs under conditions of constant volume and no work is performed; thus the heat flow equals the internal energy change for the reaction.

The molar enthalpy of combustion (ΔH_comb) is related to the molar internal energy of combustion (ΔE_comb) by the equation shown below. (Recall that H = E + PV and the volume is constant in this experiment.)

ΔH_comb = ΔE_comb + V ΔP = ΔE_comb + R Δ(n T)

The quantity n is the total moles of gas-phase species. (The assumption implicit in this analysis is that the volume occupied by solids and liquids is negligible compared to the volume of the bomb and thus condensed phases do not contribute significantly to changes in pressure.) The term R Δ(n T) is typically small compared with ΔE_comb, and thus ΔH_comb is usually very close to ΔE_comb.

For example, suppose the bomb has a volume of 271 mL and initially contains 10. mmole of methane and excess oxygen at 25.0 ^oC. Further suppose that after combustion the system reaches a temperature of 27.0 ^oC, at which time 10.0 mmole of methane and 20.0 mmole oxygen have reacted to form 10.0 mmole of carbon dioxide and 20.0 mmole of liquid water. The initial n T for gaseous species is 8.94 K mole and the final value is 3.00 K mole. The term R Δ(n T) is thus -49.4 J per 10.0 mmole methane or -4.94 kJ mole^-1. Compare this quantity with the molar heat of combustion as determined in the experiment described below.

Combustion reactions are often used to calculate the molar enthalpies of formation. For example, the standard molar enthalpy of combustion for methane can be expressed in terms of the standard molar enthalpies of formation of the reactants and products:

ΔH^o_comb = 2 ΔH^o_f,water + ΔH^o_{carbon dioxide} - ΔH^o_f,methane - 2 ΔH^o_f,oxygen

ΔH^o_comb is measured experimentally.

ΔH^o_f,oxygen = 0, because oxygen is a pure element.

The other molar enthalpies of formation are known from independent measurements. For example, one could determine the heat of combustion of hydrogen to obtain the molar enthalpy of formation for water.

For liquid water, ΔH^o_f = -285.8 kJ mole^-1

For gaseous carbon dioxide, ΔH^o_f = -393.5 kJ mole^-1

Experiment

Objective:

Determine the molar enthalpy of combustion for methane.
Determine the molar enthalpy of formation for methane.

Approach:

Pressurize the bomb with a known amount of methane gas.
Observe the temperature of the system before and after the combustion reaction occurs.
Calculate the change in temperature for the system.
Use the temperature change, the heat capacity for the calorimeter, and the heat released by burning the ignition wire to calculate the heat of combustion.
Divide the heat of neutralization by the moles of methane to determine the molar enthalpy of combustion.
Use the molar enthalpy of combustion of methane to calculate the molar enthalpy of formation of methane.

Part 1

In this part of the experiment, the calorimeter is filled with 10.0 mmole of methane gas and an excess of oxygen.

When burned, the ignition wire releases 107.2 J of heat

The heat capacity of the calorimeter (including the bomb and water) is 4.319 kJ ^oC^-1.

Part 2

Repeat the measurements made in Part 1 using a different initial pressure of methane gas in the bomb. As in Part 1, a large excess of oxygen is present.

Use the ideal gas law to calculate the amount of methane originally present.

The volume of the bomb is 271 mL.

The heat capacity of the calorimeter (including the bomb and water) is 4.319 kJ ^oC^-1.

A different length of ignition wire is used in each experiment. The heat released by combustion of the ignition wire is shown at the right.

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