Calorimetry

Enthalpy of Combustion of Methane

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 stainless steel reaction vessel (called a bomb) with a mixture of methane and oxygen gas. The calorimeter is filled with water, and the bomb is immersed in the water. An electrical current is passed through ignition wire (a fine iron wire) to ignite the wire and the gas mixture.

Provided the calorimeter is perfectly insulated, the heat balance for this calorimetry experiment is:

0   =   q_cal   +   q_comb

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

The heat released by the combustion reaction is q_comb . The molar enthalpy of combustion is the ratio of q_comb to the moles of methane burned, n . (The experiment is performed using a large excess of oxygen, making methane the limiting reactant in the combustion reaction.)

Note: The above equation is not exactly correct for this experiment. For experiments performed at constant pressure, the heat flow equals the enthalpy change. In this experiment, however, the pressure inside the bomb is not constant but the volume of the bomb is. For experiments performed at constant volume, the heat flow equals the internal energy change. To be accurate, ΔU_comb = q_comb / n . With the virtual equipment used in this experiment, the uncertainty in the value of q_comb is a few kJ mole ^-1, which is greater than the difference between ΔH and ΔU . So we will use q_comb / n as an approximation of ΔH_comb .

Standard Enthalpies of Formation

Combustion reactions are often used to calculate 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, H2O}   +   ΔH^o_{f, CO2}   -   ΔH^o_{f, CH4}   -   2 ΔH^o_{f, O2}

ΔH^o_comb is measured experimentally. (Strictly speaking, the measured value is not a standard enthalpy change, but this difference is negligibly small for the purposes of this exercise.)

ΔH^o_{f, O2} = 0, because oxygen is a pure element in its most stable allotrope.

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, H2O} = -285.8 kJ mole^-1

For gaseous carbon dioxide, ΔH^o_{f, CO2} = -393.5 kJ mole^-1

Experiment

Objectives

• Measure the molar enthalpy of combustion of methane
• Calculate the molar enthalpy of formation of methane

Procedure

1. Pressurize the bomb with methane gas to a pressure between 0.5 and 2 atm.
2. Start the experiment. The temperature of the calorimeter is measured electronically with a thermocouple and plotted on the graph.
3. Analyze the graph to determine the temperature change caused by the combustion reaction.
4. Calculate the molar enthalpy of combustion of methane.
5. Calculate the molar enthalpy of formation of methane.

The amount of methane burned is calculated from the initial pressure of methane gas, the initial temperature of the bomb, the volume of the inside of the bomb, and the Ideal Gas Law: P V   =   n R T

In addition to the methane gas, the bomb contains 25 atm of oxygen gas. Thus oxygen is present in large excess, and methane is the limiting reactant.

The heat balance equation, written above, assumes the calorimeter is perfectly insulated from the surroundings. In practice, this is not true. Heat can slowly enter or leave the system from the surroundings. This effect manifests itself as a slight drift in the temperature. To compensate for this, one measures the temperature vs time trend just before combustion occurs and again after the combustion reaction is complete and the heat from the combustion reaction has been distributed throughout the calorimeter. That is, one will draw two base lines.

The initial baseline uses the data from before the ignition of the sample to draw a straight line that accounts for heat loss or gain prior to ignition. The equation for this line will be provided based upon the points you have selected for the initial baseline.

The final baseline uses the data from the cooling trend at the end of the data set. After ignition, the temperature slowly rises to a maximum and then slowly decreases over time. The slow decrease is attributable to heat loss to the surroundings. The linear data during this cooling period is used to construct the final baseline.

Use the selection buttons to select points from the beginning of the data set for the initial baseline. The selected points will be shown in blue and the initial baseline will be drawn. Do not include any points after combustion has occurred.

Use the selection buttons to select points from the end of the data set for the final baseline. The selected points will be shown in red and the final baseline will be drawn. Include only those points on the linear cooling trend at the end of the data set.

Equations for both baselines will be shown. Both T_i and T_f are functions of time. Calculate ΔT using T_i and T_f calculated from the two baselines at the ignition time.

ΔT   =   T_f   -   T_i

Information