Question

A calorimeter that measures an exothermic heat of reaction by the quantity of ice that can be melted is called an ice calorimeter. Now consider that \(0.100 \mathrm{L}\) of methane gas, \(\mathrm{CH}_{4}(\mathrm{g}),\) at \(25.0^{\circ} \mathrm{C}\) and \(744 \mathrm{mm} \mathrm{Hg}\) is burned at constant pressure in air. The heat liberated is captured and used to melt \(9.53 \mathrm{g}\) ice at \(0^{\circ} \mathrm{C}\left(\Delta H_{\text {fusion }} \text { of ice }=6.01 \mathrm{kJ} / \mathrm{mol}\right)\) (a) Write an equation for the complete combustion of \(\mathrm{CH}_{4},\) and show that combustion is incomplete in this case. (b) Assume that \(\mathrm{CO}(\mathrm{g})\) is produced in the incomplete combustion of \(\mathrm{CH}_{4}\), and represent the combustion as best you can through a single equation with small whole numbers as coefficients. \((\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) is another . product of the combustion.)

Short answer

Part (a): The full combustion of methane is represented by the reaction \(CH₄(g) + 2O₂(g) -> CO₂(g) + 2H₂O(l)\). This combustion is incomplete in this case as less heat was released than the full combustion would typically liberate. Part (b): The incomplete combustion of methane, resulting in the production of carbon monoxide and water, can be represented by the equation \(CH₄(g) + 1.5O₂(g) -> CO(g) + 2H₂O(l)\).

Step-by-step solution

Part (a): Writing the full combustion of methane

The full combustion reaction of methane (CH₄) in the presence of oxygen (O₂) produces carbon dioxide (CO₂) and water (H₂O). This can be written as: \[CH₄(g) + 2O₂(g) -> CO₂(g) + 2H₂O(l)\]

Part (a): Analyzing incompleteness of the combustion

The fact that the heat released from the reaction was only enough to melt 9.53g of ice (equivalent to approx. 0.53 mol considering the fusion heat of ice) suggests that the combustion was incomplete - as the full combustion of one mole of methane typically releases more energy.

Part (b): Representing the incomplete combustion

When combustion is incomplete due to the insufficient supply of oxygen, carbon monoxide (CO) is produced instead of carbon dioxide. Keeping this in mind, and considering that water is also produced, the combustion can be represented by: \[CH₄(g) + 1.5O₂(g) -> CO(g) + 2H₂O(l)\] This equation assumes that for every mole of methane, one mole of carbon monoxide and two of water are produced, consuming 1.5 moles of oxygen in the process. The coefficients in this equation are all small whole numbers, as requested.

Key concepts

Calorimetry

Calorimetry is the science of measuring heat changes during physical or chemical processes. When substances undergo transformations, they often release or absorb heat. Measuring this heat change helps to understand the energy dynamics of the process.

An ice calorimeter is a specific type of calorimeter used to measure heat released in an exothermic reaction by determining how much ice can be melted by the heat. Since the melting of ice requires a specific amount of energy, known as the enthalpy of fusion, we can determine the heat release by knowing how many grams of ice were melted.

In the given exercise, the reaction's heat melts 9.53 grams of ice. Knowing the enthalpy of fusion ( 6.01 ext{ kJ/mol}), we can calculate how much heat was absorbed by the ice to cause this phase change.

Exothermic Reactions

Exothermic reactions are chemical reactions that release energy in the form of heat. This release occurs because the energy required to break the reactants' bonds is less than the energy released when new bonds are formed in the products.

The combustion of methane is an exothermic process. When methane burns in oxygen, it forms water and carbon dioxide, releasing considerable amounts of energy.

In such processes:

• The surroundings usually gain heat, leading to an increase in temperature.
• They are often spontaneous as they increase the entropy (disorder) of the system.
• The enthalpy change ( ΔH) is negative, indicating that the reaction releases heat.

In our problem, the exothermic nature is evident as the heat released from methane combustion melts the ice.

Heat of Combustion

The heat of combustion is the energy released as heat when a compound undergoes complete combustion with oxygen under standard conditions. It's an essential concept in understanding the energy efficiency of fuels.

For methane, like in our exercise, the complete combustion results in carbon dioxide and water. The released heat in this reaction ensures that methane serves as a significant energy source in various applications, like fuel for heating and cooking.

Considerations include:

• The heat of combustion is specific for each compound.
• It's measured in kJ/mol or calories, indicating how much energy is available from one mole of substance.
• The higher the heat, the more energy-efficient the fuel is.

The deviation in combustion efficiency in the problem indicates a partial reaction, limiting the energy release.

Incomplete Combustion

Incomplete combustion happens when a fuel does not burn entirely, often because there is not enough oxygen present. Instead of producing the expected products, like carbon dioxide and water, other compounds, such as carbon monoxide or soot, may form.

The performance of a combustion process can be affected, typically marked by lower energy release and formation of undesired by-products. In the exercise, methane undergoes incomplete combustion, indicated by the production of carbon monoxide rather than carbon dioxide.

Key points about incomplete combustion include:

• It results in less energy being released, reducing efficiency.
• It often creates hazardous substances like carbon monoxide.
• The environmental impact can include higher emissions of pollutants.

This exercise emphasizes the necessity of sufficient oxygen to achieve full combustion to maximize energy extraction and minimize negative side effects.