Problem 123 - Chemistry The Central Science In Si Units

Question

Gas pipelines are used to deliver natural gas (methane, \(\mathrm{CH}_{4}\) ) to the various regions of the United States. The total volume of natural gas that is delivered is on the order of \(2.7 \times 10^{12} \mathrm{~L}\) per day, measured at STP. Calculate the total enthalpy change for combustion of this quantity of methane. (Note: Less than this amount of methane is actually combusted daily. Some of the delivered gas is passed through to other regions.)

Step-by-Step Solution

Answer

The total enthalpy change for the combustion of the given methane is \(-1.07275 \times 10^{14}\) kJ.

Step 1: Identify the Reaction and Enthalpy Change

The combustion of methane (\(\mathrm{CH}_{4}\)) can be represented by the balanced chemical equation: \[\mathrm{CH}_{4}(g) + 2\ \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) + 2\ \mathrm{H}_{2}\mathrm{O}(l) \] with an enthalpy change (\(\Delta H\)) of \(-890.3\ \mathrm{kJ/mol}\).

Step 2: Calculate Moles of Methane

First, calculate the moles of methane in the given volume at standard temperature and pressure (STP). At STP, 1 mole of gas occupies 22.4 L. \[ 2.7 \times 10^{12}\ \mathrm{L} \div 22.4\ \mathrm{L/mol} = 1.2053571 \times 10^{11}\ \mathrm{mol} \]

Step 3: Calculate Total Enthalpy Change

Using the moles calculated and the enthalpy change for combustion, calculate the total enthalpy change:\[ \Delta H_{\text{total}} = 1.2053571 \times 10^{11} \ \mathrm{mol} \times (-890.3 \ \mathrm{kJ/mol}) \]\[ \Delta H_{\text{total}} = -1.07275 \times 10^{14} \ \mathrm{kJ} \]

Key Concepts

Combustion Reaction

In a combustion reaction, a substance combines with oxygen to produce energy, typically in the form of heat and light. Combustion reactions are essential for generating energy in various applications such as power plants and vehicles. For example, when methane (CH extsubscript{4}), which is a major component of natural gas, undergoes combustion, it reacts with oxygen (O extsubscript{2}) to form carbon dioxide (CO extsubscript{2}) and water (H extsubscript{2}O). This reaction releases a significant amount of energy. The balanced chemical equation for methane combustion is:

\[\mathrm{CH}_{4}(g) + 2\ \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) + 2\ \mathrm{H}_{2}\mathrm{O}(l) \]

Enthalpy change (\Delta H) indicates the amount of heat energy released or absorbed during a reaction. For methane combustion, this value is -890.3 kJ/mol, signifying an exothermic process that releases energy.

Moles Calculation

Calculating moles helps quantify substances in a chemical reaction. It is crucial for understanding how much of each reactant is needed and how much product can be formed. Moles denote a specific number of particles, such as atoms or molecules. One mole equals Avogadro's number, approximately \(6.022 \times 10^{23}\) entities.

When methane is provided at standard temperature and pressure (STP), which is 0°C and 1 atm, 1 mole of any gas occupies 22.4 liters. This makes it easy to determine how many moles are present in a given volume.

For instance, if measuring 2.7 \times 10^{12} L of methane at STP, you can calculate moles by dividing the total volume by the molar volume:\[\text{Moles of Methane} = \frac{2.7 \times 10^{12}\ \text{L}}{22.4\ \text{L/mol}} = 1.2053571 \times 10^{11}\ \text{mol} \]

Methane Combustion

Methane combustion is a significant reaction in energy production, especially in natural gas applications. The combustion of methane releases large amounts of heat, making it an efficient fuel. The equation for methane combustion entails burning one mole of methane to produce one mole of carbon dioxide and two moles of water:

\[\mathrm{CH}_{4}(g) + 2\ \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) + 2\ \mathrm{H}_{2}\mathrm{O}(l) \]

The reaction is highly exothermic, with an enthalpy change of -890.3 kJ/mol. This high energy release is why methane is often used as a fuel in heating systems, electricity generation, and vehicles. The water produced is typically in the form of steam, contributing to the overall energy output.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a set of conditions used as a reference point in chemistry to measure gases. These conditions simplify the calculation and comparison of chemical reactions involving gases.

STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm). Under these conditions, one mole of an ideal gas occupies a volume of 22.4 liters. This standardized measure is widely used to calculate the number of moles and, subsequently, the enthalpy changes in reactions involving gases.

Knowing that 1 mole occupies 22.4 L at STP allows for straightforward volume-to-mole conversions. For example, if given a volume of gas at STP, you can easily determine the amount in moles, facilitating further calculations such as those for enthalpy change.