Gas pipelines are used to deliver natural gas (methane, CH4) to the various regions of the United States. The total volume of natural gas that is delivered is on the order of 2.7 * 10^12 L per day, measured at STP. Calculate the total enthalpy change for the 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.)

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Identify the balanced chemical equation for the combustion of methane: \( \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \).

Determine the standard enthalpy change (\( \Delta H^\circ \)) for the combustion of methane using standard enthalpies of formation: \( \Delta H^\circ = [\Delta H^\circ_f(\text{CO}_2) + 2\Delta H^\circ_f(\text{H}_2\text{O})] - [\Delta H^\circ_f(\text{CH}_4) + 2\Delta H^\circ_f(\text{O}_2)] \).

Calculate the number of moles of methane using the ideal gas law at STP (Standard Temperature and Pressure, 0°C and 1 atm): \( n = \frac{PV}{RT} \), where \( P = 1 \text{ atm} \), \( V = 2.7 \times 10^{12} \text{ L} \), \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \), and \( T = 273.15 \text{ K} \).

Multiply the number of moles of methane by the standard enthalpy change of combustion to find the total enthalpy change: \( \Delta H_{\text{total}} = n \times \Delta H^\circ \).

Interpret the result: The calculated \( \Delta H_{\text{total}} \) represents the total energy released from the combustion of the given volume of methane at STP.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Combustion Reaction

Combustion is a chemical reaction that occurs when a substance reacts with oxygen, producing heat and light. In the case of methane (CH4), the combustion reaction can be represented as CH4 + 2O2 → CO2 + 2H2O. This reaction releases energy, which is quantified as the enthalpy change (ΔH) of the reaction, typically expressed in kilojoules per mole.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a reference point used in chemistry to define the conditions under which gas volumes are measured. STP is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (101.3 kPa). At STP, one mole of an ideal gas occupies 22.4 liters, which is crucial for converting the volume of methane into moles for enthalpy calculations.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is a measure of the total heat content of a system during a chemical reaction at constant pressure. It indicates whether a reaction is exothermic (releases heat, ΔH < 0) or endothermic (absorbs heat, ΔH > 0). For combustion reactions, ΔH is typically negative, reflecting the energy released when reactants are converted to products, which is essential for calculating the total energy released from the combustion of a specific volume of methane.

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