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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Enthalpy of Formation

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Textbook Question

A 4.00-g sample of a mixture of CaO and BaO is placed in a 1.00-L vessel containing CO₂ gas at a pressure of 97.33 kPa and a temperature of 25 °C. The CO₂ reacts with the CaO and BaO, forming CaCO₃ and BaCO₃. When the reaction is complete, the pressure of the remaining CO₂ is 20.0 kPa. (a) Calculate the number of moles of CO₂ that have reacted. (b) Calculate the mass percentage of CaO in the mixture.

Textbook Question

Ammonia and hydrogen chloride react to form solid ammonium chloride: NH31g2 + HCl1g2¡NH4Cl1s2 Two 2.00-L flasks at 25 °C are connected by a valve, as shown in the drawing. One flask contains 5.00 g of NH31g2, and the other contains 5.00 g of HCl(g). When the valve is opened, the gases react until one is completely consumed. (a) Which gas will remain in the system after the reaction is complete?

Textbook Question

Ammonia and hydrogen chloride react to form solid ammonium chloride: NH₃(g) + HCl(g) → NH₄Cl(s)

Two 2.00-L flasks at 25 °C are connected by a valve, as shown in the drawing. One flask contains 5.00 g of NH₃(g), and the other contains 5.00 g of HCl(g). When the valve is opened, the gases react until one is completely consumed. (b) What will be the final pressure of the system after the reaction is complete? (Neglect the volume of the ammonium chloride formed.)

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Textbook Question

Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to markets in other parts of the world are high because it is necessary to liquefy the gas, which is mainly methane and has a boiling point at atmospheric pressure of -164 °C. One possible strategy is to oxidize the methane to methanol, CH₃OH, which has a boiling point of 65 °C and can therefore be shipped more readily. Suppose that 3.03×10⁸ m³ of methane at atmospheric pressure and 25 °C is oxidized to methanol. (a) What volume of methanol is formed if the density of CH₃OH is 0.791 g/mL?