Ch.10 - Gases

Problem 125a

Chapter 10, Problem 125a

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. What volume of methanol is formed if the density of CH3OH is 0.791 g>mL?

Verified step by step guidance

Step 1: Convert the volume of methane from cubic meters to liters by using the conversion factor 1 m^3 = 1000 L.

Step 2: Use the ideal gas law, PV = nRT, to calculate the number of moles of methane. Assume the gas behaves ideally, use R = 0.0821 L atm K^{-1} mol^{-1}, and convert the temperature from Celsius to Kelvin.

Step 3: Write the balanced chemical equation for the oxidation of methane to methanol. The equation is CH4 + 1.5 O2 -> CH3OH + H2O.

Step 4: Use stoichiometry from the balanced equation to find the moles of methanol produced from the moles of methane calculated.

Step 5: Convert the moles of methanol to volume using the density of methanol (0.791 g/mL). First, calculate the mass of methanol by multiplying the moles by the molar mass of methanol (32.04 g/mol), then convert the mass to volume.

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Key Concepts

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

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this case, understanding the stoichiometry of the oxidation of methane to methanol is essential for determining the volume of methanol produced from a given volume of methane.

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. The ideal gas law (PV=nRT) is particularly useful for converting between the volume of a gas at specific conditions and the number of moles. In this question, the volume of methane at atmospheric pressure and temperature must be converted to moles to find the corresponding volume of methanol produced after the reaction.

Density and Volume Conversion

Density is defined as mass per unit volume and is a critical concept for converting between mass and volume of a substance. In this scenario, the density of methanol (0.791 g/mL) is used to convert the mass of methanol produced into its volume. Understanding how to apply density in calculations is crucial for determining the final volume of methanol that can be shipped.

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Related Practice

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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Open Question

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.)

Open Question

Chlorine dioxide gas (ClO2) is used as a commercial bleaching agent. It bleaches materials by oxidizing them. In the course of these reactions, the ClO2 is itself reduced. One method of preparing ClO2 is by the reaction of chlorine and sodium chlorite: Cl2(g) + 2 NaClO2(s) → 2 ClO2(g) + 2 NaCl(s). If you allow 15.0 g of NaClO2 to react with 2.00 L of chlorine gas at a pressure of 152.0 kPa at 21°C, how many grams of ClO2 can be prepared?

Textbook Question

Gaseous iodine pentafluoride, IF5, can be prepared by the reaction of solid iodine and gaseous fluorine: I21s2 + 5 F21g2¡2 IF51g2 A 5.00-L flask containing 10.0 g of I2 is charged with 10.0 g of F2, and the reaction proceeds until one of the reagents is completely consumed. After the reaction is complete, the temperature in the flask is 125 °C. (a) What is the partial pressure of IF5 in the flask?

Gaseous iodine pentafluoride, IF5, can be prepared by the reaction of solid iodine and gaseous fluorine: I21s2 + 5 F21g2¡2 IF51g2 A 5.00-L flask containing 10.0 g of I2 is charged with 10.0 g of F2, and the reaction proceeds until one of the reagents is completely consumed. After the reaction is complete, the temperature in the flask is 125 °C. (d) What is the total mass of reactants and products in the flask?

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