Ch.10 - Gases: Their Properties & Behavior

Problem 90b

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Chapter 10, Problem 90b

Natural gas is a mixture of hydrocarbons, primarily methane (CH₄) and ethane (C₂H₆). A typical mixture might have X_methane = 0.915 and X_ethane = 0.085. Let's assume that we have a 15.50 g sample of natural gas in a volume of 15.00 L at a temperature of 20.00 °C. (b) What is the pressure of the sample in atmospheres?

Verified step by step guidance

Step 1: Convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15.

Step 2: Calculate the total moles of gas in the sample. The molar mass of methane (CH4) is approximately 16.04 g/mol and the molar mass of ethane (C2H6) is approximately 30.07 g/mol. Use the given mass fractions and the total mass to calculate the moles of each gas.

Step 3: Use the ideal gas law, PV = nRT, to calculate the pressure. In this equation, P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(K·mol) for pressure in atmospheres), and T is the temperature in Kelvin.

Step 4: Substitute the values into the ideal gas law equation. The volume V is given as 15.00 L and the temperature T has been converted to Kelvin in step 1. The number of moles n is the total moles of gas calculated in step 2.

Step 5: Solve the equation for P, the pressure. This will give you the pressure of the gas sample in atmospheres.

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law is essential for calculating the pressure of gases under various conditions, as it allows us to manipulate these variables to find unknowns.

Molar Mass and Composition

Understanding molar mass is crucial for converting between grams and moles of a substance. In the context of natural gas, knowing the composition (e.g., the proportions of methane and ethane) allows us to calculate the average molar mass of the gas mixture. This average molar mass is necessary for determining the number of moles present in a given mass of the gas, which is a key step in applying the Ideal Gas Law.

Gas Pressure Units

Gas pressure can be measured in various units, including atmospheres (atm), pascals (Pa), and mmHg. In this problem, we need to express the final answer in atmospheres, which is a common unit in chemistry. Understanding how to convert between these units and the significance of pressure in gas behavior is important for accurately solving problems related to gas laws.

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Pressure Units

Related Practice

Chlorine gas was first prepared in 1774 by the oxidation of NaCl with MnO₂: 2 NaCl(s) + 2 H₂SO₄(l) + MnO₂(s) → Na₂SO₄(s) + MnSO₄(s) + 2 H₂O(g) + Cl₂(g) Assume that the gas produced is saturated with water vapor at a partial pressure of 28.7 mm Hg and that it has a volume of 0.597 L at 27 °C and 755 mm Hg pressure. (a) What is the mole fraction of Cl₂ in the gas?

Natural gas is a mixture of hydrocarbons, primarily methane 1CH42 and ethane 1C2H62. A typical mixture might have Xmethane = 0.915 and Xethane = 0.085. Let's assume that we have a 15.50 g sample of natural gas in a volume of 15.00 L at a temperature of 20.00 °C. (a) How many total moles of gas are in the sample?

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Textbook Question

Natural gas is a mixture of hydrocarbons, primarily methane (CH₄) and ethane (C₂H₆). A typical mixture might have X_methane = 0.915 and X_ethane = 0.085. Let's assume that we have a 15.50 g sample of natural gas in a volume of 15.00 L at a temperature of 20.00 °C. (c) What is the partial pressure of each component in the sample in atmospheres?

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Textbook Question

Gaseous compound Q contains only xenon and oxygen. When 0.100 g of Q is placed in a 50.0-mL steel vessel at 0 °C the pressure is 0.229 atm. (a) What is the molar mass of Q, and what is a likely formula?

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Textbook Question

Gaseous compound Q contains only xenon and oxygen. When 0.100 g of Q is placed in a 50.0-mL steel vessel at 0 °C the pressure is 0.229 atm. (b) When the vessel and its contents are warmed to 100 °C, Q decomposes into its constituent elements. What is the total pressure, and what are the partial pressures of xenon and oxygen in the container?

468

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