Textbook Question
Use the molar volume of a gas at STP to calculate the density (in g/L) of nitrogen gas at STP.
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Ch.5 - Gases
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831
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Table of contents
- Ch.1 - Matter, Measurement & Problem Solving107
- Ch.2 - Atoms & Elements100
- Ch.3 - Molecules, Compounds & Chemical Equations127
- Ch.4 - Chemical Quantities & Aqueous Reactions114
- Ch.5 - Gases103
- Ch.6 - Thermochemistry92
- Ch.7 - Quantum-Mechanical Model of the Atom50
- Ch.8 - Periodic Properties of the Elements89
- Ch.9 - Chemical Bonding I: The Lewis Model84
- Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory74
- Ch.11 - Liquids, Solids & Intermolecular Forces60
- Ch.12 - Solids and Modern Material50
- Ch.13 - Solutions90
- Ch.14 - Chemical Kinetics111
- Ch.15 - Chemical Equilibrium65
- Ch.16 - Acids and Bases135
- Ch.17 - Aqueous Ionic Equilibrium145
- Ch.18 - Free Energy and Thermodynamics92
- Ch.19 - Electrochemistry100
- Ch.20 - Radioactivity and Nuclear Chemistry68
- Ch.21 - Organic Chemistry121
Chapter 5, Problem 56
A sample of N2O gas has a density of 2.85 g/L at 298 K. What is the pressure of the gas (in mmHg)?
Verified step by step guidance1
Identify the ideal gas law equation: \( PV = nRT \).
Express the number of moles \( n \) in terms of mass and molar mass: \( n = \frac{m}{M} \), where \( m \) is mass and \( M \) is molar mass.
Substitute \( n = \frac{m}{M} \) into the ideal gas law to get \( PV = \frac{m}{M}RT \).
Rearrange the equation to solve for pressure \( P \): \( P = \frac{mRT}{MV} \).
Use the density formula \( \text{density} = \frac{m}{V} \) to substitute \( m/V \) with density in the pressure equation: \( P = \frac{\text{density} \times RT}{M} \).
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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 allows us to calculate one variable if the others are known, making it essential for solving gas-related problems.
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Ideal Gas Law Formula
Density of Gases
The density of a gas is defined as its mass per unit volume, typically expressed in grams per liter (g/L). For gases, density can be influenced by temperature and pressure, and it can be calculated using the formula density = mass/volume. Understanding how to manipulate this relationship is crucial for converting density into other gas properties, such as pressure.
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Conversion of Units
In chemistry, it is often necessary to convert between different units of measurement, such as from grams to moles or from liters to milliliters. For this problem, converting pressure from atmospheres or pascals to mmHg is essential, as different contexts may require different units. Familiarity with conversion factors and the relationships between units is vital for accurate calculations.
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Related Practice
Textbook Question
A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 °C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 °C?
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Textbook Question
A 248-mL gas sample has a mass of 0.433 g at a pressure of 745 mmHg and a temperature of 28 °C. What is the molar mass of the gas?
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Textbook Question
A sample of gas has a mass of 38.8 mg. Its volume is 224 mL at a temperature of 55 °C and a pressure of 886 torr. Find the molar mass of the gas.
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Textbook Question
What is the density (in g/L) of hydrogen gas at 20.0 °C and a pressure of 1655 psi?
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Textbook Question
A sample of gas has a mass of 0.555 g. Its volume is 117 mL at a temperature of 85 °C and a pressure of 753 mmHg. Find the molar mass of the gas.
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