Textbook Question
Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (c) At what temperature would the pressure in the tank equal 15.2 MPa?
Ch.10 - Gases
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
Chapter 10, Problem 43d
Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl2 gas is 8.70 L at 119.3 kPa and 24 °C. (d) At what pressure will the volume equal 5.00 L if the temperature is 58 °C?
Verified step by step guidance1
Identify the initial conditions: The initial volume (V1) is 8.70 L, the initial pressure (P1) is 119.3 kPa, and the initial temperature (T1) is 24 °C. Convert the temperature to Kelvin by adding 273.15, so T1 = 24 + 273.15 K.
Identify the final conditions: The final volume (V2) is 5.00 L, and the final temperature (T2) is 58 °C. Convert this temperature to Kelvin as well, so T2 = 58 + 273.15 K. The final pressure (P2) is what we need to find.
Use the combined gas law, which relates pressure, volume, and temperature: \( \frac{P1 \cdot V1}{T1} = \frac{P2 \cdot V2}{T2} \). This equation allows us to solve for the unknown pressure P2.
Rearrange the combined gas law to solve for P2: \( P2 = \frac{P1 \cdot V1 \cdot T2}{V2 \cdot T1} \).
Substitute the known values into the equation: P1 = 119.3 kPa, V1 = 8.70 L, T1 = (24 + 273.15) K, V2 = 5.00 L, and T2 = (58 + 273.15) K. Calculate P2 using these values.
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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 relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental in understanding gas behavior under varying conditions. In this scenario, it allows us to calculate the pressure of chlorine gas when the volume and temperature change.
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Ideal Gas Law Formula
Charles's Law
Charles's Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant. This principle is essential for understanding how changes in temperature affect the volume of a gas, which is relevant when determining the new pressure of Cl2 gas at a different volume and temperature.
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Boyle's Law
Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This concept is crucial for solving the problem, as it helps to understand how a decrease in volume (from 8.70 L to 5.00 L) will affect the pressure of the gas, given the temperature change.
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Related Practice
Textbook Question
Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (a) What mass of O2 does the tank contain?
Textbook Question
Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl2 gas is 8.70 L at 119.3 kPa and 24 °C. (b) What volume will the Cl2 occupy at STP?
Textbook Question
Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?
Textbook Question
Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl2 gas is 8.70 L at 119.3 kPa and 24 °C. (c) At what temperature will the volume be 15.00 L if the pressure is 116.8 kPa
Textbook Question
A 334-mL cylinder for use in chemistry lectures contains5.225 g of helium at 23 °C. How many grams of helium mustbe released to reduce the pressure to 7.60 MPa assuming idealgas behavior?