Textbook Question
A cylinder with a moveable piston contains 0.553 mol of gas and has a volume of 253 mL. What is its volume if an additional 0.365 mol of gas is added to the cylinder? (Assume constant temperature and pressure.)
Ch.6 - Gases
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371
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Table of contents
- Ch.1 - Matter, Measurement & Problem Solving117
- Ch.2 - Atoms & Elements106
- Ch.3 - Molecules and Compounds128
- Ch.4 - Chemical Reactions and Chemical Quantities56
- Ch.5 - Introduction to Solutions and Aqueous Solutions84
- Ch.6 - Gases112
- Ch.7 - Thermochemistry96
- Ch.8 - The Quantum-Mechanical Model of the Atom60
- Ch.9 - Periodic Properties of the Elements86
- Ch.10 - Chemical Bonding I: The Lewis Model91
- Ch.11 - Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory85
- Ch.12 - Liquids, Solids & Intermolecular Forces51
- Ch.13 - Solids & Modern Materials48
- Ch.14 - Solutions93
- Ch.15 - Chemical Kinetics114
- Ch.16 - Chemical Equilibrium68
- Ch.17 - Acids and Bases137
- Ch.18 - Aqueous Ionic Equilibrium154
- Ch.19 - Free Energy & Thermodynamics91
- Ch.20 - Electrochemistry105
- Ch.21 - Radioactivity & Nuclear Chemistry74
- Ch.22 - Organic Chemistry141
Chapter 6, Problem 33
A 48.3-mL sample of gas in a cylinder is warmed from 22 °C to 87 °C. What is its volume at the final temperature?
Verified step by step guidance1
Identify the initial and final temperatures and convert them from Celsius to Kelvin. Use the formula: \( T(K) = T(°C) + 273.15 \).
Apply Charles's Law, which states that \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \), where \( V_1 \) and \( T_1 \) are the initial volume and temperature, and \( V_2 \) and \( T_2 \) are the final volume and temperature.
Substitute the known values into the equation: \( V_1 = 48.3 \text{ mL} \), \( T_1 = 22 + 273.15 \text{ K} \), and \( T_2 = 87 + 273.15 \text{ K} \).
Rearrange the equation to solve for \( V_2 \): \( V_2 = V_1 \times \frac{T_2}{T_1} \).
Calculate \( V_2 \) using the rearranged equation to find the final volume of the gas at 87 °C.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 relationship can be expressed mathematically as V1/T1 = V2/T2, where V is volume and T is temperature. Understanding this law is essential for solving problems involving changes in temperature and volume of gases.
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Charles's Law
Temperature Conversion
In gas law calculations, temperatures must be expressed in Kelvin rather than Celsius. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. This step is crucial because gas laws are based on absolute temperature, which affects the behavior of gases.
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Ideal Gas Behavior
The ideal gas law describes the behavior of an ideal gas, which follows the relationships defined by pressure, volume, temperature, and the number of moles of gas. While real gases may deviate from ideal behavior under certain conditions, understanding this concept helps in applying gas laws effectively and predicting how gases will respond to changes in temperature and volume.
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