Chapter 12: Problem 14
When the volume of a sample of gas is decreased, the pressure of the sample of gas ______.
Short Answer
Expert verified
When the volume of a sample of gas is decreased, the pressure of the sample of gas increases.
Step by step solution
01
Recall Boyle's Law
Boyle's Law is a gas law that states the relationship between the pressure and volume of a gas sample, when the temperature and the amount of gas are kept constant. It can be mathematically expressed as:
P1 × V1 = P2 × V2
Where:
- P1 = Initial pressure
- V1 = Initial volume
- P2 = Final pressure
- V2 = Final volume
Boyle's Law shows an inverse relationship between the pressure and volume of a gas, which means that as one of them increases, the other decreases.
02
Apply Boyle's Law to the given exercise
In this exercise, we want to find out what happens to the pressure of a gas sample when the volume is decreased. Let's denote the initial state of the gas sample as (P1, V1) and the final state after volume decrease as (P2, V2). Since the volume is decreased, it means that V2 < V1.
Now, let's rearrange Boyle's Law formula to find the relationship between P1 and P2:
\(P1 \times V1 = P2 \times V2 \Rightarrow P2 = \frac{P1 \times V1}{V2}\)
Since V2 < V1, it means that the ratio (V1/V2) > 1. Therefore, P2 will be greater than P1, which indicates that the pressure of the gas sample (P2) has increased.
03
Complete the sentence
Now that we have determined the relationship between pressure and volume according to Boyle's Law, we can complete the sentence from the exercise:
When the volume of a sample of gas is decreased, the pressure of the sample of gas increases.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Gas Laws
Understanding gas laws is crucial for studying how different variables affect the behavior of gases. These laws are mathematical models that describe the relationships between pressure, volume, temperature, and the number of moles of the gas. The main gas laws include Boyle's Law, Charles's Law, Gay-Lussac's Law, and Avogadro's Law.
Gas laws are vital to various chemical processes, from understanding the function of a syringe to industrial gas storage. They provide a foundation for predicting how gases will react under varying conditions, which is essential in fields like environmental science, respiratory medicine, and chemical engineering.
By mastering these concepts, students can explain phenomena like how an airbag inflates in milliseconds or how deep-sea creatures withstand high-pressure environments without collapsing.
Importance in Chemistry
Gas laws are vital to various chemical processes, from understanding the function of a syringe to industrial gas storage. They provide a foundation for predicting how gases will react under varying conditions, which is essential in fields like environmental science, respiratory medicine, and chemical engineering.
Real-World Applications
By mastering these concepts, students can explain phenomena like how an airbag inflates in milliseconds or how deep-sea creatures withstand high-pressure environments without collapsing.
Pressure-Volume Relationship
Boyle's Law showcases the pressure-volume relationship in gases, highlighting an inverse relationship; this is key for understanding how gases will behave when subjected to changes in volume or pressure. In simpler terms, if you squish a gas into a smaller volume without changing its temperature, its pressure goes up, and vice versa.
Visualizing the inverse relationship can be done by picturing a syringe: as you push the plunger (decreasing volume), the resistance you feel increases because the pressure inside goes up, making it harder to push.
This concept is not just academic; it's used in designing equipment like bicycle pumps, hydraulic brakes, and even in understanding how our lungs work when we breathe in and out. Every time you take a breath, Boyle's Law is put into action as the volume of your lungs changes to facilitate air movement.
Understanding Inverse Relationships
Visualizing the inverse relationship can be done by picturing a syringe: as you push the plunger (decreasing volume), the resistance you feel increases because the pressure inside goes up, making it harder to push.
Boyle's Law in Action
This concept is not just academic; it's used in designing equipment like bicycle pumps, hydraulic brakes, and even in understanding how our lungs work when we breathe in and out. Every time you take a breath, Boyle's Law is put into action as the volume of your lungs changes to facilitate air movement.
Chemistry Education
Chemistry education focuses on the dissemination and understanding of chemical knowledge. It's not just about memorizing formulas and reactions; it's about developing a deeper understanding of the natural world and the properties that govern it.
Modern chemistry education utilizes a variety of methods to enhance learning. Hands-on experiments, simulations, and visual aids are all tools that can make abstract concepts like Boyle's Law more tangible.
By encouraging students to understand the 'why' behind the 'what', educators can foster a deeper appreciation and comprehension of chemistry. This approach assists in developing critical thinking and problem-solving skills, which are invaluable not just in science but in everyday life situations.
Teaching Methodologies
Modern chemistry education utilizes a variety of methods to enhance learning. Hands-on experiments, simulations, and visual aids are all tools that can make abstract concepts like Boyle's Law more tangible.
Importance of Conceptual Learning
By encouraging students to understand the 'why' behind the 'what', educators can foster a deeper appreciation and comprehension of chemistry. This approach assists in developing critical thinking and problem-solving skills, which are invaluable not just in science but in everyday life situations.
Ideal Gas Equation
The Ideal Gas Equation, expressed as PV=nRT, is a cornerstone of gas law that provides a more comprehensive description of a gas's state by incorporating its temperature and the amount of gas (number of moles).
Boyle's Law is beautifully integrated into the Ideal Gas Equation as one part of a larger picture. If the number of moles (n) and temperature (T) are constant, this vital equation simplifies to Boyle's Law.
While the Ideal Gas Equation applies to hypothetical 'ideal' gases, it often serves as an excellent approximation for real gases under a range of conditions. However, at high pressures or low temperatures, real gases deviate from ideal behavior, and that's where other more complex models come into play. Understanding these deviations is crucial for advanced study in thermodynamics and material science.
Integration of Variables
Boyle's Law is beautifully integrated into the Ideal Gas Equation as one part of a larger picture. If the number of moles (n) and temperature (T) are constant, this vital equation simplifies to Boyle's Law.
Versatility and Limitations
While the Ideal Gas Equation applies to hypothetical 'ideal' gases, it often serves as an excellent approximation for real gases under a range of conditions. However, at high pressures or low temperatures, real gases deviate from ideal behavior, and that's where other more complex models come into play. Understanding these deviations is crucial for advanced study in thermodynamics and material science.
