Chapter 8: Problem 50
The use of CFCs as refrigerants and propellants in aerosol cans has been discontinued as a result of concerns about the ozone layer. If an aerosol can contained \(350 \mathrm{~mL}\) of CFC gas at a pressure of \(5.0 \times 10^{5} \mathrm{~Pa}\), what volume would this gas occupy at \(101,325 \mathrm{~Pa}\) ?
Short Answer
Step by step solution
Identify the Gas Law
Assign Known Values
Boyle's Law Rearrangement
Substitute Known Values and Calculate
Conclusion
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
CFCs and ozone layer
The ozone layer plays a crucial role in protecting life on Earth by absorbing harmful ultraviolet (UV) radiation from the sun. When CFCs are released into the atmosphere, they eventually rise up to the stratosphere, where solar radiation breaks them down, releasing chlorine atoms. These chlorine atoms are highly reactive and can destroy ozone molecules through a catalytic cycle.
The widespread depletion of ozone can lead to increased UV radiation reaching the Earth's surface, resulting in higher risks of skin cancer, eye cataracts, and harm to various ecosystems. Due to these adverse effects, the use of CFCs has been largely phased out under global agreements such as the Montreal Protocol.
gas volume calculation
For the calculation at hand, Boyle’s Law is a perfect fit. It states that for a constant temperature, the product of a gas's initial pressure and volume is equal to the product of its final pressure and volume. In simpler terms, if the pressure on a gas increases, its volume decreases, provided the temperature remains constant, and vice versa.
To determine the new volume of gas when the pressure changes, we rearrange Boyle’s Law formula:
- Identify initial states: initial pressure (\( P_1 \)) and initial volume (\( V_1 \)).
- Identify final pressure (\( P_2 \)) and calculate the new volume (\( V_2 \)).
- The formula is rearranged as: \[ V_2 = \frac{P_1 V_1}{P_2} \]
pressure-volume relationship
This means that if you increase the pressure exerted on a gas, its volume decreases if the temperature is kept constant. Conversely, decreasing the pressure means allowing the gas volume to expand. This principle is visually represented by the hyperbolic curve on a graph of pressure versus volume.
Understanding this relationship is essential not only in lab settings but also in everyday life. For instance, it explains how air pressure in vehicle tires affects their volume, ensuring they perform correctly. Additionally, in the field of meteorology, the principles of pressure and volume help explain atmospheric dynamics.
Being familiar with these concepts enables one to solve real-world and theoretical problems involving gas behavior confidently, using relationships like \( P_1 V_1 = P_2 V_2 \). The process reinforces the idea that an increase in one variable results in a decrease in the other, emphasizing their inversely proportional link.