1. People buying food in sealed bags at high elevation often notice that the bags are puffed up because the air inside has expanded. A bag of pretzels was packed at a pressure of 1.00 atm and a temperature of 22.0 °C. When opened at a summer picnic in Santa Fe, New Mexico, at a temperature of 32.0 °C, the volume of air in the bag is 1.33 times its original volume. What is the pressure of the Santa Fe? air P P Santa Fe = atm
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![### Real-World Applications of Gas Laws: High Elevation and Sealed Food Bags
#### Understanding Pressure Changes in Sealed Bags
When people purchase food in sealed bags at high elevations, they often observe that the bags are puffed up. This phenomenon occurs because the air inside the bags expands due to changes in atmospheric conditions.
Consider the following example to understand this better:
A bag of pretzels was packed at sea level with the following conditions:
- **Pressure (P₁):** 1.00 atm
- **Temperature (T₁):** 22.0°C
When the bag is later opened at a summer picnic in Santa Fe, New Mexico, new conditions are observed:
- **Temperature (T₂):** 32.0°C
- **Volume (V₂):** 1.33 times the original volume (V₁)
### Question:
What is the pressure of the air (\( P_{\text{Santa Fe}} \)) inside the bag after it expands?
### Formula:
To find the final pressure (\( P_{\text{Santa Fe}} \)), we can use the combined gas law:
\[ \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2} \]
Given parameters:
- **P₁ = 1.00 atm**
- **V₁ = Initial volume**
- **T₁ = 22.0°C** (converted to Kelvin: 22.0 + 273.15 = 295.15 K)
- **V₂ = 1.33 V₁**
- **T₂ = 32.0°C** (converted to Kelvin: 32.0 + 273.15 = 305.15 K)
- **P₂ = \( P_{\text{Santa Fe}} \)**
Substitute these values into the equation, solving for \( P_{\text{Santa Fe}} \):
\[ \frac{1.00 \, \text{atm} \times V₁}{295.15 \, \text{K}} = \frac{P_{\text{Santa Fe}} \times 1.33 V₁}{305.15 \, \text{K}} \]
By cancelling \( V₁ \) from both sides and solving for \( P_{\text{Santa Fe}} \):
\[ P_{\text{Santa](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f42db7f-5d63-42d4-89b9-bc5373ca5a94%2F83f15e0d-58c9-4131-a68a-221eb977cd65%2Fom1l2p_processed.jpeg&w=3840&q=75)
Step by step
Solved in 3 steps with 2 images
