A 3.4 L closed container filled with helium gas at 80.4°C and 1.32 atm is cooled to 34.0°C. The container contracts to a final volume of 2.7 L. What is the final pressure of the gas? 6.
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.
![### Problem Statement
**Question 6:**
A 3.4 L closed container filled with helium gas at 80.4°C and 1.32 atm is cooled to 34.0°C. The container contracts to a final volume of 2.7 L. What is the final pressure of the gas?
### Solution Approach
To solve this problem, you need to use the Combined Gas Law, which expresses the relationship between pressure, volume, and temperature for a fixed amount of gas:
\[ \frac{P_1 \cdot V_1}{T_1} = \frac{P_2 \cdot V_2}{T_2} \]
Where:
- \(P_1\) = Initial pressure = 1.32 atm
- \(V_1\) = Initial volume = 3.4 L
- \(T_1\) = Initial temperature = (80.4 + 273.15) K = 353.55 K
- \(P_2\) = Final pressure (unknown)
- \(V_2\) = Final volume = 2.7 L
- \(T_2\) = Final temperature = (34.0 + 273.15) K = 307.15 K
Rearranging the formula to solve for \(P_2\):
\[ P_2 = \frac{P_1 \cdot V_1 \cdot T_2}{T_1 \cdot V_2} \]
Substituting in the known values:
\[ P_2 = \frac{1.32 \, \text{atm} \cdot 3.4 \, \text{L} \cdot 307.15 \, \text{K}}{353.55 \, \text{K} \cdot 2.7 \, \text{L}} \]
### Calculation
\[ P_2 \approx \frac{1.32 \cdot 3.4 \cdot 307.15}{353.55 \cdot 2.7} \]
### Final Answer
After performing the above calculation, you will find the final pressure \(P_2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5387081-05af-4c61-b379-73a2f6a67bdc%2F2a012cfb-03dc-4a72-b83a-e6281fd526bb%2Fhjelwwo_processed.jpeg&w=3840&q=75)
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