The stopcock connecting a l.13 L bulb containing xenon gas at a pressure of 5.08 atm, and a 4.71 L bulb containing krypton gas at a pressure of 1.31 atm, is opened and the gases are allowed to mix. Assuming that the temperature remains constant, the final pressure in the system is 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.
![### Gas Laws and Mixing Gases: A Practical Application
**Problem Statement**:
The stopcock connecting a 1.13 L bulb containing xenon gas at a pressure of 5.08 atm, and a 4.71 L bulb containing krypton gas at a pressure of 1.31 atm, is opened and the gases are allowed to mix. Assuming that the temperature remains constant, the final pressure in the system is ______ atm.
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**Explanation**:
To find the final pressure in the system after the gases have been allowed to mix, we can use the combined gas law. Since the temperature remains constant, we can apply Dalton's Law of Partial Pressures. Dalton's Law states:
\[ P_{final} = \frac{(P_1 \times V_1) + (P_2 \times V_2)}{V_{total}} \]
Where:
- \( P_1 \) and \( V_1 \) are the initial pressure and volume of xenon gas
- \( P_2 \) and \( V_2 \) are the initial pressure and volume of krypton gas
- \( V_{total} \) is the total volume of the mixed gases
**Given Data**:
- \( P_1 \) (Xenon gas pressure) = 5.08 atm
- \( V_1 \) (Xenon gas volume) = 1.13 L
- \( P_2 \) (Krypton gas pressure) = 1.31 atm
- \( V_2 \) (Krypton gas volume) = 4.71 L
- \( V_{total} \) = \( V_1 + V_2 \) = 1.13 L + 4.71 L = 5.84 L
**Calculation**:
\[ P_{final} = \frac{(5.08 \times 1.13) + (1.31 \times 4.71)}{5.84} \]
Let's compute the values:
\[ P_{final} = \frac{(5.7404) + (6.1701)}{5.84} \]
\[ P_{final} = \frac{11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9bc6dc7-2424-4f69-956a-285f3752d785%2Fb95be550-ff19-4005-ad3c-08ab81b9481e%2Ftd31d2vm_processed.jpeg&w=3840&q=75)
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