Consider the apparatus shown below in which the valve is closed. If the temperature is kept constant and the valve opened, what will be the pressure inside the apparatus? H₂ Vacuum Valve 9.00 L 3.00 L 1.00 atm 0.250 atm 1.00 atm 0.500 atm cannot be determined
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.
**Details of the Apparatus:**
- **H₂ Container:** 3.00 L, 1.00 atm
- **Vacuum Chamber:** 9.00 L, initially at 0.00 atm (since it’s a vacuum)
**Answer Choices:**
- ⓐ 0.250 atm
- ⓑ 1.00 atm
- ⓒ 0.500 atm
- ⓓ cannot be determined
**Solution Explanation:**
To determine the final pressure inside the combined apparatus, apply the principle of conservation of mass (moles of gas) and Boyle’s Law:
Boyle’s Law states: \( P_1V_1 = P_2V_2 \)
Here:
- Initial Pressure, \( P_1 \) = 1.00 atm
- Initial Volume, \( V_1 \) = 3.00 L
- Final Volume, \( V_2 \) = (3.00 L + 9.00 L) = 12.00 L
- Final Pressure, \( P_2 \) = ?
Using the formula:
\[ P_1 \times V_1 = P_2 \times V_2 \]
\[ 1.00 \, \text{atm} \times 3.00 \, \text{L} = P_2 \times 12.00 \, \text{L} \]
\[ P_2 = \frac{1.00 \, \text{atm} \times 3.00 \, \text{L}}{12.00 \, \text{L}} \]
\[ P_2 = 0.250 \, \text{atm} \]
**Correct Answer: ⓐ 0.250 atm**
### Conclusion
Opening the valve allows the hydrogen gas](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2F4d01a0e2-f81b-41e0-91c6-e3d084ac00dc%2Fk9t2i09_processed.png&w=3840&q=75)
Step by step
Solved in 4 steps
