The pressure of a sample of argon gas was increased from 2.59 atm to 7.43 atm at constant temperature. If the final volume of the argon sample was 11.9 L, what was the initial volume of the argon sample? Assume ideal behavior. L V =
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:**
The pressure of a sample of argon gas was increased from 2.59 atm to 7.43 atm at constant temperature. If the final volume of the argon sample was 11.9 L, what was the initial volume of the argon sample? Assume ideal behavior.
**Solution:**
To solve this problem, we can apply Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is held constant. Mathematically, Boyle's Law is expressed as:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) is the initial pressure
- \( V_1 \) is the initial volume
- \( P_2 \) is the final pressure
- \( V_2 \) is the final volume
Given:
- \( P_1 = 2.59 \) atm
- \( P_2 = 7.43 \) atm
- \( V_2 = 11.9 \) L
We need to find \( V_1 \).
Rearranging Boyle's Law to solve for \( V_1 \):
\[ V_1 = \frac{P_2 \times V_2}{P_1} \]
Substitute in the given values:
\[ V_1 = \frac{7.43 \text{ atm} \times 11.9 \text{ L}}{2.59 \text{ atm}} \]
\[ V_1 = \frac{88.417}{2.59} \]
\[ V_1 \approx 34.14 \text{ L} \]
So, the initial volume of the argon sample was approximately 34.14 L.
### **Conclusion:**
The above steps and calculations demonstrate that by applying Boyle's Law, we can determine that the initial volume of the argon sample was about 34.14 liters, provided that the gas behaves ideally.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21c88a28-f807-464d-9079-e9051da21a49%2F074e4436-cb0b-4029-97ff-f4e6e410ca3f%2Fvpjnpwa_processed.jpeg&w=3840&q=75)
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