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.
![### Educational Content: Gas Properties Problems
#### Problem 3 (13.29)
**Question:**
What is the pressure inside a 38.0-L container holding 105.0 kg of argon gas at 21.6°C?
**Explanation:**
To solve this problem, you will need to use the Ideal Gas Law:
\[ PV = nRT \]
Where:
- \(P\) = Pressure (in atmospheres, atm or Pascals, Pa)
- \(V\) = Volume (in Liters, L)
- \(n\) = Number of moles of gas
- \(R\) = Ideal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K))
- \(T\) = Temperature (in Kelvin, K). Note: 21.6°C needs to be converted to Kelvin.
#### Problem 4 (13.49)
**Question:**
If the pressure in a gas is tripled while its volume is held constant, by what factor does \(v_{\text{rms}}\) change?
**Explanation:**
The root mean square speed (\(v_{\text{rms}}\)) of gas molecules is given by:
\[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \]
or for an ideal gas,
\[ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \]
Where:
- \(v_{\text{rms}}\) = Root mean square speed of the gas molecules
- \(k\) = Boltzmann constant
- \(T\) = Temperature in Kelvins
- \(m\) = Mass of a gas molecule
- \(R\) = Ideal gas constant
- \(M\) = Molar mass of the gas
When pressure is tripled and volume is constant, according to the Ideal Gas Law (\(PV = nRT\)), the temperature must also triple. Consequently, the factor change in \(v_{\text{rms}}\) can be deduced considering this relationship.
**Note:**
For detailed numerical solutions to these problems, students should perform the appropriate calculations using the indicated formulas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F529e4fe6-e8c4-4722-88aa-75bc8f350b68%2F78ff8099-aadb-4b66-9b87-7728be5d5db4%2Fwpyaecl_processed.jpeg&w=3840&q=75)
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