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.
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### Understanding Gas Behavior: Ideal Gas Conditions and Calculations
#### Problem Statement
**2)** Consider a 12.0 L container filled with Argon (Ar) gas. The pressure of this container is 3.50 atm when it is at room temperature (298 K).
**a.** What is the ideal gas law? Define each variable.
**b.** If the gas is behaving as an ideal gas, how many moles of Ar are present in the container?
**c.** If the temperature of the gas in the container is raised to 410 K but the volume remains constant, what is the new pressure of the gas?
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#### Solution
**a. Ideal Gas Law**
The Ideal Gas Law is expressed as:
\[ PV = nRT \]
Where:
- \( P \) = Pressure of the gas (atm)
- \( V \) = Volume of the gas (L)
- \( n \) = Number of moles of gas
- \( R \) = Ideal gas constant (0.0821 L·atm/mol·K)
- \( T \) = Temperature of the gas (K)
**b. Calculate the Number of Moles of Argon (Ar)**
Given:
- Pressure (\( P \)) = 3.50 atm
- Volume (\( V \)) = 12.0 L
- Temperature (\( T \)) = 298 K
- Ideal Gas Constant (\( R \)) = 0.0821 L·atm/mol·K
To find the number of moles (\( n \)), rearrange the ideal gas law equation:
\[ n = \frac{PV}{RT} \]
Substitute the known values:
\[ n = \frac{(3.50 \, \text{atm}) \times (12.0 \, \text{L})}{(0.0821 \, \text{L·atm/mol·K}) \times (298 \, \text{K})} \]
\[ n \approx 1.71 \, \text{moles of Ar} \]
**c. Calculate the New Pressure at 410 K**
Since volume is constant, use the formula:
\[ \frac{P_1}{T_1} = \frac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4135d71c-aee1-4e76-ad8d-862c86d61623%2F6d06d6d1-69ed-4e1a-a4dd-adc3891102eb%2Fgn50ymw_processed.jpeg&w=3840&q=75)
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