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: Calculating Total Pressure of a Gas Mixture
#### Problem Statement:
A 10.0 L container at 19°C contains 32.0 g of CH₄ and 15.0 g of C₂H₆. What is the total pressure of the system?
**Given:**
- Volume (V) = 10.0 L
- Temperature (T) = 19°C (which needs to be converted to Kelvin)
- Mass of CH₄ = 32.0 g
- Mass of C₂H₆ = 15.0 g
**To Find:**
- Total pressure of the system (P_T) in atm
The ideal gas law equation will be used for this calculation, which is given by:
\[ PV = nRT \]
Where:
- \( P \) is pressure,
- \( V \) is volume,
- \( n \) is the number of moles,
- \( R \) is the ideal gas constant (\( R = 0.0821 \, \text{L·atm·K}^{-1}\text{·mol}^{-1} \)),
- \( T \) is temperature in Kelvin.
To calculate the total pressure, first find the moles of each gas (CH₄ and C₂H₆) using their respective molar masses.
#### Steps:
1. **Convert temperature to Kelvin:**
\[ T(K) = T(°C) + 273.15 \]
\[ T = 19 + 273.15 = 292.15 \, \text{K} \]
2. **Calculate moles of CH₄:**
\[ \text{Molar mass of CH₄} = 12.01 (\text{C}) + 4 \times 1.01 (\text{H}) = 16.05 \, \text{g/mol} \]
\[ n_{\text{CH4}} = \frac{\text{Mass of CH₄}}{\text{Molar mass of CH₄}} = \frac{32.0 \, \text{g}}{16.05 \, \text{g/mol}} = 1.993 \, \text{mol} \]
3. **Calculate moles of C₂H₆:**
\[ \text{Molar mass of C₂H₆} = 2 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a6c8a3a-a03f-49e8-8199-eeea6dc66d27%2Ffc567c1c-02ac-4a47-a405-128c898823e9%2Fwzp51kr_processed.jpeg&w=3840&q=75)
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