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:**
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?
**Solution:**
To find the total pressure of the system, we can use the Ideal Gas Law equation:
\[ PV = nRT \]
Where:
- \( P \) is the pressure in atm
- \( V \) is the volume in liters
- \( n \) is the number of moles of gas
- \( R \) is the ideal gas constant (0.0821 L·atm·K⁻¹·mol⁻¹)
- \( T \) is the temperature in Kelvin
We need to find the total number of moles (\( n \)) of both gases in the mixture.
**Step 1: Calculate the number of moles of CH₄**
Molecular weight of CH₄ (Methane) = 12.01 (Carbon) + 4 × 1.01 (Hydrogen) = 16.05 g/mol
Number of moles of CH₄ = \(\frac{32.0 \text{ g}}{16.05 \text{ g/mol}} \approx 1.993 \text{ mol}\)
**Step 2: Calculate the number of moles of C₂H₆**
Molecular weight of C₂H₆ (Ethane) = 2 × 12.01 (Carbon) + 6 × 1.01 (Hydrogen) = 30.07 g/mol
Number of moles of C₂H₆ = \(\frac{15.0 \text{ g}}{30.07 \text{ g/mol}} \approx 0.499 \text{ mol}\)
**Step 3: Find the total number of moles**
Total moles (\( n_T \)) = moles of CH₄ + moles of C₂H₆
\[ n_T = 1.993 \text{ mol} + 0.499 \text{ mol} \approx 2.492 \text{ mol} \]
**Step 4: Convert the temperature to Kelvin**
\[ T = 19°C + 273.15 = 292.15 \text{ K} \]
**Step 5: Use the Ideal Gas Law](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F700c4a60-c23b-4831-bc86-570cd868908f%2F9d1b5b16-c758-49d6-9766-4d3e1c22da6c%2Fxqi8xx_processed.jpeg&w=3840&q=75)
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