Kinetic Molecular Theory of Gases
The Kinetic Molecular Theory (KMT) provides a microscopic model to explain the macroscopic behavior of gases. Its core postulates include:
- Particle Size: Gases consist of a large number of particles that are in constant, random motion.
- Volume: The actual volume of gas particles is negligible compared to the total volume of the gas.
- Intermolecular Forces: There are no attractive or repulsive forces between gas particles.
- Collisions: Collisions between particles and with container walls are perfectly elastic (no energy is lost).
- Temperature: The average kinetic energy of gas particles is directly proportional to the absolute temperature (Kelvin).
Ideal vs. Real Gases
- Ideal Gas: Obeys the ideal gas law ($PV = nRT$) under all conditions. Assumes zero molecular volume and no intermolecular forces.
- Real Gas: Deviates from ideal behavior at high pressures and low temperatures. Accounts for molecular volume and inter-particle attractions (modeled by the Van der Waals equation).
Step-by-Step Problem Solution
Given:
- Mass of empty vessel = $50\text{ g}$
- Mass of vessel + liquid = $148\text{ g}$
- Density of liquid = $0.98\text{ g/cc}$
- Mass of vessel + gas = $50.5\text{ g}$
- Pressure ($P_1$) = $760\text{ mm Hg} = 1\text{ atm}$
- Temperature ($T_1$) = $27^\circ\text{C} = 300\text{ K}$
1. Determine Vessel Volume
Since the liquid fills the vessel, $V = \frac{\text{Mass of liquid}}{\text{Density}} = \frac{148 - 50}{0.98} = \frac{98}{0.98} = 100\text{ mL} = 0.1\text{ L}$.
2. Calculate Volume at STP
STP is $P_2 = 1\text{ atm}$, $T_2 = 273.15\text{ K}$. Using the Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
$V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1}$ $V_2 = 0.1\text{ L} \times \frac{1\text{ atm}}{1\text{ atm}} \times \frac{273.15\text{ K}}{300\text{ K}}$ $V_2 = 0.1 \times 0.9105 = 0.09105\text{ L} \approx 91.05\text{ mL}$.