Step 1: Understanding the Concept:
Vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.
At the microscopic level, molecules in a liquid are in constant motion, possessing a distribution of kinetic energies.
Evaporation occurs when molecules at the surface possess enough kinetic energy to overcome the attractive intermolecular forces holding them in the liquid phase.
In a closed container, these escaped molecules exert pressure on the walls of the container and the surface of the liquid.
Eventually, the rate of evaporation equals the rate of condensation, establishing a dynamic equilibrium.
Step 2: Detailed Explanation:
The relationship between temperature and vapor pressure is rooted in the Kinetic Molecular Theory.
According to the Maxwell-Boltzmann distribution, as the temperature of a liquid increases, the average kinetic energy of the molecules increases.
\[ K.E._{avg} = \frac{3}{2}kT \]
Where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature.
As the temperature rises, the energy distribution curve shifts to the right, meaning a larger fraction of molecules acquires sufficient energy (activation energy for vaporization) to break free from the intermolecular attractions.
This leads to a higher rate of evaporation and, consequently, a higher concentration of molecules in the gas phase.
According to the ideal gas law \( P = \frac{nRT}{V} \), an increase in the number of moles of vapor (\( n \)) and the temperature (\( T \)) leads to a significant increase in pressure (\( P \)).
Mathematically, this relationship is expressed by the Clausius-Clapeyron equation:
\[ \ln(P) = -\frac{\Delta H_{vap}}{RT} + C \]
This equation shows that the logarithm of vapor pressure is inversely proportional to the reciprocal of temperature, meaning \( P \) grows exponentially as \( T \) increases.
Step 3: Analyzing Options:
(1) Incorrect: Kinetic theory proves that higher heat leads to higher molecular escape, not lower.
(2) Incorrect: Vapor pressure is highly sensitive to thermal changes.
(3) Correct: Increased thermal energy directly correlates to increased molecular density in the vapor phase.
(4) Incorrect: As temperature increases toward the critical point, vapor pressure increases drastically until the distinction between liquid and gas disappears.
Step 4: Final Answer:
Vapor pressure increases with increase in temperature because more molecules gain the required energy to enter the gaseous state.