A liquid is in equilibrium with its vapour at its boiling point. On average, the molecules in the two phases have equal

Options

A. inter-molecular forces
B. potential energy
C. total energy
D. kinetic energy

Answer

To solve the question, we need to analyze the relationship between the liquid and its vapor at the boiling point. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Boiling Point
At the boiling point, a liquid is in equilibrium with its vapor. This means that the rate of evaporation of the liquid equals the rate of condensation of the vapor.

**Hint:** Remember that boiling occurs when the vapor pressure of the liquid equals the atmospheric pressure.

### Step 2: Apply the Kinetic Theory of Gases
According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the temperature of the system. The formula for the average kinetic energy (KE) of gas molecules is given by:

\[ KE = \frac{3}{2} k_B T \]

where \( k_B \) is the Boltzmann constant and \( T \) is the absolute temperature.

**Hint:** Kinetic energy is a measure of the energy of motion of the molecules.

### Step 3: Relate Temperature to Kinetic Energy
Since the boiling point is a specific temperature at which the liquid and vapor are in equilibrium, we can conclude that both phases (liquid and vapor) are at the same temperature at the boiling point.

**Hint:** Equilibrium at boiling point means both phases have the same temperature.

### Step 4: Conclude About Kinetic Energy
Because the average kinetic energy of molecules is directly proportional to the temperature, if both the liquid and vapor are at the same temperature, they must also have the same average kinetic energy.

**Hint:** Kinetic energy equality is a direct consequence of temperature equality.

### Final Answer
Thus, the molecules in the two phases (liquid and vapor) at the boiling point have equal **kinetic energy**.