What is the relationship between boiling point and vapour pressure?

The relationship between boiling point and vapor pressure is a fundamental concept in thermodynamics and the behavior of liquids.

Boiling Point:

The boiling point of a substance is the temperature at which its vapor pressure equals the atmospheric pressure or the external pressure applied to the liquid.
When you heat a liquid, its molecules gain energy and move more rapidly. Eventually, at the boiling point, enough molecules have sufficient energy to overcome the attractive forces holding them in the liquid phase, and they escape into the gas phase.
Vapor Pressure:

Vapor pressure is the pressure exerted by the vapor (gas phase) molecules of a substance when it is in equilibrium with its liquid phase at a given temperature.
At any temperature, some molecules in the liquid phase have enough kinetic energy to escape into the vapor phase. The vapor pressure is the result of the dynamic equilibrium between the rate of molecules leaving the liquid phase and the rate of molecules returning to it.
Vapor pressure increases with temperature because higher temperatures provide more energy to the liquid molecules, allowing more of them to transition into the vapor phase.
The key relationship between boiling point and vapor pressure is as follows:

As the temperature of a liquid increases, its vapor pressure also increases.
At the boiling point, the vapor pressure equals the external pressure (usually atmospheric pressure). This is why a liquid boils at a specific temperature; further heating does not increase its temperature until all of the liquid has converted to vapor.
In summary, the boiling point of a substance is the temperature at which its vapor pressure matches the external pressure, allowing the substance to transition from the liquid phase to the gas phase. Increasing temperature increases vapor pressure, and when it reaches the boiling point, the liquid boils and turns into a gas.