# Capstone Project

Based on our chemistry knowledge, as the atmospheric pressure decrease, the boiling point would also decrease. As being said, why does this happen? How can the water molecules have enough energy to escape the hydrogen bond? Where does the energy come from?

In order to find out the reason, I did some research of the vapor pressure, which water vapor is in thermodynamic equilibrium with its condensed state. At higher pressures water would condense. The water vapor pressure is the partial pressure of water vapor in any gas mixture in equilibrium with solid or liquid water. As for other substances, water vapor pressure is a function of temperature and can be determined with Clausiusâ€“Clapeyron relation.

Derive it, get

R is the constant in the equation, which is 8.314 J/Kmol; deltaH is 40.68 is this case(Heat of vaporization of water). For convenience, I choose to pick temperature at 313K, and get 7.4KPa as the vapor pressure, which is T1 and P1 in the equation.

Explanation of equations:

1. Fnet = -Patmo(A) + Pvapor(A)

we know force = pressure * area. in this case, the area is just the area of the water molecule. then use this equation to find out the net force that made by the atmospheric pressure acting on the water molecule. in the normal condition, the net force should be zero, but under a lower temperature, the vapor pressure does not change and atmospheric pressure decrease, which results a negative number.

2. Pf = Pi + Fnet*(t)

After we figure out the net force, use p = f * t to find out the impulse. then plus the impulse already exist under the normal condition, and get a final value, which is the energy that the water molecules receive by the new atmospheric pressure

We know that the process of water molecule leaves the surface of water called evaporation.

While the water molecule at its boiling point, it would break its hydrogen bond, because the molecule absorbs enough Kinetic energy from heat, aka thermal energy.

Thus, we conclude that at when the atmospheric pressure is equal to the vapor pressure, water molecules would escape.

several screen shoots of computational module

at 373K, 101.3KPa

at 353K ,47.3KPa

at 333K, 19.9KPa

at 313K, 7.4KPa

we can see as the atmospheric pressure decrease,the molecules are more active, because the vapor pressure is always at a constant value, which means the temperature is always constant as well, thus, it's kinetic energy always stays the same. So if there is a decreasing number of force acting on the water molecule. Therefore, the molecules would have more energy as the atmospheric pressure decreases, while the atmospheric pressure is equal to vapor pressure, it would eventually escape the hydrogen bond.