Vapour Pressure

Vapour pressure or equilibrium vapour pressure is defined as the pressure exerted by a vapour in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The vapour pressure equilibrium expresses the rate of evaporation of a liquid. It is the tendency of the particles to escape the solid or the liquid state into the gaseous state. Thus the more the vapour pressure of a liquid or a solid at normal temperature, the more volatile the substance is. Thus, the vapour pressure can be alternatively expressed as the pressure exerted by the vapour over the surface of the liquid. It is because as the temperature increases, the kinetic energy in the molecules also increases that will, in turn, raise the molecules transitioning between the liquid or the solid surface to the vapour phase and therefore the vapour pressure also increases accordingly. 

According to the Clausius–Clapeyron relation, the vapour pressure of any substance increases non-linearly with the increase in temperature. The vapour pressure boiling point which is also referred to as the normal boiling point is the point where the ambient atmospheric pressure becomes equal with the vapour pressure. When the temperature increases, the vapour pressure eventually surpasses the atmospheric pressure and creates vapour bubbles inside the bulk of the substance. To form the bubble deeper into the bulk of the substance requires a higher temperature due to higher fluid pressure as the vapour pressure can overcome the ambient atmospheric pressure when there is an increase in the depth. Moreover, in the shallow depths, a very high temperature is required to start the bubble formation in the bulk of the substance. The surface tension of the bubble wall creates overpressure in the initial bubbles that are very small in size.

Now the partial pressure can be defined as the vapour pressure that a single component in the mixture is contributing to the total vapour pressure of the mixture as a whole. The example of vapour pressure and partial pressure is the vapour pressure by the air at the sea level and saturated with water vapour at 20 °C has partial pressures of about 2.3 kPa of water, 78 kPa of nitrogen, 21 kPa of oxygen and 0.9 kPa of argon, totalling 102.2 kPa creating the base for the standard atm pressure. The standard unit of pressure is the measurement of vapour pressure. The SI unit of pressure is Pascal (Pa) where One pascal is one newton per square meter (N·m-2 or kg·m-1·s-2).

The relation between the vapour pressure and the temperature of the pure liquid or solid substance according to the  Antoine equation is as follows:

Log P = A - [B / (C +  T)]

It can be converted into the temperature explicit form as:

T = [B / (A - log P)] - C

Where,

A, B, C are the  substance-specific coefficients (i.e., constants or parameters)

P is the absolute vapour pressure of a substance

T is the temperature of the substance

The log is typically either log10 or loge

Reid Vapour Pressure

Reid vapour pressure which is commonly abbreviated as RVP is a common measurement of the volatility of gasoline and other petroleum products. It is defined as the absolute vapour pressure exerted by the vapour of the liquid and any dissolved gases/moisture at 37.8 °C (100 °F). This method is known as the test method ASTM-D-32 which was developed for the first time in the year 1930 and has been revised many times since then. The vapour pressure of gasoline, volatile crude oil, jet fuels, naphtha, and other volatile petroleum products are measured by this test method but liquefied petroleum gases are not included in this test method. It is because this test method requires the liquid to be chilled at 0 to 1-degree Celsius and then poured into the apparatus but any liquid that solidifies at this temperature is not applicable for the test method. The SI unit of Reid vapour pressure is kilopascal (KPa) or it is expressed in pounds per square inch (psi). It measures the volatilization of the liquid at the vapour pressure as the test method determines the gauge pressure of the sample in a non-evacuated chamber.

The Reid vapour pressure differs from the true vapour pressure in the following subsequent ways:

Vapour Pressure of water

Vapour pressure of water is the pressure exerted by the molecules of the water vapour in the gaseous state which can either be in the pure form or in the form of a mixture of other gases such as air. The saturation vapour pressure is the pressure of the water vapour that is in the thermodynamics equilibrium with its condensed state. When the atmospheric pressure is higher than the vapour pressure, the water condenses while when the atmospheric pressure is lower than the vapour pressure, the water starts subliming or boiling. The saturation vapour pressure can be determined by the Clausius–Clapeyron relation and increases with the increase in the temperature. When the saturation vapour pressure becomes equal to the ambient vapour pressure it becomes the boiling point of the water. Commonly the meteorology uses the calculation of the saturation water vapour. The boiling point of water and the pressure is inversely related to the temperature-vapour pressure. This explains both pressure cooking and cooking at higher altitudes. 

Some of the approximation formulae for the calculation of saturated vapour pressure over water and over ice is given below:

1. P = exp [20.386 - (5132 / T)]

Where P is vapour pressure at mmHg

T is the temperature in kelvin.

2. P = 0.61094 exp (17.625 T / T + 243.04)

Where, P is vapour pressure at kilopascal (KPa)

T is temperature in 0C.

3. .P = 0.61078 exp (17.27 T / T + 273.3)

Where, P is vapour pressure at kilopascal (KPa)

T is temperature in 0C.

4. P = 0.61121 exp [(18.67 - (T / 234.5) ) (T / 275.14 + T)]

Where, P is vapour pressure at kilopascal (KPa)

T is temperature in  0C.

Similarly, the vapour pressure of methanol at 250 C is 94 torr or 12.5323 KPa and the vapour pressure of ethanol is 44 torr or 5.86 Kpa at 250 C

Vapour Pressure and Boiling Point Equation

The Clausius-Clapeyron equation describes the equation between the vapour pressure. The different function of the vapour pressure with respect to the variation in the boiling point uses the Clausius-Clapeyron equation. The boiling point of a substance is inversely proportional to the increase in the boiling point and vice-versa. 

Thus the Clausius-Clapeyron equation is derived from the following equation that incorporates two different temperatures. 

VP2 = VP1e-△ (Hv / RT)

Thus the classic form is:-

ln(P1/P2)=Hvap/R(1/T2 – 1/T1)

Where P1 and P2 are the vapour pressures

T1 and T2 are the temperatures

Hvap is that the Enthalpy (heat) of Vaporization and

R is the universal gas constant (8.3145 J mol^-1 K^-1).