# 3 Vapor Pressure And Temperature Graph: Several Graphs And Insights

The vapor pressure measures the quantity of the vapors present in the system under consideration.

As the temperature rises, more and more vapors are escaped from the molecular attractive forces from the liquid phase into the gaseous state thus raising the vapor pressure. The vapor pressure and temperature graph give an idea about the number of molecules turned into the gaseous form.

## Saturation Vapor Pressure vs Temperature Graph

Every liquid has a specific boiling point depending upon the chemical composition and the number of hydrogen bonding. Above the boiling point, the temperature of the liquid does not rise but the phase of the liquid is turned into the gaseous state.

The vapor pressure is in corresponds to the temperature or the heat energy given out by the evaporation of vapors. The temperature of the liquid rises up to the boiling point of the liquid and thus the vapor pressure above the surface of the boiling liquid is maintained constant this is called the saturation vapor pressure.

If we look at the above graph of vapour pressure v/s the temperature, TF is a temperature at which the liquid starts boiling. At this temperature, the temperature of the liquid does not rise further and the vapour pressure increases at a certain value and gets saturated, this length of the curve is denoted as saturation of vapour pressure curve.

Once the temperature of the liquid reaches the boiling point, the heat energy grasped is turned into the kinetic energy and the molecules break the intermolecular bonds and evaporate from the liquid surface. But as the vapours evaporate, the heat energy of the vapour is given out and the vapour gets cool down and eventually condenses forming drops of liquid and flows down to the volume thus the number of vapors above the surface of the liquid remains fixed and hence we say that the vapour pressure saturates at the boiling point.

## Vapor Pressure vs Temperature Graph for Water

If you keep the volume of water for boiling and measure the variations in the vapor pressure above the level of the boiling water, you will notice that vapour pressure will increase exponentially with rising temperature.

Let us plot the graph for vapor pressure v/s temperature for water. The vapour pressure for every 100 C rise in temperature of the water from 00C to 1000C is noted until the boiling point of the water.

The graph of vapor pressure v/s temperature shows an exponential curve. At the freezing point of the water, the vapour pressure is 4.6 torr and the final vapor pressure which is also called the saturated vapor pressure as discussed above is 760 torr.

Beyond this vapor pressure at the boiling point of water, there is no further increase in the vapor pressure as the water vapors will condense and falls down due to gravity. Initially, at low temperature, as the amount of heat supplied to the water is less, very few vapors will be capable of escaping to the vapor form.

As the temperature of the water keeps rising, more and more molecules will break the bonds and escape into the atmosphere in the form of vapors depending on the temperature. Hence, the temperature of the water is directly proportional to the vapor pressure generated above the surface of the boiling water.

## How to Find Vapor Pressure From a Graph?

We have seen that the graph of vapour pressure v/s temperature shows exponential behaviour.

Thus, the slope of a graph of ln(P) v/s 1/T will give the value of the ratio of heat of vaporization and gas constant through which we can find the vapour pressure.

The exponential function of the vapour pressure v/s temperature graph we can formulate as

Where A is a constant related to the boiling point

R is a gas constant equal to 8.314 J/K.mol

is a heat of vaporisation of liquidP Solving this equation using logarithm, we get,

This is in the form of a linear equation,

Thus we can plot a graph of lnP v/s 1/T and the slop of the graph will give us the value of

The above graph also satisfies the Clausius – Clapeyron equation according to which, the temperature difference depends upon the vapour pressure of the system.

Upon finding the slope of this graph, we shall find the value of Inserting this value in equation (1), we can find the vapour pressure at any temperature of the liquid.

## What is the heat of vaporization of chloroform if the vapour pressure at 200C is 48 KPa and at -100C is 10 KPa?

Given: T1=-100C =-10+273=263K

T2=200C =20+273=293K

P1=10KPa

P2=48KPa

Using Claussius – Clapeyron equation

The heat of vaporisation of chloroform is 32.6k J/mol

## What is the vapour pressure at a temperature of 600C if the slope of a graph of ln(P) v/s inverse of temperature is found to be 360.8K? Also, find the heat of vaporization.

The slope of graph ln(P) v/s 1/T is

Hence,

T=600C= 60+273=333K

We have,

Thus the vapour pressure at a temperature of 600C is 2.95kPa.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122