# why do we obtain a sigmoid curve in vapour pressure versus temperature graph

i have recently got a question in an assignment, which was somewhat like this

what would be the shape of curve obtained in a graph between vapour pressure & temperature of a binary solution in a closed vessel

generally we do all the experiments regarding vapour pressure in a closed vessel, so the volume must remain constant and from the formula $PV=nRT$, the number of moles remains constant in a binary solution, as volume is remaining constant we get the equation as $Y=mX$, which is a straight line passing through the origin, but the answer was a sigmoid curve, how did we get that, can i get an elaborate answer for this quiery.

the answer already present over here is absolutely excellent but, as an extention i would add some points to it

the equation of $PV=nRT$ is made for gases and for a solution of gas and liquid in which the volatile solvent shows some vapour pressure on its solution

the curve sigmoid curve you get is through the Clausius Clapeyron equation which suits this condition [i.e. the situation of solutions]

after the whole solution is evaporated then you get pure solvent in the vapour phase after which your equation for an ideal gas $PV=nRT$ is applicable and you will get a striaght line there after

Above is a graph of the Maxwell Boltzmann distribution at several temperatures. Imagine a point on the x axis being the point at which a liquid particle has enough kinetic energy to leave the solution. As you can see, each increase in temperature results in a larger number of particles with enough energy to vaporize. This generates an exponential graph for VP vs T. However, eventually you reach the point where all of the liquid has reached the gas phase. Then you have a linear graph of P vs T.

• can i get the equation from which you've got this graph Aug 13 '14 at 17:06
• The graph is a generic Maxwell Boltzmann distribution. Look up the Clausius Clapeyron equation. It gives the vapor pressure vs temperature for a given enthalpy of vaporization. Aug 13 '14 at 17:21
• but where did my concept of the equation of $Y=mX$ went wrong could you please explain it Aug 13 '14 at 17:23
• The graph is not linear while there is still liquid present. Every successive unit of energy added by increasing temperature results in more particles having enough energy to vaporize. Look at the v in the word velocity on the graph. What is the area under the red curve vs the blue curve. A doubling in T more than doubled the number of particles in the vapor phase. Aug 13 '14 at 17:54
• yes now the thing stuck my mind, anyway thanks for your assistance Aug 13 '14 at 17:56