Vapor Pressure Formula

Raoult’s law formula applies to substances mixed in a solution. This law was named after a French chemist named François-Marie Raoult after its establishment in the year 1887.

It states that a solvent’s partial vapor pressure in a mixture is equal to or identical to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution.

On this page, we will understand the above Taoult’s law formula along with the mole fraction in vapor phase formula and the relative lowering of vapor pressure formula.

Vapor Pressure Formula

Now, let’s understand how to calculate the vapor pressure? Well! For this, we have a vapor pressure formula, which is as follows:

From the above text, we understand that the vapor pressure increases with the increase in temperature. So, at higher temperatures, the energy is also increased.

We know that the pressure of the component is an increasing function of the temperature, so the equation is given as;

\[P \alpha\ exp (-\frac{\triangle H(vap)}{RT}) \]

Here,

∆HVap  =  the enthalpy of vapourization, calculated in Joule (J). 

R   =  Universal Gas Constant whose value is 8.314 JK-1mol-1.

Let’s suppose that P1 and P2 are the pressures of two liquids, each having temperatures as T1 and T2. 

So, the simple relationship found by integrating Equation (1)  between two pressure-temperature endpoints is given by:

ln \[(\frac{P1}{P2}) = \frac{\triangle H(vap)}{R}(\frac{1}{T2}-\frac{1}{T1})\]....(2)

The above equation (2) is the Clausius-Clapeyron Equation. This equation is considered the vapor pressure formula. 

Also, the above vapor pressure formula is helpful to calculate vapor pressures when the values of P1 and P2 are known to us.

Besides this, the above vapor pressure formula helps us to calculate the vapor pressure at another temperature when the vapor pressure is known at some temperature with the enthalpy of vapourization.

Formula of Raoult’s Law

So, the Raoult’s law equation goes like this:

PSolution   =  xSolvent. P0Solvent

Here, the mole fraction of the solvent is the ratio of the amount (mol) of the solute to the amount or mole of the entire solution. This statement is well explained with the help of Raoult’s law equation.

Raoult’s Law Formula

Now, let us derive the formula of Raoult’s law:

P1  x1 

Or,

P1   =  P1 0 x1

Also, for the second component having a mole fraction of x2,  we have:

P2 x2

Or,

P2  = P20 x2

Here, 

P1 and P2 are the pressures of components 1 and 2 at a pure state

And, x1 and x2 are the solution’s mole fraction in the vapor phase formula.

Now, applying Dalton’s law of partial pressure here:

P   =   P1   + P2

So, 

P  =    P10 x1   +  P20 x2 

Also, 

x1 + x2  = 1

Or,

x1   =  1  -  x2

P  =    P10 (1  -  x2)   +   P20 x2 

P  =  P10    +   ( P20  -   P10). x2

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So, this is the required Raoult’s law formula.

Relative Lowering of Vapor Pressure

As per the formula of Raoult’s law, we have:

P   =   vapor pressure of the pure solvent, and

P0   =  vapor pressure of the solvent in a solution

The lowering of vapor pressure formula is:

∆p    =   (P0  -  P)

The definition of the relative lowering of vapor pressure formula goes like this:

A relative lowering of vapor pressure is the ratio between the lowering of vapor pressure and the vapor pressure of the pure solvent, i.e.,

\[\frac{\triangle p}{Po} = \frac{(Po - P)}{Po}\]

From the above formula of vapor pressure, when we prepare a solution or a mixture by mixing non-volatile solute B and the solvent A, we get the following mole fraction in vapor phase formula:

xA + xB  = 1

Or,

xA   =  1  -  xB

Here,          

xB   =    the mole fraction of solute

Also,

\[\frac{Pa}{Po(a)}\] = xA   

So, 

1  -\[\frac{Pa}{Po(a)}\] = 1 - xA = xB   

=>\[\frac{Po (a) - Pa}{Po(a)}\]=  xB

=>\[\frac{\triangle p}{Po} = \frac{n}{n + N}\]…..(a)

Here,

n  =  number of moles of a solute

N = number of moles of a solvent

Thus, the above equation (a) is the required relative lowering of vapor pressure formula.

Conclusion

Vapor pressure depends on temperature. Raoult’s law when vapor pressure of the liquid equals the atmospheric pressure, the material has a temperature and its pressure is the boiling/freezing point. 

States that the solution’s vapor pressure varies directly with the solvent’s mole fraction.