A Brief Note on the Relative Lowering of Vapour Pressure

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The physical properties of a solution depend on the number of solute particles in the solution and not on their nature are called colligative properties. 

There are four properties:

1. a) Vapour pressure lowering
2. b) Boiling point elevation
3. c) Freezing point depression
4. d) Osmotic pressure. 

The ratio of vapour pressure lowering to the pure solvent’s vapour pressure is known as the relative lowering of vapour pressure. The solute and solvent vapour pressures are P1 and P2, respectively. As the solute is nonvolatile, it does not affect the overall vapour pressure, i.e. P2 = 0. 

The relative lowering of vapour pressure is the colligative pressure of solutions. The vapour pressure of a pure solvent is higher than the vapour pressure of a nonvolatile liquid solution. The reduced vapour pressure causes the boiling point to rise. As a result, the vapour pressure decreases.

Relative lowering of vapour pressure formula

pº = vapour pressure of the pure solvent 

p = vapour pressure of the solvent in the solution

• The lowering of vapour pressure:

∆p = (pº-p)

The ratio of the lowering of the vapour pressure of the solvent divided by the vapour pressure of the pure solvent is called the relative lowering of vapour pressure.

∆p/p0 =p0-p/p0  (Relative lowering of vapour pressure)

• When nonvolatile solute B and solvent A are combined to make a solution:

XA + XB = 1

XB = 1−XA

Here, XB is the mole fraction of solute as:

PA/ pº A = XA

1-PA/pº A = 1-XA = XB 1-XA = XB

pº A- PA/pº A = XB,   ∆p/ pºA = n/n+N

Here,

n be the number of moles of the solute, and

N be the number of moles of the solvent.

When a nonvolatile solute is dissolved in a liquid, the solution’s vapour pressure drops below the pure solvent’s vapour pressure. 

Consider a solution in which n moles of a nonvolatile solute are dissolved in N moles of a volatile solvent. Then the solvent mole fraction, X 1 = N/(n+N), and the solute mole fraction is X 2 = n /(N +n).

As the solute is nonvolatile, it has a very low vapour pressure. As a result, the vapour pressure of the solution is simply the solvent’s vapour pressure.

 A solution containing a nonvolatile solute has a relative decrease in vapour pressure equal to the mole fraction of the solute in the solution.

Raoult’s law and relative lowering of vapour pressure 

The only thing that changes vapour pressure is temperature. A liquid’s vapour pressure is independent of the volume of liquid in the container. Whether it is one litre or thirty litres, both samples will have the same vapour pressure at the same temperature.

 The connection between temperature and vapour pressure is exponential, implying that as the temperature rises, so does the vapour pressure. It’s worth remembering that a liquid’s vapour pressure matches air pressure when it boils. 

When a nonvolatile solute is dissolved in a solvent, the vapour pressure of the solution is reduced. The amount of solute supplied determines the magnitude of the fall in vapour pressure in the solution.

Let’s have a look at a solution with the following characteristics on which relative lowering of vapour pressure depends: 

Mole fraction of the solvent = XA

Mole fraction of the solute = XB

Vapour pressure of the pure solvent = Pº A

Vapour pressure of solution = P

The vapour pressure of the solution is solely due to the solvent because the solute is nonvolatile.

As a result, the solution’s vapour pressure (P) and the solvent’s vapour pressure (PA) over the solution will be equal, i.e., P = PA.

Raoult’s law states that the solvent’s vapour pressure over the solution equals the product’s vapour pressure in a pure state and its mole fraction.

PA = P°A XA or

P = PºA XA

What is the relationship between the relative lowering of vapour pressure and osmotic pressure?

The equilibrium of a column of solution separated at the bottom from the pure solvent by a semipermeable membrane and placed in an atmosphere of vapour from the solvent is widely used to explore the relationship between the relative lowering of vapour pressure and the osmotic pressure of a solution.

Why is the relative lowering of vapour pressure a colligative property?

Because the concentration of a nonelectrolyte solute in a solution and the number of particles of electrolyte solute in solution are both important, a relative reduction of vapour pressure is a colligative feature. The nature of solute molecules or particles has no bearing on this.

Water has the highest vapour pressure at which temperature?

It is important to note that the boiling point changes depending on the applied pressure and that its normal boiling point is the temperature at which the vapour pressure is equal to the standard atmospheric pressure at sea level (760 mm [29.92 inches] of mercury). 212 degrees Fahrenheit (100 degrees Celsius) is the boiling point of water at sea level.

Conclusion

Because the solute was added to the solvent, the liquid surface has molecules from the pure liquid and the solute. 

The vapour pressure decreases due to the decrease in the number of solvent molecules escaping into the vapour phase. 

The pressure produced by the vapour phase decreases, and this is called relatively reduced vapour pressure. 

This decrease in vapour pressure is a colligative property based on the amount of nonvolatile solute added to the solution, regardless of its type.