# Chemistry: Solutions: Raoult՚s Law for Solutions and Containing Non-Volatile Solute (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Raoult՚s Law for Solutions

• The relationship between vapour pressure of a liquid and its mole fraction is given by Raoult՚s law.
• Raoult՚s law states that for a solution of volatile liquids, the partial vapour pressure of each liquid in the solution is directly proportional to its mole fraction.
• Raoult՚s law is applicable only for miscible liquids.
• The partial vapour pressure of each liquid will depend upon its mole fraction in the solution.
• Let the mole fractions of the liquids A and B be XA and XB, respectively. Also, if PA and PB are the partial vapour pressures of A and B respectively, then PA α XA or PA = P0A XA
• Similarly, PB = p0B XB (where, P0A and p0B are the vapour pressures of pure liquids A and B respectively)
• If the values of PA and PB are plotted against the values of XA and XB for a solution, two straight lines are obtained.
• The total vapour pressure P of the solution is given by the sum of partial vapour pressures PA and PB.
• Thus, P = PA + PB, p = p0AXA + p0BXB
• The total vapour pressure (P) of a solution is represented by the line joining p0A and p0B.
• The solutions which obey Raoult՚s law are known as ideal solutions.
• A solution which obeys Raoult՚s law over concentration at all temperatures is called an ideal solution.

## Raoult՚s Law for Solutions Containing Non-Volatile Solute

• The vapour phase of an aqueous solution consists of vapour՚s of solvent (A) only because the solute is non-volatile.
• Since the mole fraction of the solvent in solution is less than one, therefore according to Raoult՚s law, the vapour pressure of the solution will be less than the vapour pressure of the pure solvent.
• If the total vapour pressure of the solution is P, then

PA = pA0XA … Equation 1

XA + XB = 1

XA = 1- XB

Substituting XA in Equation 1

PA = pA0 (1-XB)

Where, (P0A – PA) = lowering of the vapour pressure p0A = relative lowering of the vapour pressure of the solution.

Raoult՚s law for solutions of non-volatile solute lowers at vapour pressure for a solution is equal to the mole fraction of the solute, only when the solvent is volatile.

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