Question

Express Raoult’s law in words. Is Raoult’s law valid for a solution of a volatile solute? Explain.

Short answer

According to the Raoult's law, the vapor pressure of a non-volatile solute solution is equal to the mole fraction of a pure solvent's vapor pressure at that temperature. It can be mathematically presented as: $P_{solution}=X_{solvent}\times P_{solvent}^{\circ }$

Yes, the Raoult’s law is valid for a solution of a volatile solute.

Step-by-step solution

Raoult’s law

The Raoult’s law can be mathematically presented as$P_{solution}=X_{solvent}\times P_{solvent}^{\circ }$where P and$P^{\circ }$are the vapor pressures of a solution and a pure solvent respectively, and X is the solvent's mole fraction.

The vapor pressure of a solvent above a solution $\left({\mathrm{P}}_{\mathrm{solution}}\right)$equals the mole fraction of a solvent in a solution $\left({\mathrm{X}}_{\mathrm{solvent}}\right)$times the vapor pressure of a pure solvent role="math" localid="1663327649258" $\left(P_{solvent}^{\circ }\right)$.

In a solution role="math" localid="1663327769116" ${\mathrm{X}}_{\mathrm{solvent}}$, is always less than 1, so ${\mathrm{P}}_{\mathrm{solution}}$is always less than $P_{solvent}^{\circ }$.

For volatile solutes, Raoult’s law

The Raoult’s law is valid for both volatile and non-volatile solutes because it refers to the partial vapor pressure and not the total vapor pressure.

For volatile solutes, the vapor pressure of any component at a given temperature is the product of a mole fraction of a component in a solution with the vapor pressure of the component in a pure state.

The total pressure for a mixture of a volatile solute (A) and a solvent (B) is equal to the sum of the two partial pressures, as in:

$$\begin{gathered} P_T={P^{\circ }}_{A.}{X}_A+{P^{\circ }}_{B.}{X}_B;X_A=1-X_B \\ ={P^{\circ }}_{A.}\left(1-X_B\right)+{P^{\circ }}_{B.}{X}_{B.} \end{gathered}$$

For non-volatile solutes,role="math" localid="1663328401094" ${P^{\circ }}_{A.}=0.$

Thus,$P_T={P^{\circ }}_{B.}{X}_{B.}$

Hence, the Raoult’s law is valid for a solution with a volatile solute.