Q81P - Chemistry: Molecular Nature Of Matter And Change

Question

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

Step-by-Step Solution

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.

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 $\left(P_{solvent}^{\circ }\right)$.

In a solution  ${\mathrm{X}}_{\mathrm{solvent}}$, 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,  ${P^{\circ }}_{A.}= 0.$

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

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