# State Raoult’s law for a solution containing volatile components. Write two characteristics of the solution which obeys Raoult’s law at all concentrations.

In a solution, the vapour presence of a compound at a given temperature is equal to the mole fraction of that compound in the solution multiplied by the vapour pressure of that component in the pure state.

Let's consider a mixture of two volatile liquids A & B, having mole fraction $x_A$ & $x_B$ and partial vapour pressure $p_A$ & $p_B$, and $p^o_A$$p^o_B$ be their vapour pressure in the pure state respectively.

$p_A = x_Ap^o_A \qquad p_B = x_Bp^o_B \\ p = p_A + p_B$

$= x_Ap^o_A + x_Bp^o_B$

$= (1- x_B)p^o_A + x_Bp^o_B$

$p = (p^o_B - p^o_A)x_B + p^o_A$

The two characteristics of the solution which obeys Rault's law at all concentrations are as:

1. $\Delta H_{mix} = 0$, ie the enthalpy of mixing of pure components to form the solution should be zero.
2. $\Delta V_{mix} = 0$, the volume of mixing pure components should be zero.

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