Solution | Raoult's Law#
Raoult's Law to calculate Vapour Pressure#
- Raoult's Law states that the partial pressure or vapour pressure of any volatile constituent of solution at a given temperature is equal to the product of vapour pressure of pure constituent and its mole fraction in the solution.
\[p = {p^o\ Χ}\]
- For a solution containing two volatile liquids A and B, we can write:
\[p_A = {p^o_A\ Χ_A}\]
\[p_B = {p^o_B\ Χ_B}\]
where,
pA = partial pressure of A
pB = partial pressure of B
poA = partial pressure of pure liquid A
poB = partial pressure of pure liquid B
ΧA = mole fraction of A in solution
ΧB = mole fraction of B in solution
- From Dalton's law, we can calculate total pressure, P:
\[P = {p_A + p_B}\]
\[P = {p^o_A\ Χ_A + p^o_B\ Χ_B}\]
\[P = {p^o_A\ Χ_A + p^o_B\ (1-Χ_A)}\]
\[P = {(p^o_A-p^o_B)Χ_A + p^o_B}\]
- The graph of Raoult's law will be a straight line because it is of the form y = mx+c.
Image credit: https://en.wikipedia.org/wiki/Raoult's_law
Raoult's Law as a special case of Henry's Law#
- According to Henry's law, partial pressure of a gas over the surface of a solution is directly proportional to its mole fraction dissolved in the solution and is given by:
\[p = {K_H\ Χ}\]
- According to Raoult's law, partial pressure of a volatile liquid in gaseous form over the surface of a solution is also directly proportional to its mole fraction dissolved in the solution and is given by:
\[p = {p^o\ Χ}\]
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From the above two equations, it can be clearly seen that there is a difference in proportionality constant between two equations. If a volatile liquid is dissolved in solution, then KH becomes po.
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Thus, Raoult's law is the special case of Henry's law where KH = po.