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| Vapor Pressure and Raoult's Law |
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| In 1886 the French chemist Francois Marie Raoult carried out a series of experiments to study the vapor pressure of a number of binary solutions containing non-volatile as well as volatile non electrolyte solutes. On the basis of the results of the experiment he stated a law known as Raoult's law. |
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| It states that, |
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| "In a solution of volatile components, the partial vapor pressure of a component at a given temperature is equal to the mole fraction of that component in the solution multiplied by the vapor pressure of that component in the pure state". |
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| Now, let us consider a mixture of two completely miscible volatile liquids A and B, having the mole fraction xA and xB. Suppose at a given temperature their partial vapor pressures are pA and pB and the vapor pressure in pure state are: |
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| The total vapor pressure, P exerted by the solution is the sum of PA and PB as required by Dalton's law of partial pressures. |
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| P = PA + PB |
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| or P = PoA cA + PoB cB |
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| = PoA (1-cB) + PoB cB [because cA + cB = 1] |
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| = PoA - PoA cB + PoB cB |
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| P = (PoB - PoA)cB + PoA |
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| Similarly by putting cB = 1-cA the vapor pressure of the solution |
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| P = (PoA - PoB)cA + PoB |
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| fig 3.5 |
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| As the values of PoA and PoB are constants at a particular temperature, it reveals that total pressure is a linear function of cB or cA i.e. the plot of P versus cA or P versus cB should be a straight line. The variation of P with mole fraction is given by the solid line III in the graph. The solutions which obey Raoult's law are called ideal solutions. For such solutions, the vapor pressure of the solution always lies between the vapor pressure of the pure components. |
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| The vapor pressure of a solution containing non-volatile solute is directly proportional to the mole fraction of the solvent. That is because, there is no contribution towards the vapor pressure of the solution from non volatile component (PB = 0). |
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| where K is proportionality constant, |
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| Thus, PA = PoA cA or, Psolution = PPure solvent x mole fraction of solvent. |
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| In terms of symbols, |
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| But xA + xB = 1 |
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| or xA = 1-xB ……(2) |
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| From equations (1) and (2) |
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| Rearranging |
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| In the above equation pAo- ps represents lowering of vapor pressure and |
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| the mole fraction of the non-volatile solute in the solution. |
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