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Question

# i). State Raoult's Law. ii). The vapour pressure of pure benzene at a certain temperature is 0.850 bar. A non-volatile non-electrolyte solid weighing 0.5 g when added to 39.0 g of benzene (molar mass 78 g mol−1). Vapour pressure of the solution, then is 0.845 bar. What is the molar mass of the solid substance?

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Solution

## i). Raoult's law: The partial vapour pressure of any volatile component of a solution is the product of vapour pressure of that pure component and the mole fraction of the component in the solution.p=poX ----aWhere p is the vapour pressure of a component of the solution, po is the vapour pressure of pure component and X is the mole the fraction of that component in the solution.ii). Let the molar mass of the solid substance be M g/mol.The number of moles of solid substance =0.5gMg/mol39.0 g of benzene (molar mass 78 g /mol) corresponds to the number of moles 39.078=0.5 moles.The mole fraction of solid substance is X=0.5M0.5+0.5MThe relative lowering in vapour pressure is equal to its mole fraction.Po−PPo=X0.850−0.8450.850=0.5M0.5+0.5M 0.00588=0.5M0.5+0.5M 0.5+0.5M=0.5M0.005880.5+0.5M=85MMultiply both sides with M0.5M+0.5=850.5M=84.5M=169g/molHence, the molar mass of the solid substance is 169 g/mol.

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