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  4. x grams of water is mixed in 69 g ethanol. Mole fraction of ethanol in the resultant solution is 0.6. What is the value of x in grams?

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Q. $ x $ grams of water is mixed in 69 g ethanol. Mole fraction of ethanol in the resultant solution is 0.6. What is the value of $ x $ in grams?

CMC MedicalCMC Medical 2013

Solution:

$ {{w}_{A}}=xg, $ $ {{m}_{A}}=18, $ $ {{x}_{A}}=1-0.6=0.4 $ $ {{w}_{B}}=69g, $ $ {{m}_{B}}=46, $ $ {{x}_{B}}=0.6, $ $ {{x}_{A}}=\frac{{{n}_{A}}}{{{n}_{A}}+{{n}_{B}}} $ $ 0.4=\frac{{{w}_{A}}/{{m}_{A}}}{{{w}_{A}}/{{m}_{A}}+{{w}_{_{2}}}/{{m}_{B}}}=\frac{x/18}{\frac{x}{18}+\frac{69}{45}} $ $ x=18 $