calculating molarity from mole fraction

[beth]

how would you calculate molarity of you were given the mole fraction of a compound and its density

[sharan]

Hey Beth,,

In order to find molarity from mole fraction and density,,
I can show you an example to do so..
For example you have an aquos ethanol (C₂H₅OH) solution with mole fraction of 0.05 and density of .997 gm/mL .
we also know the Molar mass of C₂H₅OH is 46 gms/Mol and water is 18 gm/ Mol

Step 1: Mole fraction of Ethanol (Xe) = No. of moles of E / Moles of E + moles of W = .05
Step 2: Mole fraction of Water (Xw) = No. of moles of W / Moles of E + moles of W = .95
(1-.05 = .95 Since sum of mole fractions is always 1)
Step 3: Step₁/Step₂= Xe/Xw = Moles of E/ Moles of W= .05/.95= 1/19
Or Moles of Water= Moles of Ethanol * 19
(Since the denominators of both step1 and step 2 cancels out)
Step 4: In 1 mL of solution, the mass of solution= .997 gm (coming from density) or in 1000 mL of Soln, the mass of solution = 997 gm
Step 2: 997 gm= Mass of ethanol+Mass of water
997 gm = (Moles of Ethanol * 46) + (Moles of Water * 18)
997 gm = 46 * moles of Ethanol + 18 * 19 * Moles of Ethanol
(You can see this relationship from Step 3 )
You calculate,
Moles of Ethanol = 2.57 or 2.57 M
It is the molarity because you can see that we calculated everything in terms of 997 gm which is equal to 1000ml or 1 L. As we know molarity is moles of solute (in this case ethanol) in 1 litre of solution.

I hope that helps.

- Sharan

[sharan]

I dunt noe how but that turned out to be a emotion but it is actaully 18, molar mass of water ... sorry for that ...