The partial molar volumes of water and ethanol in a solution with xH2O=0.45 at 25 ∘C are 17.0 and 57.0 cm3⋅mol−1, respectively. Calculate the volume change upon mixing sufficient ethanol with 4.30 mol of water to give this concentration. The densities of water and ethanol are 0.997 and 0.7893 g⋅cm−3, respectively, at this temperature.Express your answer to two significant figures and include the appropriate units.

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Asked Oct 28, 2019
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The partial molar volumes of water and ethanol in a solution with xH2O=0.45 at 25 ∘C are 17.0 and 57.0 cm3⋅mol−1, respectively. 
Calculate the volume change upon mixing sufficient ethanol with 4.30 mol of water to give this concentration. The densities of water and ethanol are 0.997 and 0.7893 g⋅cm−3, respectively, at this temperature.
Express your answer to two significant figures and include the appropriate units.
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Expert Answer

Step 1

In a mixture containing two miscible liquids, the partial molar volume refers to the contribution which is made by a given component that is present in the mixture to the overall volume of the given solution.

Step 2

In a two- component system which is maintained at a constant temperature, the volume of the mixture can be calculated using the following formula as follows:

V=nAVA +nBVB
V is the total volume of the mixture
nA and ng are the moles of the component A and B respectively
VA and V are the molar volume of the component A and B respectively
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V=nAVA +nBVB V is the total volume of the mixture nA and ng are the moles of the component A and B respectively VA and V are the molar volume of the component A and B respectively

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Step 3

The molar volume of ethanol and water...

18.0153g/mol
0.997g/cm
- 18.07 cm3/mol
water
46.068 g/mol
0.7893 g/cm3
V
ethano
-58.36 cm3/mol
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18.0153g/mol 0.997g/cm - 18.07 cm3/mol water 46.068 g/mol 0.7893 g/cm3 V ethano -58.36 cm3/mol

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