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MMLU-Pro / 9491 / The partial molar volumes of water and ethanol in a solution with…

Problem

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question

The partial molar volumes of water and ethanol in a solution with xH2O=0.45x_{\mathrm{H}_2 \mathrm{O}}=0.45 at 25∘C25^{\circ} \mathrm{C} are 17.0 and $57.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$, respectively. Calculate the volume change upon mixing sufficient ethanol with $3.75 \mathrm{~mol}$ of water to give this concentration. The densities of water and ethanol are 0.997 and $0.7893 \mathrm{~g} \mathrm{~cm}^{-3}$, respectively, at this temperature.
Plain-text mathematical notation (without MathML)
The partial molar volumes of water and ethanol in a solution with x_(H₂O)=0.45 at 25^(∘)C are 17.0 and $57.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$, respectively. Calculate the volume change upon mixing sufficient ethanol with $3.75 \mathrm{~mol}$ of water to give this concentration. The densities of water and ethanol are 0.997 and $0.7893 \mathrm{~g} \mathrm{~cm}^{-3}$, respectively, at this temperature.
Original LaTeX notation
The partial molar volumes of water and ethanol in a solution with $x_{\mathrm{H}_2 \mathrm{O}}=0.45$ at $25^{\circ} \mathrm{C}$ are 17.0 and $57.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$, respectively. Calculate the volume change upon mixing sufficient ethanol with $3.75 \mathrm{~mol}$ of water to give this concentration. The densities of water and ethanol are 0.997 and $0.7893 \mathrm{~g} \mathrm{~cm}^{-3}$, respectively, at this temperature.

category

physics

options

  1. -16 $\mathrm{~cm}^3$
  2. -12 $\mathrm{~cm}^3$
  3. -14 $\mathrm{~cm}^3$
  4. -4 $\mathrm{~cm}^3$
  5. 4 $\mathrm{~cm}^3$
  6. -8 $\mathrm{~cm}^3$
  7. 2 $\mathrm{~cm}^3$
  8. -10 $\mathrm{~cm}^3$
  9. 0 $\mathrm{~cm}^3$
  10. -6 $\mathrm{~cm}^3$

src

scibench-thermo

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Source and history

upstream_id / Original problem ID
9491
task_id
c5e1cf7b-b8e9-54b1-839a-c9e292f6c705
task_key
default--test--9491
task_revision_id
1
config / split
default / test

Official source

initial import