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MMLU-Pro / 4276 / The mass density of water vapour at 327.6 mathrm{~atm} and …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The mass density of water vapour at $327.6 \mathrm{~atm}$ and $776.4 \mathrm{~K}$ is $133.2 \mathrm{~kg} \mathrm{~m}^{-3}$. Given that for water $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, and $M=18.02 \mathrm{~g} \mathrm{~mol}^{-1}$, calculate the compression factor from the virial expansion of the van der Waals equation.
Plain-text mathematical notation (without MathML)
The mass density of water vapour at $327.6 \mathrm{~atm}$ and $776.4 \mathrm{~K}$ is $133.2 \mathrm{~kg} \mathrm{~m}^{-3}$. Given that for water $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, and $M=18.02 \mathrm{~g} \mathrm{~mol}^{-1}$, calculate the compression factor from the virial expansion of the van der Waals equation.
Original LaTeX notation
The mass density of water vapour at $327.6 \mathrm{~atm}$ and $776.4 \mathrm{~K}$ is $133.2 \mathrm{~kg} \mathrm{~m}^{-3}$. Given that for water $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, and $M=18.02 \mathrm{~g} \mathrm{~mol}^{-1}$, calculate the compression factor from the virial expansion of the van der Waals equation.

category

chemistry

options

  1. 0.9283
  2. 0.6889
  3. 0.5594
  4. 0.8457
  5. 0.7671
  6. 0.7846
  7. 0.6523
  8. 0.8312
  9. 0.7158
  10. 0.6017

src

scibench-atkins

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Source and history

upstream_id / Original problem ID
4276
task_id
b11a04cf-7c31-565c-bcda-745cc0d3b42c
task_key
default--test--4276
task_revision_id
1
config / split
default / test

Official source

initial import