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Q43

FAILMCQpage 20holdmath reviewREVIEW_MATHP2UNREVIEWED
type=MCQ · page=20–21 · marks=2 · content_conf=0.7999999999999999 · math_conf=0.739

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Source / evidence

file: GATE CH 2020 (with Solutions).pdf
pages: 20–21
assets/questions/Q043/residual_152a38414261.png

Extracted43 / 67

Consider the gas phase reaction [VISUAL / REVIEW — NO INVENTED LATEX]Source math clip NO₂₂
occurring in an isothermal and isobaric reactor maintained at 298 K and 1.0 bar. The standard Gibbs energy change of the reaction at 298 K is
..
ses at 1.0 bar. The equilibrium mixture in the reactor behaves as in the ideal gas. The value of the universal gas constant is 8.314 J mol⁻1K−1.⁻¹ K^{ - 1}. If one mole of pure N2O4N_2 O_4 is initially charged to the reactor, the fraction of N2O4N_2 O_4 that decomposes into NO₂₂
at equilibrium is

Options

  1. A.
    0
  2. B.
    0.17
  3. C.
    0.38
  4. D.
    1

Answer

B

Solution

N2O4←⎯⎯⎯⎯/rightarrow2NO2N_2O_4←⎯⎯⎯⎯ /rightarrow 2NO_2
As you know that
..
5253=−8.314/times298/lnk5253 = −8.314 /times 298/lnk
k=0.12k = 0.12
k=kyP/sum/gammaik = k_{yP}/sum /gamma{}^i
ky=/fracyNO2yN2O4k_y = /frac{yNO_2}{yN_2}O_4
yNO2=/frac2ε[(1+ε)]yNO_2 = /frac{2ε}{[(1+ε)]}
yN2O4=/frac(1−ε)(1+ε)yN_2O_4 = /frac{(1-ε)}{(1+ε)}
k=/frac((/frac2ε(1+ε))2)(/frac(1−ε)(1+ε))k = /frac{((/frac{2ε}{(1+ε)})^2)}{(/frac{(1-ε)}{(1+ε)})}
0.12=/frac(2ε)2(1−ε2)0.12 = /frac{(2ε)^2}{(1-ε^2)}
ε=0.17ε = 0.17
Hence, the correct option is (B).

Why review

Category: REVIEW_MATH · Priority: P2 · Disposition: extraction_defect

Extractor validation_status=low_confidence.

Suggested action: compare_pdf_and_extracted

Human review

state=UNREVIEWED · resolution=— · trust=UNRESOLVED · WAVE-12 priority=P2
Review actions

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Math review evidence

stem · REVIEW_REQUIRED · —
Source clip
source clip
page=20 bbox=[36,574.04,190.51,589.43]
asset=assets/questions/Q043/residual_152a38414261.png
Raw text
N₂ O₄2
Current normalized
[VISUAL / REVIEW — NO INVENTED LATEX]
method=unicode_normalize
Resolver / candidate
[VISUAL / REVIEW — NO INVENTED LATEX]
status=REVIEW
reason=fraction_bar_ambiguous
Reason for review: residual_pua, unresolved_pua_preserved_in_raw, fraction_bar_ambiguous

Provenance status

Source PDF: GATE CH 2020 (with Solutions).pdf
SegmentPageBBoxAssetEquationLink
stem20[36,574.04,190.51,589.43]assets/questions/Q043/residual_152a38414261.pngsource—PASS
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Equations:none

Dimensions

  • structurePASS
  • question_textFAIL
  • optionsPASS
  • answerPASS
  • solutionPASS
  • mathREVIEW
  • cross_entityPASS

Issues

  • operator_set_changed_raw_vs_derived
  • stem_math_review_required