Verified Solution • 2025–26 Session moderate

QJEEM23Cheb62: JEE Main 2023 Chemistry - Class 11 JEEM23Cheb62 Solution: For complete combustion of ethene. C 2 H 4 ( g ) + 3 O 2 ( g )…

For complete combustion of ethene.

C2H4(g)+3O2(g)→2CO2(g)+2H2O(l)

the amount of heat produced as measured in bomb calorimeter is 1406 kJ mol−1 at 300 K. The minimum value of TΔS needed to reach equilibrium is (−) _________ kJ. (Nearest integer)

Given : R=8.3 J K−1 mol−1

Step-by-Step Verified Solution

In the given combustion reaction, the number of moles of gaseous products ( Δng\Delta n_g ) is -2 (since we have 2 moles of CO₂ gas on the product side and 4 moles of gaseous reactants).

The change in internal energy ( ΔU\Delta U ) is given as -1406 kJ/mol.

We can calculate the change in enthalpy ( ΔH\Delta H ) using the equation ΔH=ΔU+ΔngRT\Delta H = \Delta U + \Delta n_gRT , where RR is the ideal gas constant and TT is the temperature.

Substituting the given values:

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padding-right: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd extra="true"></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em;"><mjx-mi class="mjx-n"></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2248"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c34"></mjx-c><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-texatom texclass="ORD"><mjx-mi class="mjx-n"><mjx-c class="mjx-c6B"></mjx-c><mjx-c class="mjx-c4A"></mjx-c></mjx-mi><mjx-texatom texclass="ORD"><mjx-mo class="mjx-n"><mjx-c class="mjx-c2F"></mjx-c></mjx-mo></mjx-texatom><mjx-mi class="mjx-n"><mjx-c class="mjx-c6D"></mjx-c><mjx-c class="mjx-c6F"></mjx-c><mjx-c class="mjx-c6C"></mjx-c></mjx-mi></mjx-texatom><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr></mjx-itable></mjx-table></mjx-mtable></mjx-math><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="3pt"><mtr><mtd><mi mathvariant="normal">Δ</mi><mi>H</mi></mtd><mtd><mi></mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mi>U</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><msub><mi>n</mi><mi>g</mi></msub><mi>R</mi><mi>T</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mo>−</mo><mn>1406</mn><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">kJ</mi><mrow data-mjx-texclass="ORD"><mo>/</mo></mrow><mi data-mjx-auto-op="false">mol</mi></mrow><mo>+</mo><mo stretchy="false">(</mo><mo>−</mo><mn>2</mn><mo stretchy="false">)</mo><mo>×</mo><mn>8.3</mn><mo>×</mo><msup><mn>10</mn><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>3</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">kJ</mi><mrow data-mjx-texclass="ORD"><mo>/</mo></mrow><mi mathvariant="normal">K</mi><mrow data-mjx-texclass="ORD"><mo>/</mo></mrow><mi data-mjx-auto-op="false">mol</mi></mrow><mo>×</mo><mn>300</mn><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">K</mi></mrow></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mo>−</mo><mn>1406</mn><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">kJ</mi><mrow data-mjx-texclass="ORD"><mo>/</mo></mrow><mi data-mjx-auto-op="false">mol</mi></mrow><mo>−</mo><mn>4.98</mn><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">kJ</mi><mrow data-mjx-texclass="ORD"><mo>/</mo></mrow><mi data-mjx-auto-op="false">mol</mi></mrow></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>≈</mo><mo>−</mo><mn>1411</mn><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">kJ</mi><mrow data-mjx-texclass="ORD"><mo>/</mo></mrow><mi data-mjx-auto-op="false">mol</mi></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>

At equilibrium, ΔG=0\Delta G = 0 , so ΔH=TΔS\Delta H = T \Delta S , which gives TΔS=ΔHT \Delta S = \Delta H .

Therefore, the minimum value of TΔST \Delta S needed to reach equilibrium is -1411 kJ

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