For a reaction, A ⇌ P, the plots of [A]and [P] with time at temperatures T _ 1 and T _ 2 are given below. If T _ 2 > T _ 1 , the correct statement(s) is (are) (Assume ∆ H ^ ⊝ and ∆ S ^ ⊝ are independent of temperature

Correct answer: A. ∆ H ^ ⊝ T _ 1 ln K _ 1 ln K _ 2 > T _ 2 T _ 1 ⇒ T _ 1 ln k _ 1 > T _ 2 ln k _ 2 ⇒ - ∆ G _ 1 ^ 0 > - ∆ G _ 2 ^ 0 ⇒ (- ∆ H ^ 0 + T _ 1 ∆ S ^ 0 ) > (- ∆ H ^ 0 + T _ 2 ∆ S ^ o ) ⇒ T _ 1 ∆ S ^ 0 > T _ 2 ∆ S ^ 0 ⇒ ∆ S ^ o At T _ 2 temperature concentration of product is decreases that shows reaction is exothermic.

JEE Advanced 2018Paper 2

Exam: JEE Advanced
Year: 2018
Paper: Paper 2
Subject: Chemistry
Chapter: Thermodynamics (C)

JEE Advanced 2018 · Paper 2 · Chemistry · Thermodynamics (C)

For a reaction, A ⇌ P, the plots of [A]and [P] with time at...

For a reaction, A ⇌ P, the $plots of \left[A\right]and \left[P\right] with time at temperatures$ {T}_{1}and{T}_{2} $are given below.<br ><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/hfvjypyvnjrofprcwoemnluhkwpvqmdqzwkmbeapzfebsdgrwp.jpeg"/><br >If$ {T}_{2} > {T}_{1} $, the correct statement(s) is (are)<br >(Assume$ ∆ {H}^{⊝}and ∆ {S}^{⊝} $are independent of temperature and ratio of$ lnKat{T}_{1}tolnKat{T}_{2} $is greater than$ {T}_{2} / {T}_{1} $. Here H, S , G and K are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)</p>$

Options

A $∆ {H}^{⊝} < 0, ∆ {S}^{⊝} < 0$
B $∆ {G}^{⊝} < 0, ∆ {H}^{⊝} < 0$
C $∆ {G}^{⊝} < 0, ∆ {S}^{⊝} < 0$
D $∆ {G}^{⊝} > 0, ∆ {S}^{⊝} > 0$

Correct answer

A. $∆ {H}^{⊝} < 0, ∆ {S}^{⊝} < 0$

Step-by-step solution

$A ⇌ P$
Given ${T}_{2} > {T}_{1}$
$\dfrac{ln {K}_{1}}{ln {K}_{2}} > \dfrac{{T}_{2}}{{T}_{1}}$
$⇒ {T}_{1}ln {k}_{1} > {T}_{2}ln {k}_{2}$
$⇒ - ∆ {G}_{1}^{0} > - ∆ {G}_{2}^{0}$
$⇒ \left(- ∆ {H}^{0} + {T}_{1} ∆ {S}^{0}\right) > \left(- ∆ {H}^{0} + {T}_{2} ∆ {S}^{o}\right)$
$⇒ {T}_{1} ∆ {S}^{0} > {T}_{2} ∆ {S}^{0}$
$⇒ ∆ {S}^{o} < 0$

At ${T}_{2}$ temperature concentration of product is decreases that shows reaction is exothermic.

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