1. Tardigrade
  2. Question
  3. Chemistry
  4. Consider the following reaction approaching equilibrium at 27° C and 1 atm pressure A + B xrightleftharpoons[k r=102]kf=1 03C + D The standard Gibb's energy change (Δr G°) at 27° C is (-) kJ mol -1 (Nearest integer). (Given: R =8.3 J K -1 mol -1 and ln 10=2.3 )

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Q. Consider the following reaction approaching equilibrium at $27^{\circ} C$ and $1 atm$ pressure
$A + B \xrightleftharpoons[k _r=10^2]{k_{f}=1 0^3}C + D$
The standard Gibb's energy change $\left(\Delta_r G^{\circ}\right)$ at $27^{\circ} C$ is $(-)$___ $kJ mol ^{-1}$
(Nearest integer).
(Given: $R =8.3 J K ^{-1} mol ^{-1}$ and $\ln 10=2.3$ )

JEE MainJEE Main 2023Thermodynamics

Solution:

$ \because \Delta G ^{ o }=- RT \ln K _{ eq } $
$ \text { and } K _{ eq }=\frac{ K _{ f }}{ K _{ b }} $
$ \therefore K _{ eq }=\frac{10^3}{10^2}=10$
$ \therefore \Delta G =- RT \ln 10 $
$\Rightarrow-(8.3 \times 300 \times 2.3)=-5.7 \,kJ \,mole ^{-1} \approx 6 kJ$
$ \text { mole }^{-1}(\text { nearest integer }) $
$ \text { Ans }=6$