For the reaction at 298 K, 2A + B → C, Δ H = 400 KJ mol-1 and Δ S = 0.2 KJ K-1 mol-1 At what temperature will the reaction become spontaneous considering Δ H and Δ S to be constant over the temperature range

Question

For the reaction at 298 K, 2A + B → C, Δ H = 400 KJ mol-1 and Δ S = 0.2 KJ K-1 mol-1 At what temperature will the reaction become spontaneous considering Δ H and Δ S to be constant over the temperature range (A) 200 K (B) 1000 K (C) 3000 K (D) 2000 K

Tardigrade Admin · Accepted Answer

According to Gibbs Helmholtz equation, Δ G =Δ H -T Δ S Temperature at equilibrium i.e., when Δ G=0, T =(Δ H/Δ S)=(400/0.2) =(4000/2) = 1200 K Thus the reaction will be spontaneous at temperature above 2000 K as above 2000 K Δ G =-ve

Q. For the reaction at $298 K, 2 A + B \to C, Δ H = 400 K J m o l^{- 1}$ and $Δ S = 0.2 K J K^{- 1} m o l^{- 1}$ At what temperature will the reaction become spontaneous considering $Δ H$ and $Δ S$ to be constant over the temperature range

$200 K$

$1000 K$

$3000 K$

$2000 K$

According to Gibbs Helmholtz equation,
$Δ G = Δ H - T Δ S$
Temperature at equilibrium i.e., when $Δ G = 0$ ,
$T = \frac{Δ H}{Δ S} = \frac{400}{0.2} = \frac{4000}{2} = 1200 K$
Thus the reaction will be spontaneous at temperature above $2000 K$ as above $2000 K$ $Δ G = - v e$

Q. For the reaction at 298K,2A+B→C,ΔH=400KJmol−1 and ΔS=0.2KJK−1mol−1 At what temperature will the reaction become spontaneous considering ΔH and ΔS to be constant over the temperature range

200K

1000K

3000K

2000K