A chemical reaction has #\ \ DeltaH^{circ}=-5.8\ text{kJmol}^{-1]\ \ # and an equilibrium constant of #\ \ 2.1\ \ # at #\ \ T=298\ K.\ \ #...?

A chemical reaction has #\ \ DeltaH^{circ}=-5.8\ text{kJmol}^{-1]\ \ # and an equilibrium constant of #\ \ 2.1\ \ # at #\ \ T=298\ K.\ \ #...?

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1 Answer

#K_(eq) '~~ 1.26#

Explanation:

As @truong-son-n has mentioned, the van't Hoff equation relates the equilibrium constant to temperature given the enthalpy change of the reaction under standard conditions (#"T" = 298 color(white)(l) "K"#.)

Apply the van't Hoff equation:

#ln((K_2)/(K_1)) = (- Delta H^"o")/(R) * (1/(T_2) - 1/(T_1))#
#color(white)(ln((K_2)/(K_1))) = -(-5.8 * 10^3 color(white)(l) color(navy)("J") * mol^(-1)) /(8.314 color(white)(l) color(navy)("J") * mol^(-1) * "K"^(-1)) * (1/(382.0 color(white)(l) "K") - 1/(298.0 color(white)(l) "K"))#
#color(white)(ln((K_2)/(K_1))) = ‐0.515 #

#(K_2) / (K_1) = e^(‐0.515) ~~0.598#

Therefore

#K_2 = 0.598 * 2.1 = 1.26#

Given that #K_1 = 2.1# at #"T" = 298 color(white)(l) "K"#.