The formation of methanol is important to the processing of new fuels. At 298.0 K, Kp = 2.25 × 104 for the reaction CO(g) + 2 H2(g) ⇌ CH3OH(l) If ΔH o rxn = −128 kJ/ mol CH3OH, calculate Kp at 3°C. × 10 (Enter your answer in scientific notation.)

Kp = 1.39 x 10⁶

Explanation:

The strategy here is to utilize the van´t Hoff relation  to calculate Kp at 3 ºC:

ln ( K₂ / K₁ ) = - ΔHºrxn / R x [1/T₂ - 1/T₁]

where K₂ and K₁ are the equilibrium constants at temperatures T₂ and T₁ ,  ΔHºrxn is the enthalpy change for the reaction and R is the gas constant.

Thus,

Let K₂ equal the equilibrium constant at 3ºC ( 3 + 273 ) K,  then:

T₂ = 276 K

T₁ = (25 + 273) K  = 298 K ( standard temperature in thermodymics)

ΔHºrxn = -128 kJ/mol x 1000 J /kJ = -1.28 x 10⁵ J / mol

ln ( K₂ / 2.25 x 10⁴ ) = - (-1.28 x 10⁵ J / mol/ 8.314 J/K mol )  x [ 1 / 276 K - 1 / 298 K]

=  4.12

Taking inverse natural log function to both sides of the equation,

K₂ / 2.25 x 10⁴ = e^(4.12)

K₂ = 1.39 x 10⁶

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