# Problem: The decomposition of isopropanol to form acetone and hydrogen gas (reaction shown below) has an equilibrium constant of 0.44 at 452 K. Assume ΔH° and ΔS° are temperature-independent.(CH3)2CHOH (g) ⇋ (CH3)2CO (g) + H2 (g)isopropanol              acetoneUseful data (at 298 K):(CH3)2CHOH (g)    ΔH°f = -261.1 kJ/mol(CH3)2CO (g)          ΔH°f = -218.5 kJ/molUnder standard conditions at 570 K, is this reaction spontaneous as written? Justify your answer with appropriate calculations.

###### FREE Expert Solution

We’re being asked to determine the if is this reaction spontaneous as written at 570 K.

(CH3)2CHOH(g) ⇋ (CH3)2CO(g) + H2(g)

Recall that if:

• ΔG < 0 or ΔG = (–); the reaction is spontaneous

ΔG = 0; the reaction is at equilibrium

• ΔG > 0 or ΔG = (+); the reaction is non-spontaneous

Recall that ΔG˚rxn and K are related to each other:

$\overline{){\mathbf{\Delta G}}{{\mathbf{°}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{RTlnK}}}$

Recall that ΔH˚rxn and K are related to each other:

$\overline{){\mathbf{ln}}\mathbf{\left(}\frac{{\mathbf{K}}_{\mathbf{2}}}{{\mathbf{K}}_{\mathbf{1}}}\mathbf{\right)}{\mathbf{=}}\frac{\mathbf{-}\mathbf{∆}{\mathbf{H}}_{\mathbf{rxn}}}{\mathbf{R}}\mathbf{\left[}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}\mathbf{\right]}}$

We’re given the ΔH˚f  of each reactant and product:

(CH3)2CHOH (g)    ΔH°f = -261.1 kJ/mol

(CH3)2CO (g)          ΔH°f = -218.5 kJ/mol

For this problem, we need to do the following steps:

Step 1: Calculate ΔH˚rxn.

Step 2: Calculate K at 570 K

Step 3: Calculate for ΔGrxn at 570 K ###### Problem Details

The decomposition of isopropanol to form acetone and hydrogen gas (reaction shown below) has an equilibrium constant of 0.44 at 452 K. Assume ΔH° and ΔS° are temperature-independent.

(CH3)2CHOH (g) ⇋ (CH3)2CO (g) + H2 (g)

isopropanol              acetone

Useful data (at 298 K):

(CH3)2CHOH (g)    ΔH°f = -261.1 kJ/mol

(CH3)2CO (g)          ΔH°f = -218.5 kJ/mol

Under standard conditions at 570 K, is this reaction spontaneous as written? Justify your answer with appropriate calculations.