Gibbs Free Energy Video Lessons

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# 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/molWill the reaction proceed spontaneously as written at 452 K when the partial pressures of each of the three species are 0.25 atm? Justify your answer with appropriate calculations.

###### FREE Expert Solution

We’re being asked to determine the if the reaction proceed spontaneously as written at 452 K when the partial pressures of each of the three species are 0.25 atm.

(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:

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

When the system is not at equilibrium the equation of Gibbs Free energy changes to:

$\overline{){{\mathbf{\Delta G}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{\Delta G}}{{\mathbf{°}}}_{{\mathbf{rxn}}}{\mathbf{+}}{\mathbf{RTlnQ}}}$

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

Step 1: Calculate for ΔG˚rxn at 452 K

Step 2: Calculate for Q

Step 3: Calculate ΔGrxn.

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###### 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

Will the reaction proceed spontaneously as written at 452 K when the partial pressures of each of the three species are 0.25 atm? Justify your answer with appropriate calculations.