Question

a) (10 points) The gas phase reaction between methanol (CH,OH) and water that produces carbon dioxide and hydrogen is accompanied by an increase in entropy under standard conditions (AS。-17691/mol). At approximately what temperature does this reaction become spontaneous? 6. (AH for gaseous CH,OH, H20 and CO, are-200.7,-241 8 and-393.5kJ/mol, respectively) b) (10 points) What is the value of the equilibrium constant for the reaction described in part (a) at 25°C?

Answer 1

Q6

In order to compare equilibirum vs. spontaneous/nonspontaneous reactions, we better use a criteria.

Recall that if dSuniverse > 0, this is spontaneous, if dSuniverse = 0, this is inequilbirium and if dSuniverse < 0 this is never possible.

Then, recall that

dSuniverse = dSsurroundings + dSsystem

dSsystem = Sproducts - Sreactants

dSsurroundings = Qsurroundings/T = -dHsystem/T

therefore

dSystem =  -dHsystem/T + dSsystem

If we multiply by -T

dGrxn = dHrxn - T*dSrxn

Now, analysis of dG value... which is the "free energy" available for a process to follow

if dG <0 , this will be spontaneous

if dG = 0 , this is in equilibrium

if dG > 0, this will not be spontaneous

then

CH3OH + H2O = CO2 + H2 --> dS = 176.9

dH = Hprod - Hreact = -393.5 + 0 - (-200.7 -241.8) = 49

dG= dH - T*dS

dH - T*dS < 0

49*1000 - T*176.9 <0

49*1000<T*176.9

T >  49*1000 /176.9

T >  276.992 K

b)

dG = -RT*ln(K)

dG = (dH - T*dS) = (49*100-298*176.9) = -47816.2

K = exp(-DG/(RT))

K = exp(-47816.2/(8.314*298))

K = 4.1522*10^-9