Determine whether the system is at equilibrium?
One of the methods for synthesizing Methanol (CH_3OH) involves reacting CO with H_2 . the equilibrium is CO(g) + 2H_2(g) harr CH_3OH(g) . At 427 degrees Celsius a mixture of CO, H_2 , and CH_3OH having the following Partial pressures; P_(CO)=2.0*10^-3 atm , P_(H_2)=1.0*10^-6 atm and P_(CH_3OH)=1.0*10^-6 . For this reaction DeltaG_(700K)=13.5kJ . Determine whether the system is at equilibrium?
I know that when K=Q the system is at equilibrium, but where does DeltaG_(700K) come in?
Is there a specific difference between the formulas for working out Q and K?
Thank you very much in advance?
One of the methods for synthesizing Methanol
I know that when K=Q the system is at equilibrium, but where does
Is there a specific difference between the formulas for working out Q and K?
Thank you very much in advance?
1 Answer
I think the question has an error... In order to determine whether the system is at equilibrium or not, we require the value of
So, I ASSUME that
DeltaG = DeltaG^@ + RTlnQ where
Q is the reaction quotient,R is the universal gas constant,T is temperature in"K" , and""^@ indicates the reference state for the change in the Gibbs' free energyDeltaG .
(Furthermore, the Gibbs' free energy is a state function, so it should AT LEAST be
At equilibrium, by definition,
DeltaG^@ = -RTlnK
Therefore, at equilibrium, for a gas-phase reaction (where
K_p^@ = e^(-DeltaG^@//RT)
= e^(-"13.5 kJ/mol"//("0.008314 kJ/mol"cdot"K" cdot "700 K"))
= 0.0983
in implied units of
"CO"(g) + 2"H"_2(g) rightleftharpoons "CH"_3"OH"(g)
Q_p^@ = (P_(CH_3OH)//P^@)/((P_(CO)//P^@)(P_(H_2)//P^@)^2)
= ((1.0 xx 10^(-6) "atm"//"1 atm"))/((2.0 xx 10^(-3) "atm"//"1 atm")(1.0 xx 10^(-6) "atm"//"1 atm")^2)
= 5.0 xx 10^8
This would definitely not be at equilibrium.