Answer :
Answer: The [tex]\Delta G[/tex] of the reaction at given temperature is -12.964 kJ/mol.
Explanation:
For the given chemical reaction:
[tex]CH_3OH(g)\rightleftharpoons CO(g)+2H_2(g)[/tex]
The expression of [tex]K_p[/tex] for the given reaction:
[tex]K_p=\frac{(p_{CO})\times (p_{H_2}^2)}{p_{CH_3OH}}[/tex]
We are given:
[tex]p_{CO}=0.140atm\\p_{H_2}=0.180atm\\p_{CH_3OH}=0.850atm[/tex]
Putting values in above equation, we get:
[tex]K_p=\frac{(0.140)\times (0.180)^2}{0.850}\\\\K_p=5.34\times 10^{-3}[/tex]
To calculate the Gibbs free energy of the reaction, we use the equation:
[tex]\Delta G=\Delta G^o+RT\ln K_p[/tex]
where,
[tex]\Delta G[/tex] = Gibbs' free energy of the reaction = ?
[tex]\Delta G^o[/tex] = Standard gibbs' free energy change of the reaction = 0 J (at equilibrium)
R = Gas constant = [tex]8.314J/K mol[/tex]
T = Temperature = [tex]25^oC=[25+273]K=298K[/tex]
[tex]K_p[/tex] = equilibrium constant in terms of partial pressure = [tex]5.34\times 10^{-3}[/tex]
Putting values in above equation, we get:
[tex]\Delta G=0+(8.314J/K.mol\times 298K\times \ln(5.34\times 10^{-3}))\\\\\Delta G=-12963.96J/mol=-12.964kJ/mol[/tex]
Hence, the [tex]\Delta G[/tex] of the reaction at given temperature is -12.964 kJ/mol.
The study of carbon with hydrogen is called hydrocarbon. The Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure
The correct answer to the question is -12.964.
What is partial pressure?
- The pressure applied by the gas molecule in the mixture to another gas molecule is called partial pressure.
The balanced reaction is as follows:-
[tex]CH_3OH(g)<---->CO(g)+2H_2[/tex]
The expression which is used to solve the question is as follows:-
[tex]k_p =\frac{P_{co}*P_2H^2}{Pch_3oh} [/tex]
The data is given as follows:-
- PCH3OH= 0.850 atm
- PCO= 0.140 atm
- PH2= 0.180 atm
Placed all the values to the equation
[tex]K_p =\frac{[0.140]*[0.180]^2}{0.850} [/tex]
[tex]K_p =5.34*10^{-3}[/tex].
The Gibbs free equation is as follows:-
[tex]G = G^o+RTlnK_P[/tex]
where,
- G= Gibbs' free energy of the reaction
- [tex]G^o[/tex]= Standard gibbs' free energy change of the reaction = 0 J (at equilibrium)
- R = Gas constant
- T = Temperature
- [tex]K_P[/tex]= equilibrium constant in terms of partial pressure
Placed all the value in the equation,
[tex]G = 0+(8.314*298*In(5.34*10^{-3})\\ =-12.946kj[/tex]
Hence, the correct answer is -12.946
For more information about Gibbs free energy, refer to the link:-
https://brainly.com/question/9552459