Answer : The value of
is, ![8.867kJ/mole](https://tex.z-dn.net/?f=8.867kJ%2Fmole)
Explanation :
The formula used for
is:
............(1)
where,
= Gibbs free energy for the reaction
= standard Gibbs free energy
R = gas constant = 8.314 J/mole.K
T = temperature = ![25^oC=273+25=298K](https://tex.z-dn.net/?f=25%5EoC%3D273%2B25%3D298K)
Q = reaction quotient
First we have to calculate the
.
Formula used :
![\Delta G^o=-RT\times \ln K_p](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-RT%5Ctimes%20%5Cln%20K_p)
Now put all the given values in this formula, we get:
![\Delta G^o=-(8.314J/mole.K)\times (298K)\times \ln (2.26\times 10^{4})](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-%288.314J%2Fmole.K%29%5Ctimes%20%28298K%29%5Ctimes%20%5Cln%20%282.26%5Ctimes%2010%5E%7B4%7D%29)
![\Delta G^o=-24839.406J/mole=-24.83\times 10^3J/mole=-24.83kJ/mole](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-24839.406J%2Fmole%3D-24.83%5Ctimes%2010%5E3J%2Fmole%3D-24.83kJ%2Fmole)
Now we have to calculate the value of 'Q'.
The given balanced chemical reaction is,
![CO(g)+2H_2(g)\rightarrow CH_3OH(g)](https://tex.z-dn.net/?f=CO%28g%29%2B2H_2%28g%29%5Crightarrow%20CH_3OH%28g%29)
The expression for reaction quotient will be :
![Q=\frac{(p_{CH_3OH})}{(p_{CO})\times (p_{H_2})^2}](https://tex.z-dn.net/?f=Q%3D%5Cfrac%7B%28p_%7BCH_3OH%7D%29%7D%7B%28p_%7BCO%7D%29%5Ctimes%20%28p_%7BH_2%7D%29%5E2%7D)
In this expression, only gaseous or aqueous states are includes and pure liquid or solid states are omitted.
Now put all the given values in this expression, we get
![Q=\frac{(1.4)}{(1.2\times 10^{-2})\times (1.2\times 10^{-2})^2}](https://tex.z-dn.net/?f=Q%3D%5Cfrac%7B%281.4%29%7D%7B%281.2%5Ctimes%2010%5E%7B-2%7D%29%5Ctimes%20%281.2%5Ctimes%2010%5E%7B-2%7D%29%5E2%7D)
![Q=8.1\times 10^{5}](https://tex.z-dn.net/?f=Q%3D8.1%5Ctimes%2010%5E%7B5%7D)
Now we have to calculate the value of
by using relation (1).
![\Delta G_{rxn}=\Delta G^o+RT\ln Q](https://tex.z-dn.net/?f=%5CDelta%20G_%7Brxn%7D%3D%5CDelta%20G%5Eo%2BRT%5Cln%20Q)
Now put all the given values in this formula, we get:
![\Delta G_{rxn}=-24.83kJ/mole+(8.314\times 10^{-3}kJ/mole.K)\times (298K)\ln (8.1\times 10^{5})](https://tex.z-dn.net/?f=%5CDelta%20G_%7Brxn%7D%3D-24.83kJ%2Fmole%2B%288.314%5Ctimes%2010%5E%7B-3%7DkJ%2Fmole.K%29%5Ctimes%20%28298K%29%5Cln%20%288.1%5Ctimes%2010%5E%7B5%7D%29)
![\Delta G_{rxn}=8.867\times 10^3J/mole=8.867kJ/mole](https://tex.z-dn.net/?f=%5CDelta%20G_%7Brxn%7D%3D8.867%5Ctimes%2010%5E3J%2Fmole%3D8.867kJ%2Fmole)
Therefore, the value of
is, ![8.867kJ/mole](https://tex.z-dn.net/?f=8.867kJ%2Fmole)