Question

A chemist fills a reaction vessel with 3.82 atm methanol (CH,OH) gas, 7.56 am oxygen (O2) gas, 5.29 atm carbon dioxide (CO2) gas, and 3.89 atm water (H0) gas at a temperature of 25.0°C. Under these conditions, calculate the reaction free energy AG for the following chemical reaction: 2CH, OH() + 30266) 2002) + 4H20) Use the thermodynamic information in the ALEKS Data tab. Round your answer to the nearest kilojoule. x 5 ?

Answer 1

Answer: The Gibbs free energy of the given reaction is
`1.379* 10^3kJ`

Step-by-step explanation:

The equation used to calculate Gibbs free energy change is of a reaction is:

`\Delta G^o_(rxn)=\sum [n* \Delta G^o_f_((product))]-\sum [n* \Delta G^o_f_((reactant))]`

For the given chemical reaction:

`2CH_3OH(g)+3O_2(g)\rightarrow 2CO_2(g)+4H_2O(g)`

The equation for the Gibbs free energy change of the above reaction is:

`\Delta G^o_(rxn)=[(2* \Delta G^o_f_((CO_2(g))))+(4* \Delta G^o_f_((H_2O(g))))]-[(2* \Delta G^o_f_((CH_3OH(g))))+(3* \Delta G^o_f_((O_2(g))))]`

We are given:

`\Delta G^o_f_((H_2O(g)))=-228.57kJ/mol\\\Delta G^o_f_((CO_2(g)))=-394.36kJ/mol\\\Delta G^o_f_((CH_3OH(g)))=-161.96kJ/mol\\\Delta G^o_f_((O_2(g)))=0kJ/mol`

Putting values in above equation, we get:

`\Delta G^o_(rxn)=[(2* (-394.36))+(4* (-228.57))]-[(2* (-161.96))+(3* (0))]\\\\\Delta G^o_(rxn)=-1379.08kJ/mol`

The equation used to Gibbs free energy of the reaction follows:

`\Delta G=\Delta G^o+RT\ln Q_(p)`

where,

`\Delta G` = free energy of the reaction

`\Delta G^o` = standard Gibbs free energy = -1379.08 kJ/mol = -1379080 J/mol (Conversion factor: 1 kJ = 1000 J)

R = Gas constant = 8.314 J/K mol

T = Temperature =
`25^oC=[273+25]K=298K`

`Q_(p)` = Ratio of concentration of products and reactants =
`((p_(CO_2))^2(p_(H_2O))^4)/((p_(CH_3OH))^2(p_(O_2))^3)`

`p_(CO_2)=5.29atm\\p_(H_2O)=3.89atm\\p_(CH_3OH)=3.82atm\\p_(O_2)=7.56atm`

Putting values in above expression, we get:

`\Delta G=-1379080J/mol+(8.314J/K.mol* 298K* \ln (((5.29)^2* (3.89)^4)/((3.82)^2* (7.56)^3)))\\\\\Delta G=-1379039J=1379.039kJ=1.379* 10^3kJ`

Hence, the Gibbs free energy of the given reaction is
`1.379* 10^3kJ`