Gibbs free energy and spontaneity (8296)

, por F_y_Q

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The standard enthalpy of reaction between methane and dichlorine to produce chloromethane and hydrogen chloride is -114\ kJ\cdot mol^{-1}. Knowing the standard entropy change is 11.1\ J\cdot K^{-1}\cdot mol^{-1}, calculate the standard Gibbs free energy change at a given temperature, and determine if the process is spontaneous under these conditions.

P.-S.

The reaction to be studied is:

\color[RGB]{2,112,20}{\textbf{\ce{CH4(g) + Cl2(g) -> CH3Cl(g) + HCl(g)}}}

The expression to calculate the Gibbs free energy is:

\color[RGB]{2,112,20}{\bm{\Delta G^0 = \Delta H^0 - T\Delta S^0}}

Simply substitute the values provided in the statement, considering that the enthalpy is given in kJ, and perform the calculation:

\Delta G^0 = - 114\cdot 10^3\ \frac{J}{mol} - 298\ \cancel {K}\cdot 11.1\ \frac{J}{\cancel {K}\cdot mol} = \fbox{\color[RGB]{192,0,0}{\bm{-1.17\cdot 10^5\frac {J}{mol}}}}