Question

From data in Appendix 4, calculate $∆\mathrm{H}°,∆\mathrm{S}°\mathrm{and}∆\mathrm{G}°$for each of the following reactions at$25°\mathrm{C}$

Short answer

Answer

a. Standard free energy $∆G_{298}^{°}=-801kJ/mol$

Standard free entropy$∆{\mathrm{S}}_{298}^{°}=-4\mathrm{J}/\mathrm{Kmol}$

Standard free enthalpy$∆{\mathrm{H}}_{298}^{°}=-802.5\mathrm{kJ}/\mathrm{mol}$

b. Standard free energy$∆{\mathrm{G}}_{298}^{°}=2875\mathrm{kJ}/\mathrm{mol}$

Standard free entropy $∆{\mathrm{S}}_{298}^{°}=-262\mathrm{J}/\mathrm{Kmol}$

Standard free enthalpy $∆{\mathrm{H}}_{298}^{°}=2802\mathrm{kJ}/\mathrm{mol}$

c. Standard free energy $∆{\mathrm{G}}_{298}^{°}=-356\mathrm{kJ}/\mathrm{mol}$

Standard free entropy$∆{\mathrm{S}}_{298}^{°}=-209\mathrm{J}/\mathrm{Kmol}$

Standard free enthalpy $∆{\mathrm{H}}_{298}^{°}=-416\mathrm{kJ}/\mathrm{mol}$

d. Standard free energy $∆{\mathrm{G}}_{298}^{°}=-91\mathrm{kJ}/\mathrm{mol}$

Standard free entropy $∆{\mathrm{S}}_{298}^{°}=-284\mathrm{J}/\mathrm{Kmol}$

Standard free enthalpy$∆{\mathrm{H}}_{298}^{°}=-176\mathrm{kJ}/\mathrm{mol}$

Step-by-step solution

Definition of Standard free energy, Standard enthalpy and Standard entropy

The free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under standard conditions is defined as standard free energy

A measure of the energy released or consumed when one mole of a substance is created under standard conditions from its pure elements is defined as Standard enthalpy

The standard entropy is its entropy at 1 atm pressure

Calculation of ∆H°, ∆S° and ∆G° for reaction at  25°C

a. The reaction is ${\mathrm{CH}}_4\left(\mathrm{g}\right)+2{\mathrm{O}}_2\to {\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

The mathematical expression for standard free energy at room temperature is

The mathematical expression for standard free energy at room temperature is

b. The reaction is ${\text{6CO}}_2\text{(g)}+{\text{6H}}_2\text{O(l)}\to {\text{C}}_6{\text{H}}_{12}{\text{O}}_6\text{(s)}+6{\text{O}}_{\text{2}}\text{(g)}$

The mathematical expression for standard free energy at room temperature is

The mathematical expression for standard free energy at room temperature is

The mathematical expression for standard free energy at room temperature is

c. The reaction is ${\mathrm{CH}}_4\left(\mathrm{g}\right)+2{\mathrm{CO}}_2\to {\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

The mathematical expression for standard free energy at room temperature is

The mathematical expression for standard free energy at room temperature is

The mathematical expression for standard free energy at room temperature is

d. The reaction is ${\mathrm{CH}}_4\left(\mathrm{g}\right)+2{\mathrm{O}}_2\to {\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

The mathematical expression for standard free energy at room temperature is

The mathematical expression for standard free energy at room temperature is

The mathematical expression for standard free energy at room temperature is