Question

The value of$\mathbf{∆}\mathbf{G}\mathbf{°}$for the reaction $\mathbf{2}{\mathbf{C}}_{\mathbf{4}}{\mathbf{H}}_{\mathbf{10}}\left(g\right)\mathbf{+}\mathbf{13}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{8}{\mathbf{CO}}_{\mathbf{2}}\left(g\right)\mathbf{+}\mathbf{10}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(I\right)\mathbf{}\mathbf{is}\mathbf{}\mathbf{-}\mathbf{5490}\mathbf{.}\mathbf{KJ}$Use this value and data from appendix 4 to calculate the standard free energy of formation for ${\mathbf{C}}_{\mathbf{4}}{\mathbf{H}}_{\mathbf{10}}\left(g\right)$

Short answer

Answer

The standard free energy change of formation for C₄H₁₀(g) is 16kJ/mol

Step-by-step solution

Definition of standard free energy

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 fee energy

Calculate the standard free energy

$2{\mathrm{C}}_4{\mathrm{H}}_{10}\left(\mathrm{g}\right)+13{\mathrm{O}}_2\left(\mathrm{g}\right)\to 8{\mathrm{CO}}_2\left(\mathrm{g}\right)+10{\mathrm{H}}_2\mathrm{O}\left(\mathrm{I}\right)$

Based on the equation,

$∆{\mathrm{G}}_{\mathrm{R}}^{°}=\left[8∆{\mathrm{G}}_{\mathrm{f}}^{°}\left({\mathrm{CO}}_2\left(\mathrm{g}\right)+10∆{\mathrm{G}}_{\mathrm{f}}^{°}\left({\mathrm{H}}_2\mathrm{O}\right)\left(\mathrm{I}\right)\right)\right]-\left[2∆{\mathrm{G}}_{\mathrm{f}}^{°}\left({\mathrm{C}}_4{\mathrm{H}}_{10}\left(\mathrm{g}\right)\right)+13∆{\mathrm{G}}_{\mathrm{f}}^{°}\left({\mathrm{O}}_2\left(\mathrm{g}\right)\right)\right]$

-5490 = -3152-2370-$2∆{\mathrm{G}}_{\mathrm{f}}^{°}\left({\mathrm{C}}_4{\mathrm{H}}_{10}\left(\mathrm{g}\right)\right)+0$

$∆{\mathrm{G}}_{\mathrm{f}}^{°}\left({\mathrm{C}}_4{\mathrm{H}}_{10}\left(\mathrm{g}\right)\right)=-16\mathrm{kJ}/\mathrm{mol}$

The standard free energy change of formation for${\mathrm{C}}_4{\mathrm{H}}_{10}\left(\mathrm{g}\right)\mathrm{is}16\mathrm{kJ}/\mathrm{mol}$