Question

Question : Given the following data:

$$\begin{gathered} {\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}\left(g\right)\mathbf{}\mathbf{+}\mathbf{}\mathbf{5}\mathbf{/}\mathbf{2}{\mathbf{O}}_{\mathbf{2}}\mathbf{g}\mathbf{}\mathbf{\to }\mathbf{}\mathbf{}\mathbf{2}{\mathbf{CO}}_{\mathbf{2}}\mathbf{}\mathbf{g}\mathbf{}\mathbf{+}\mathbf{}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{}\mathbf{∆}\mathbf{H}\mathbf{=}\mathbf{-}\mathbf{1300}\mathbf{}\mathbf{kJ} \\ \mathbf{C}\left(s\right)\mathbf{}\mathbf{+}\mathbf{}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{}\mathbf{\to }\mathbf{}{\mathbf{CO}}_{\mathbf{2}}\left(g\right)\mathbf{}\mathbf{∆}\mathbf{H}\mathbf{=}\mathbf{-}\mathbf{394}\mathbf{kJ} \\ {\mathbf{H}}_{\mathbf{2}}\left(g\right)\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}\mathbf{/}\mathbf{2}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{}\mathbf{\to }\mathbf{}\mathbf{}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(l\right)\mathbf{}\mathbf{∆}\mathbf{H}\mathbf{=}\mathbf{-}\mathbf{286}\mathbf{}\mathbf{kJ} \end{gathered}$$

Calculate ∆H for the reaction

$\mathbf{2}\mathbf{C}\left(s\right)\mathbf{}\mathbf{+}\mathbf{}{\mathbf{H}}_{\mathbf{2}}\left(g\right)\mathbf{}\mathbf{\to }\mathbf{}{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}\left(g\right)$

Short answer

∆H for the reaction = 226 kJ

Step-by-step solution

Reverse equation no. 1

$2{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{C}}_2{\mathrm{H}}_{2\left(\mathrm{g}\right)}+\frac{5}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)∆\mathrm{H}=1300\mathrm{kJ}$

Reverse equation no. 2 and multiply by 2

${\text{2C+2O}}_{\text{2}}\to {\text{2CO}}_{\text{2}}\text{ΔH=2×394=788kJ}$

Write and solve equations by Hess law

$\begin{array}{l}{\text{2CO}}_{\text{2}}{\text{+H}}_{\text{2}}\text{O}\to {\mathrm{C}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{g}\right)\text{+}\frac{\text{5}}{\text{2}}{\text{O}}_{\text{2}}\left(\text{g}\right)\text{ΔH=1300kJ}\\ {\text{2C+2O}}_{\text{2}}\to {\text{2CO}}_{\text{2}}\text{ΔH=2×394=788kJ}\\ {\text{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\text{ΔH=-286kJ}\\ \text{2C}\left(\text{s}\right){\text{+H}}_{\text{2}}\left(\text{g}\right)\to {\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\left(\text{g}\right)\text{ΔH=226kJ}\end{array}$