Chemistry - Thermochemistry Question with Solution | TestHub

We have to find $2{\mathrm{C}}_{(\mathrm{s})}+{\mathrm{H}}_{2(\mathrm{g})}⟶{\mathrm{C}}_2{\mathrm{H}}_{2(\mathrm{g})}\Delta \mathrm{H}=?$ This is the equation for formation of acelytene Given $2{\mathrm{C}}_{(\mathrm{s})}+2{\mathrm{O}}_{2(\mathrm{g})}⟶2{\mathrm{CO}}_{2(\mathrm{g})};\Delta \mathrm{H}=-787\mathrm{kJ}$ ...(1) ${\mathrm{H}}_{2(\mathrm{g})}+\frac{1}{2}{\mathrm{O}}_{2(\mathrm{g})}⟶{\mathrm{H}}_2{\mathrm{O}}_{(\ell )};\Delta \mathrm{H}=-286\mathrm{kJ}$ ...(2) $\begin{array}{rl}{\mathrm{C}}_2{\mathrm{H}}_{2(\mathrm{g})}+2\frac{1}{2}{\mathrm{O}}_{2(\mathrm{g})}& \\ & ⟶2{\mathrm{CO}}_{2(\mathrm{g})}+{\mathrm{H}}_2{\mathrm{O}}_{(\ell )}\\ & \Delta \mathrm{H}=-1310\mathrm{kJ}...(3)\end{array}$ Addeq.(1) and (2) $\begin{array}{l}2{\mathrm{C}}_{(\mathrm{s})}+{\mathrm{H}}_{2(\mathrm{g})}+2\frac{1}{2}{\mathrm{O}}_{2(\mathrm{g})}⟶2{\mathrm{CO}}_{2(\mathrm{g})}\\ +{\mathrm{H}}_2{\mathrm{O}}_{(\ell )};\Delta \mathrm{H}=-1073\mathrm{kJ}...(4)\end{array}$ Subtract eq. (3) form eq. (4) we get $\begin{array}{l}2{\mathrm{C}}_{(\mathrm{s})}+{\mathrm{H}}_{2(\mathrm{g})}⟶{\mathrm{C}}_2{\mathrm{H}}_{2(\mathrm{g})}\\ \Delta \mathrm{H}=+237\mathrm{kJ}\end{array}$