Chemistry - Thermodynamics - I Question with Solution | TestHub

${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{O}{\mathrm{H}}_{\left(\mathrm{l}\right)}+3{\mathrm{O}}_{2\left(\mathrm{g}\right)}\to 2\mathrm{C}{\mathrm{O}}_{2\left(\mathrm{g}\right)}+3{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{l}\right)}$…(i)
0.138 kg of ethanol$\equiv \frac{138\mathrm{g}}{46\mathrm{g}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}}=3$moles
By multiplying equation (i) by 3, we get
$3{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{O}{\mathrm{H}}_{\left(\mathrm{l}\right)}+9{\mathrm{O}}_{2\left(\mathrm{g}\right)}\to 6\mathrm{C}{\mathrm{O}}_{2\left(\mathrm{g}\right)}+9{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{l}\right)}$
$\mathrm{\Delta }{\mathrm{n}}_{\mathrm{g}}=6-9=3$
$\mathrm{w}=-\mathrm{P}\mathrm{\Delta }\mathrm{V}$
$\mathrm{w}=-\mathrm{\Delta }{\mathrm{n}}_{\mathrm{g}}\mathrm{R}\mathrm{T}=-(-3)\times 8.314\times 300$$(\because \mathrm{P}\mathrm{V}=\mathrm{n}\mathrm{R}\mathrm{T})$
$=7482.6$J