The heat of combustion \(\left(\Delta H_{c}^{\theta}\right)\) is the heat liberated when one mole of an element or compound is burnt completely in excess oxygen. When a substance undergoes combustion, it loses heat \((q)\) which causes a rise in the temperature \((\Delta Q)\) of water in the calorimeter. If \(m\) is the mass of water in calorimeter, then
\(q=m c \Delta \theta\)
where \(c\) - specific heat capacity of wateror the question,
\(q=? m=100 g , c=4.2 Jg ^{-1} c ^{-1}\)
\(\Delta \theta=30^{\circ} C\)
\(\therefore q=100 \times 4.2 \times 30=12.6 kJ\)
\(M_{C_{2} H_{3} O H}=(2 \times 12)+(1 \times 5)+16+1=46 g / mol\)
No of mole of burnt ethanol \(\left( C _{2} H _{5} OH \right)\)
\(=\frac{0.40 g }{46 g / mol }=0.01 mol\)
\(\therefore 0.01 mol\) released \(12.6 kJ\)
\(1 mol\) will release \(=\frac{1 mol \times 12.6 kJ }{0.01 mol }\)
\(=1260 kJ\)
Hence, the heat of combustion is \(1260 kJmol ^{-1}\).