# The heat of combustion of ethanol determined by a bomb calorimeter is -670.48 Kcal/mol at 25°C. What is $\Delta U$ at 25°C for the following reaction?$C_{2}H_{5}OH\left ( l \right )+ \frac{7}{2}O_{2}\left ( g \right )\rightarrow 2CO_{2}\left ( g \right )+ 3H_{2}O\left ( g \right )$ Option 1) -335.24 Kcal Option 2) -669.28 Kcal Option 3) -670.48 Kcal Option 4) + 670.48 Kcal

As learnt in

Enthalpy of combustion -

Amount of Enthalpy change when 1 mole of substance is completly burn in excess of Oxygen

- wherein

$CO_{(g)}+\frac{1}{2}O_{2}(g)\rightarrow CO_{2(g)}+283\ KJ$

$\Delta H_{comb} \: of\: CO= 283\, KJ$

Reversible and Irreversible Isochoric process -

$dV= 0$

- wherein

$W= -P_{ext}\, dV =0$

Bomb calorimeter works under constant volume conditions

Therefore, $\Delta u=-670.48 kcal$

Option 1)

-335.24 Kcal

Incorrect

Option 2)

-669.28 Kcal

Incorrect

Option 3)

-670.48 Kcal

correct

Option 4)

+ 670.48 Kcal

Incorrect

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