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# The enthalpies of combustion of cyclohexane, cyclohexene and ${H_2}$​ are respectively$- 3920$,$- 3800$ and $- 241$ $kJ{\text{ }}mo{l^{ - 1}}$. The heat of hydrogenation of cyclohexene is:A.$- 121kJ/mol$B.$121{\text{ }}kJ/mol$C.$- 242{\text{ }}kJ/mol$D.$242{\text{ }}kJ/mol$

Last updated date: 19th Sep 2024
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Hint: According to the cycle of heat combustion, in a profoundly temperature exothermic redox substance reaction between a reductant and an oxidant, a combustion happens in which a lot of heat and light energy are delivered. This reaction is known as quick combustion.

Heat of hydrogenation ( $\Delta {H_{hydro}}$, ) of an alkene is the standard enthalpy of catalytic hydrogenation of an alkene. Catalytic hydrogenation of an alkene is consistently exothermic. Along these lines, the heat of hydrogenation of alkenes is consistently negative.
Enthalpy is an ability to reflect to accomplish non-mechanical work and furthermore mirror the ability to deliver heat. It is a thermodynamic property. Enthalpy is the amount of the inward energy of a framework added to the result of the pressing factor and its volume. It’s symbol is $H$. The formula utilized is appeared as below:
$- H = E + PV$
Here, $H{\text{ }} =$enthalpy, $E{\text{ }} =$inner energy of the framework, $P{\text{ }} =$pressure and $V{\text{ }} =$volume
Presently, $dH = TdS + PdV$
The necessary reaction is appeared as below:
${C_6}{H_{10}} + {H_2} \to {C_6}{H_{12}}...(1)$
Allow us to specify the given realities
${H_2} + \dfrac{1}{2}{O_2} \to {H_2}O...(2)$
$\Delta {H_2} = - 241kJ/mol$
${C_6}{H_{10}} + \dfrac{{17}}{2}{O_2} \to 6C{O_2} + 5{H_2}O...(3)$
$\Delta {H_4} = - 3800kJ/mol$
${C_6}{H_{12}} + 9{O_2} \to 6C{O_2} + 6{H_2}O...(4)$
$\Delta {H_4} = - 3920kJ/mol$
The necessary reaction ($1$) can be acquired by adding condition ($2$) and ($3$), and deducting ($4$) from the amount of ($2$) and ($3$).
${C_6}{H_{10}} + {H_2} \to {C_6}{H_{12}}$
Heat of hydrogenation $= {\Delta _c}\;\left( {cyclohexene} \right){\text{ }} + \;{\Delta _c}({H_2}) - {\Delta _c}\;\left( {cyclohexane} \right)$
$\Delta {H_1} = (\Delta {H_2} + \Delta {H_3}) - \Delta {H_4}$
$= {\text{ }}\left[ { - 241 + \left( { - 3800} \right)} \right]{\text{ }} - {\text{ }}\left( { - 3920} \right)$
$= {\text{ }}\left( { - 241 - 3800} \right){\text{ }}-{\text{ }}\left( { - 3920} \right)$
$= {\text{ }} - 4041{\text{ }} + {\text{ }}3920$
$= {\text{ }} - 121{\text{ }}kJ/mol$
In this way, the heat of hydrogenation of cyclohexene is $- 121{\text{ }}kJ/mol$.
The correct option is ($A$) $- 121{\text{ }}kJ/mol$.

Note:
Enthalpy of hydrogenation is characterized as the adjustment in enthalpy, which happens when one mole of an unsaturated compound responds with an overabundance of hydrogen to turn out to be completely soaked at air pressing factor and room temperature, the reactants and items being in their characteristic states under these conditions. This is the enthalpy change that happens during catalytic hydrogenation. It is utilized to think about the steadiness of $pi -$ bonded atoms, and as a test of alkene security.