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Determine the standard enthalpy of formation of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) from its standard enthalpy of combustion \((-1367.4 \mathrm{~kJ} / \mathrm{mol})\)

Short Answer

Expert verified
The standard enthalpy of formation for ethanol \((C_{2}H_{5}OH)\) is \(-277.6 \, kJ/mol\).

Step by step solution

01

Write down the chemical reaction for the formation of ethanol

We start by writing the chemical equation for the formation of ethanol from its elements: \[ 2\, C (s) + 6\, H (g) + O (g) \to C_2H_5OH (g) \] Here carbon is in solid form, hydrogen is in gaseous form, and oxygen is in gaseous form as they are in their standard states.
02

Write down the chemical reaction for the combustion of ethanol

Next, we write the equation for the complete combustion of ethanol: \[ C_2H_5OH (g) + 3\, O_2 (g) \to 2\, CO_2 (g) + 3\, H_2O (g) \] This equation describes how a mole of ethanol (C2H5OH) reacts with oxygen to produce carbon dioxide and water.
03

Combine the formation and combustion reactions

We now use Hess's Law, which states that the total enthalpy change for a chemical reaction does not depend on the route by which the reaction is carried out. The combustion reaction can be viewed as the sum of the reverse formation reaction for ethanol and the formation reactions for the combustion products, carbon dioxide and water. So, we rearrange and add the equations as follows: \[ -[ 2\, C (s) + 6\, H (g) + O (g) \to C_2H_5OH (g) ] \] (We've reversed the first equation, indicating that we're considering the decomposition of ethanol into its elements rather than its formation.) \[ 2\, [ C (s) + O_2 (g) \to CO_2 (g) ] \] (The formation of two moles of carbon dioxide from carbon and oxygen.) \[ 3\, [ 2\, H_2 (g) + O_2 (g) \to 2\, H_2O (g) ] \] (The formation of three moles of water from hydrogen and oxygen.) Adding these equations results in the combustion reaction: \[ C_2H_5OH (g) + 3\, O_2 (g) \to 2\, CO_2 (g) + 3\, H_2O (g) \]
04

Calculate the standard enthalpy of formation of ethanol

Lastly, we use the standard enthalpies of formation for carbon dioxide (\(-393.5 \, kJ/mol\)) and water (\(-285.8 \, kJ/mol\)) to calculate the standard enthalpy of formation for ethanol. The standard enthalpy change for the combustion reaction equals the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants. Setting this equal to the given standard enthalpy of combustion for ethanol, we have: \[ -1367.4 \, kJ = [(2)(-393.5\, kJ) + (3)(-285.8\, kJ)] - [1\, \Delta H_f (C_2H_5OH)] \] Solving for \(\Delta H_f (C_2H_5OH)\), we find: \[ \Delta H_f (C_2H_5OH) = (2)(-393.5\, kJ) + (3)(-285.8\, kJ) + 1367.4 \, kJ = -277.6 \, kJ/mol \]

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Most popular questions from this chapter

The combustion of \(0.4196 \mathrm{~g}\) of a hydrocarbon releases \(17.55 \mathrm{~kJ}\) of heat. The masses of the products are \(\mathrm{CO}_{2}=1.419 \mathrm{~g}\) and \(\mathrm{H}_{2} \mathrm{O}=0.290 \mathrm{~g} .\) (a) What is the empirical formula of the compound? (b) If the approximate molar mass of the compound is \(76 \mathrm{~g}\), calculate its standard enthalpy of formation.

From the following heats of combustion, $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-726.4 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-393.5 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-285.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ calculate the enthalpy of formation of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) from its elements: \(\mathrm{C}\) (graphite) \(+2 \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\)

On what law is the first law of thermodynamics based? Explain the sign conventions in the equation \(\Delta E=q+w\)

A 2.10 -mole sample of crystalline acetic acid, initially at \(17.0^{\circ} \mathrm{C}\), is allowed to melt at \(17.0^{\circ} \mathrm{C}\) and is then heated to \(118.1^{\circ} \mathrm{C}\) (its normal boiling point) at 1.00 atm. The sample is allowed to vaporize at \(118.1^{\circ} \mathrm{C}\) and is then rapidly quenched to \(17.0^{\circ} \mathrm{C}\), so that it recrystallizes. Calculate \(\Delta H^{\circ}\) for the total process as described.

From these data, $$ \begin{aligned} \mathrm{S}(\text { rhombic })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) \\ \Delta H_{\mathrm{rxn}}^{\circ} &=-296.06 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{S}(\text { monoclinic })+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{SO}_{2}(g) \\ \Delta H_{\mathrm{rxn}}^{\circ} &=-296.36 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ calculate the enthalpy change for the transformation $$ S \text { (rhombic) } \longrightarrow \mathrm{S} \text { (monoclinic) } $$ (Monoclinic and rhombic are different allotropic forms of elemental sulfur.)

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