Complete combustion of 1 mol of acetone \(\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)\) liberates \(1790 \mathrm{kJ} :\) $$\begin{aligned} \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l)+4 \mathrm{O}_{2}(g) \longrightarrow & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) \\ & \quad \quad \quad \quad \quad \quad \quad \Delta H^{\circ}=-1790 \mathrm{kJ} \end{aligned}$$ Using this information together with the standard enthalpies of formation of \(\mathrm{O}_{2}(g), \mathrm{CO}_{2}(g),\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) from Appendix \(\mathrm{C},\) calculate the standard enthalpy of formation of acetone.

Short Answer

Expert verified
The standard enthalpy of formation of acetone is -1380.9 kJ/mol.

Step by step solution

01

Write the equations for the standard enthalpies of formation

The standard enthalpies of formation are the enthalpies required to form 1 mol of a substance from its elements in their standard states. The equation for the formation of acetone is: \(C(s) + 3H_2(g) + \frac{1}{2}O_2(g) \to C_{3}H_{6}O(l)\) The equations for the formation of CO2 and H2O are: \(C(s) + O_2(g) \to CO_{2}(g)\) \(H_2(g) + \frac{1}{2}O_2(g) \to H_{2}O(l)\)
02

Determine the ∆H°f for CO2 and H2O

The standard enthalpies of formation for CO2(g) and H2O(l) can be found in Appendix C. Using this information, we have: ∆H°f(CO2(g))=-393.5 kJ/mol ∆H°f(H2O(l))=-285.8 kJ/mol
03

Set up the Hess's Law equation

Hess's Law states that the total enthalpy change for a reaction is the sum of the individual enthalpy changes for each step in the reaction. For the given problem, we can write the Hess's Law equation using the balanced equation of acetone combustion and the standard enthalpies of formation, as follows: \(\Delta H_{combustion}^{°} = 3\Delta H_{f(CO2(g))}^° + 3\Delta H_{f(H2O(l))^° − (\Delta H_{f(acetone)}^° + 4\Delta H_{f(O2(g))}^°)\) We know that, for O2(g), ∆H°f = 0 kJ/mol, since it is an element in its standard state. So we can simplify the equation: \(\Delta H_{combustion}^{°} = 3\Delta H_{f(CO2(g))}^° + 3\Delta H_{f(H2O(l))^° − \Delta H_{f(acetone)}^°\)
04

Calculate the ∆H°f of acetone

Now, plug in the known values and solve for the standard enthalpy of formation of acetone: \(-1790 kJ/mol = 3(-393.5 kJ/mol) + 3(-285.8 kJ/mol) – \Delta H_{f(acetone)}^°\) Solve the equation for ∆H°f(acetone): \(\Delta H_{f(acetone)}^° = 3(-393.5 kJ/mol) + 3(-285.8 kJ/mol) + 1790 kJ/mol\) \(\Delta H_{f(acetone)}^° = -1380.9 kJ/mol\) So, the standard enthalpy of formation of acetone is -1380.9 kJ/mol.

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Most popular questions from this chapter

(a) What is meant by the term standard conditions with reference to enthalpy changes? (b) What is meant by the term enthalpy of formation? (c) What is meant by the term standard enthalpy of formation?

Write balanced equations that describe the formation of the following compounds from elements in their standard states, and then look up the standard enthalpy of formation for each substance in Appendix C: (a) \(\mathrm{H}_{2} \mathrm{O}_{2}(g),(\mathbf{b}) \mathrm{CaCO}_{3}(s)\) (c) \(\mathrm{POCl}_{3}(l),(\mathbf{d}) \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) .\)

(a) When a 0.235 -g sample of benzoic acid is combusted in a bomb calorimeter (Figure 5.19\()\) , the temperature rises \(1.642^{\circ} \mathrm{C} .\) When a \(0.265-\mathrm{g}\) sample of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) is burned, the temperature rises \(1.525^{\circ} \mathrm{C} .\) Using the value 26.38 \(\mathrm{kJ} / \mathrm{g}\) for the heat of combustion of benzoic acid, calculate the heat of combustion per mole of caffeine at constant volume. (b) Assuming that there is an uncertainty of \(0.002^{\circ} \mathrm{C}\) in each temperature reading and that the masses of samples are measured to \(0.001 \mathrm{g},\) what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

The Sun supplies about 1.0 kilowatt of energy for each square meter of surface area \(\left(1.0 \mathrm{kW} / \mathrm{m}^{2},\) where a watt \(=1 \mathrm{J} / \mathrm{s}\right)\) Plants produce the equivalent of about 0.20 \(\mathrm{g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) per hour per square meter. Assuming that the sucrose is produced as follows, calculate the percentage of sunlight used to produce sucrose. $$\begin{array}{c}{12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+12 \mathrm{O}_{2}(g)} \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad {\Delta H=5645 \mathrm{kJ}}\end{array}$$

Consider the following reaction: $$2 \mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \quad \Delta H=+252.8 \mathrm{kJ}$$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when 24.0 of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) is decomposed by this reaction at constant pressure. (c) For a given sample of \(\mathrm{CH}_{3} \mathrm{OH},\) the enthalpy change during the reaction is 82.1 kJ. How many grams of methane gas are produced? (\mathbf{d} ) How many kilojoules of heatare released when 38.5 \(\mathrm{g}\) of \(\mathrm{CH}_{4}(g)\) reacts completely with \(\mathrm{O}_{2}(g)\) to form \(\mathrm{CH}_{3} \mathrm{OH}(g)\) at constant pressure?

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