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Chapter 5: Problem 79

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is blended with gasoline as an automobile fuel. (a) Write a balanced equation for the combustion of liquid ethanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming \(\mathrm{H}_{2} \mathrm{O}(g)\) as a product. (c) Calculate the heat produced per liter of ethanol by combustion of ethanol under constant pressure. Ethanol has a density of $0.789 \mathrm{~g} / \mathrm{mL}$. (d) Calculate the mass of \(\mathrm{CO}_{2}\) produced per kJ of heat emitted.

Short Answer

Expert verified
(a) The balanced equation for the combustion of liquid ethanol in air is: \(C_2H_5OH (l) + 3O_2 (g) ⟶ 2CO_2 (g) + 3H_2O (g)\) (b) The standard enthalpy change for the reaction is -1366.9 kJ/mol. (c) The heat produced per liter of ethanol under constant pressure is approximately -23414 kJ/liter. (d) The mass of \(\mathrm{CO}_{2}\) produced per kJ of heat emitted is approximately 0.064 g CO2 / kJ.

Step by step solution

01

(a) Balanced Equation for Combustion of Ethanol

: For the complete combustion of ethanol in air (oxygen), the products formed are carbon dioxide and water. The balanced equation for this reaction is: \(C_2H_5OH (l) + 3O_2 (g) ⟶ 2CO_2 (g) + 3H_2O (g)\)
02

(b) Calculate standard enthalpy change for the reaction

: To calculate the standard enthalpy change for the reaction, we can use the following formula: ΔH° = ΣnΔH°f[products] - ΣmΔH°f[reactants], where ΔH° is the standard enthalpy change, ΔH°f is the standard enthalpy of formation, and n and m are the stoichiometric coefficients of the products and reactants, respectively. Using the standard enthalpy of formation values: ΔH°f(C2H5OH) = -277.7 kJ/mol, ΔH°f(O2) = 0 kJ/mol, ΔH°f(CO2) = -393.5 kJ/mol, and ΔH°f(H2O) = -241.8 kJ/mol, We can calculate the standard enthalpy change: ΔH° = [(2 × (-393.5)) + (3 × (-241.8))] - [(-277.7) + (0)] ΔH° = -1366.9 kJ/mol.
03

(c) Calculate heat produced per liter of ethanol

: First, we need to find the mass of ethanol in one liter. Using the density of ethanol: Mass of ethanol = Density × volume = 0.789 g/mL × 1000 mL = 789 g Now, we need to find the moles of ethanol: Moles of ethanol = mass / molar mass = 789 g / (2 × 12.01g/mol + 6 × 1.01g/mol + 1 × 16.00g/mol) = 789 g / 46.08 g/mol ≈ 17.13 mol Next, we multiply the moles of ethanol by the molar enthalpy change to find the heat produced: Heat produced = Moles × ΔH° = 17.13 mol × (-1366.9 kJ/mol) ≈ -23414 kJ/liter
04

(d) Calculate mass of CO2 produced per kJ of heat emitted

: We will first find the number of moles of CO2 produced per mole of ethanol. From the balanced equation, we deduce that 2 moles of CO2 are produced for every mole of ethanol: Moles of CO2 = Moles of ethanol × (2 moles CO2 / 1 mole C2H5OH) = 17.13 mol × 2 = 34.26 mol Now, we will find the mass of CO2 produced: Mass of CO2 = moles × molar mass = 34.26 mol × (12.01 g/mol + 2 × 16.00 g/mol) = 34.26 mol × 44.01 g/mol ≈ 1507.5 g Lastly, we can find the mass of CO2 produced per kJ of heat emitted: Mass of CO2 / kJ of heat = 1507.5 g / 23414 kJ ≈ 0.064 g CO2 / kJ

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Most popular questions from this chapter

Consider the following reaction: $$ 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) \quad \Delta H=-1204 \mathrm{~kJ} $$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when \(3.55 \mathrm{~g}\) of \(\mathrm{Mg}(s)\) reacts at constant pressure. (c) How many grams of \(\mathrm{MgO}\) are produced during an enthalpy change of \(-234 \mathrm{~kJ}\) ? (d) How many kilojoules of heat are absorbed when \(40.3 \mathrm{~g}\) of \(\mathrm{MgO}(s)\) is decomposed into \(\mathrm{Mg}(s)\) and \(\mathrm{O}_{2}(g)\) at constant pressure?

Indicate which of the following is independent of the path by which a change occurs: (a) the change in potential energy when a book is transferred from table to shelf, (b) the heat evolved when a cube of sugar is oxidized to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g),(\mathbf{c})\) the work accomplished in burning a gallon of gasoline.

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) $$ Calculate the \(\Delta H^{\circ}\) for this reaction using the following thermochemical data: $$ \begin{aligned} \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-890.3 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-571.6 \mathrm{~kJ} \\ 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-3120.8 \mathrm{~kJ} \end{aligned} $$

Three hydrocarbons that contain four carbons are listed here, along with their standard enthalpies of formation: $$ \begin{array}{llc} \hline \text { Hydrocarbon } & \text { Formula } & \Delta H_{f}^{0}(\mathrm{~kJ} / \mathrm{mol}) \\ \hline \text { Butane } & \mathrm{C}_{4} \mathrm{H}_{10}(g) & -125 \\ \text { 1-Butene } & \mathrm{C}_{4} \mathrm{H}_{8}(g) & -1 \\ \text { 1-Butyne } & \mathrm{C}_{4} \mathrm{H}_{6}(g) & 165 \\ \hline \end{array} $$ (a) For each of these substances, calculate the molar enthalpy of combustion to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) (b) Calculate the fuel value, in \(\mathrm{kJ} / \mathrm{g}\), for each of these compounds. (c) For each hydrocarbon, determine the percentage of hydrogen by mass. (d) By comparing your answers for parts (b) and (c), propose a relationship between hydrogen content and fuel value in hydrocarbons.

Suppose an Olympic diver who weighs \(52.0 \mathrm{~kg}\) executes a straight dive from a 10 -m platform. At the apex of the dive, the diver is $10.8 \mathrm{~m}$ above the surface of the water. (a) What is the potential energy of the diver at the apex of the dive, relative to the surface of the water? (b) Assuming that all the potential energy of the diver is converted into kinetic energy at the surface of the water, at what speed, in $\mathrm{m} / \mathrm{s}$, will the diver enter the water? (c) Does the diver do work on entering the water? Explain.
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