| Specific Energy, Heat of Combustion (per Mass) Converter. How much heat is produced by the combustion of 125 g of acetylene? (The engine is able to keep the car moving because this process is repeated many times per second while the engine is running.) We also can use Hess’s law to determine the enthalpy change of any reaction if the corresponding enthalpies of formation of the reactants and products are available. The direct process is written: \[\ce{C}_{(s)}+\ce{O}_{2(g)}⟶\ce{CO}_{2(g)}\;\;\;ΔH^∘_{298}=\mathrm{−394\;kJ} \label{ 5.4.11}\]. \(\mathrm{7.19\:\cancel{g}×\dfrac{1\:mol}{122.5\:\cancel{g}}=0.0587\:mol\:KClO_3}\) available. When 1.42 g of iron reacts with 1.80 g of chlorine, 3.22 g of \(\ce{FeCl}_{2(s)}\) and 8.60 kJ of heat is produced. Some of this energy is given off as heat, and some does work pushing the piston in the cylinder. Table \(\PageIndex{1}\) gives this value as −5460 kJ per 1 mole of isooctane (C8H18). Before we further practice using Hess’s law, let us recall two important features of ΔH. Reactants \(\frac{1}{2}\ce{O2}\) and \(\frac{1}{2}\ce{O2}\) cancel out product O2; product \(\frac{1}{2}\ce{Cl2O}\) cancels reactant \(\frac{1}{2}\ce{Cl2O}\); and reactant \(\dfrac{3}{2}\ce{OF2}\) is cancelled by products \(\frac{1}{2}\ce{OF2}\) and OF2. &\frac{1}{2}\ce{Cl2O}(g)+\dfrac{3}{2}\ce{OF2}(g)⟶\ce{ClF3}(g)+\ce{O2}(g)&&ΔH°=\mathrm{−266.7\:kJ}\\ &\mathrm{1.00\:L\:\ce{C8H18}⟶1.00×10^3\:mL\:\ce{C8H18}}\\ We can write this reaction as the sum of the decompositions of 3NO2(g) and 1H2O(l) into their constituent elements, and the formation of 2 HNO3(aq) and 1 NO(g) from their constituent elements. ), The enthalpy changes for many types of chemical and physical processes are available in the reference literature, including those for combustion reactions, phase transitions, and formation reactions. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. A reaction equation with \(\frac{1}{2}\) mole of N2 and 1 mole of O2 is correct in this case because the standard enthalpy of formation always refers to 1 mole of product, NO2(g). Because the CO produced in Step 1 is consumed in Step 2, the net change is: \[\ce{C}_{(s)}+\ce{O}_{2(g)}⟶\ce{CO}_{2(g)} \label{5.4.15}\]. Algae can yield 26,000 gallons of biofuel per hectare—much more energy per acre than other crops. (b) Combustion of compounds CH 4 (g) + O 2 (g) → CO 2 (g) + 2H 2 O(l) When 1 mole of methane burns completely in oxygen to form carbon dioxide and water, 890 kJ of heat is released. Emerging Algae-Based Energy Technologies (Biofuels). & The following conventions apply when we use \(ΔH\): \[\begin {align*} &\textrm{(two-fold increase in amounts)}\label{5.4.7}\\ &\ce{2H2}(g)+\ce{O2}(g)⟶\ce{2H2O}(l)\hspace{20px}ΔH=\mathrm{2×(−286\:kJ)=−572\:kJ}\\ &\textrm{(two-fold decrease in amounts)}\\ &\frac{1}{2}\ce{H2}(g)+\dfrac{1}{4}\ce{O2}(g)⟶\frac{1}{2}\ce{H2O}(l)\hspace{20px}ΔH=\mathrm{\frac{1}{2}×(−286\:kJ)=−143\:kJ} \end {align*} \label{5.4.6B}\], \[\ce{ H2(g) + 1/2 O2(g) ⟶ H2O(g)} \;\;\; ΔH=\ce{−242\:kJ} \label{5.4.7B}\], Example \(\PageIndex{1}\): Measurement of an Enthalpy Change. We are trying to find the standard enthalpy of formation of FeCl3(s), which is equal to ΔH° for the reaction: \[\ce{Fe}(s)+\frac{3}{2}\ce{Cl2}(g)⟶\ce{FeCl3}(s)\hspace{20px}ΔH^\circ_\ce{f}=\:? This ratio, \[\mathrm{\dfrac{−2.9 \; kJ}{0.0500\; mol\; HCl}} \nonumber\]. \[\ce{H2}(g)+\ce{Cl2}(g)⟶\ce{2HCl}(g)\hspace{20px}ΔH^\circ_{298}=\mathrm{−184.6\:kJ}\nonumber\], Example \(\PageIndex{5}\): Writing Reaction Equations for \(ΔH^\circ_\ce{f}\). However, we often find it more useful to divide one extensive property (ΔH) by another (amount of substance), and report a per-amount intensive value of ΔH, often “normalized” to a per-mole basis. As Figure \(\PageIndex{3}\) suggests, the combustion of gasoline is a highly exothermic process. The concept of specific energy applies to a particular (e.g. By their definitions, the arithmetic signs of ΔV and w will always be opposite: Substituting Equation \ref{5.4.4} and the definition of internal energy (Equation \ref{5.4.1}) into Equation \ref{5.4.3} yields: \[ \begin{align} ΔH&=ΔU+PΔV \\[5pt] &=q_\ce{p}+\cancel{w}−\cancel{w} \\[5pt] &=q_\ce{p} \label{5.4.5} \end{align}\]. &\mathrm{1.00×10^3\:mL\:\ce{C8H18}⟶692\:g\:\ce{C8H18}}\\ The heat given off when you operate a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place, since it occurs at the essentially constant pressure of the atmosphere. the species also play a significant role in determining the heats of combustion in kJ/mL. This is usually rearranged slightly to be written as follows, with \(\sum\) representing “the sum of” and n standing for the stoichiometric coefficients: \[ΔH^\circ_\ce{reaction}=\sum n×ΔH^\circ_\ce{f}\ce{(products)}−\sum n×ΔH^\circ_\ce{f}\ce{(reactants)} \label{5.4.20B}\]. Common units are J/kg or cal/kg. Enthalpies of combustion for many substances have been measured; a few of these are listed in Table \(\PageIndex{1}\). We can apply the data from the experimental enthalpies of combustion in Table \(\PageIndex{1}\) to find the enthalpy change of the entire reaction from its two steps: \[\begin {align*} than for the alcohols. This can be attributed to the fact that the alcohols are already in Since summing these three modified reactions yields the reaction of interest, summing the three modified ΔH° values will give the desired ΔH°: Aluminum chloride can be formed from its elements: (i) \(\ce{2Al}(s)+\ce{3Cl2}(g)⟶\ce{2AlCl3}(s)\hspace{20px}ΔH°=\:?\), (ii) \(\ce{HCl}(g)⟶\ce{HCl}(aq)\hspace{20px}ΔH^\circ_{(ii)}=\mathrm{−74.8\:kJ}\), (iii) \(\ce{H2}(g)+\ce{Cl2}(g)⟶\ce{2HCl}(g)\hspace{20px}ΔH^\circ_{(iii)}=\mathrm{−185\:kJ}\), (iv) \(\ce{AlCl3}(aq)⟶\ce{AlCl3}(s)\hspace{20px}ΔH^\circ_{(iv)}=\mathrm{+323\:kJ/mol}\), (v) \(\ce{2Al}(s)+\ce{6HCl}(aq)⟶\ce{2AlCl3}(aq)+\ce{3H2}(g)\hspace{20px}ΔH^\circ_{(v)}=\mathrm{−1049\:kJ}\). The heat of combustion of ethanol, C2H5OH(l), is -1367 kJ/mol. FREE Expert Solution Since the question stated that the mileage is directly proportional to the heat of combustion of the fuel, we can make a direct comparison of the energy they produce per liter. This is the enthalpy change for the exothermic reaction: \[\ce{C}(s)+\ce{O2}(g)⟶\ce{CO2}(g)\hspace{20px}ΔH^\circ_\ce{f}=ΔH^\circ_{298}=−393.5\:\ce{kJ} \label{5.4.9}\]. What is the standard enthalpy change for the reaction: \[\ce{3NO2}(g)+\ce{H2O}(l)⟶\ce{2HNO3}(aq)+\ce{NO}(g)\hspace{20px}ΔH°=\:? Example \(\PageIndex{2}\): Another Example of the Measurement of an Enthalpy Change, A gummy bear contains 2.67 g sucrose, C12H22O11. Hydrogen gas, H2, reacts explosively with gaseous chlorine, Cl2, to form hydrogen chloride, HCl(g). Ultraviolet radiation is the source of the energy that drives this reaction in the upper atmosphere. The value of ΔH for a reaction in one direction is equal in magnitude, but opposite in sign, to ΔH for the reaction in the opposite direction, and ΔH is directly proportional to the quantity of reactants and products. \nonumber\]. For example, when 1 mole of hydrogen gas and 12 mole of oxygen gas change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released. Calculate the heat of combustion of 1 mole of ethanol, C2H5OH(l), when H2O(l) and CO2(g) are formed. If we have values for the appropriate standard enthalpies of formation, we can determine the enthalpy change for any reaction, which we will practice in the next section on Hess’s law. The cost of algal fuels is becoming more competitive—for instance, the US Air Force is producing jet fuel from algae at a total cost of under $5 per gallon. The heat of combustion of methane is -890 kJ mol-1.The energy level diagram for the combustion of methane is as shown in Figure. &\overline{\ce{ClF}(g)+\ce{F2}⟶\ce{ClF3}(g)\hspace{130px}}&&\overline{ΔH°=\mathrm{−139.2\:kJ}} \[\ce{N2}(g)+\ce{2O2}(g)⟶\ce{2NO2}(g) \nonumber\], \[\ce{N2}(g)+\ce{O2}(g)⟶\ce{2NO}(g)\hspace{20px}ΔH=\mathrm{180.5\:kJ} \nonumber\], \[\ce{NO}(g)+\frac{1}{2}\ce{O2}(g)⟶\ce{NO2}(g)\hspace{20px}ΔH=\mathrm{−57.06\:kJ} \nonumber\]. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. We see that ΔH of the overall reaction is the same whether it occurs in one step or two. On the other hand, the heat produced by a reaction measured in a bomb calorimeter is not equal to \(ΔH\) because the closed, constant-volume metal container prevents expansion work from occurring. Energy is stored in a substance when the kinetic energy of its atoms or molecules is raised. How much heat (kJ) would be liberated by completely burning \(\mathrm{0.0587\:mol\:KClO_3×\dfrac{1\:mol\:\ce{C12H22O11}}{8\:mol\:KClO_3}=0.00734\:mol\:\ce{C12H22O11}}\). Examples of enthalpy changes include enthalpy of combustion, enthalpy of fusion, enthalpy of vaporization, and standard enthalpy of formation. The stepwise reactions we consider are: (i) decompositions of the reactants into their component elements (for which the enthalpy changes are proportional to the negative of the enthalpies of formation of the reactants), followed by (ii) re-combinations of the elements to give the products (with the enthalpy changes proportional to the enthalpies of formation of the products). Determine the enthalpy change for the reaction, \[\ce{C12H22O11}(aq)+\ce{8KClO3}(aq)⟶\ce{12CO2}(g)+\ce{11H2O}(l)+\ce{8KCl}(aq) \nonumber\], We have \(\mathrm{2.67\:\cancel{g}×\dfrac{1\:mol}{342.3\:\cancel{g}}=0.00780\:mol\:C_{12}H_{22}O_{11}}\) available, and. ΔH for a reaction in one direction is equal in magnitude and opposite in sign to ΔH for the reaction in the reverse direction. The relationship between internal energy, heat, and work can be represented by the equation: as shown in Figure \(\PageIndex{1}\). A) -686 KJ B) -519 KJ C) -715 KJ D) -597 KJ E) -469 KJ \end {align*}\]. (credit: modification of work by Paul Shaffner). (c) Assuming that an automobile’s mileage is directly proportional to the heat of combustion of the fuel, calculate how much farther an automobile could be expected to travel on 1 L of gasoline than on 1 L of ethanol.

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