# 2C4H10 (g) + 13O2 (g) → 8CO2

2C_{4}H_{10} (*g*) + 13O_{2}(*g*) → 8CO_{2} (*g*)+10H_{2}O (*g*)

Δ*H*_{rxn} = Σ(bond energy of bonds broken) −Σ(bond energy of bonds formed)Eqn. 1

Δ*H*_{rxn} = Σ(Δ*H*_{f}, products)− Σ(Δ*H*_{f}, reactants)Eqn. 2

Look up all the bond enthalpies for the reactants and products.Calculate the sum of the bond energies (in kJ) in all of thereactants and in all of the products, paying attention to thenumber of bonds in the molecules and the stoichiometriccoefficients for each molecule from the balanced chemical equation.(Enter unrounded values.)

Σ(bond energy of bonds broken)= ———– kJ

Σ(bond energy of bonds formed)= ———– kJ

Calculate the enthalpy of combustion, using Eqn. 1. Express thefinal answer as kJ/mol of butane. Pay attention to thestoichiometric coefficient of the fuel in the balanced chemicalequation. (Enter an unrounded value.)

——- kJ/mole of butane

b) Use enthalpies of formation to calculate the enthalpy ofcombustion for butane with the same balanced reaction written in(a)(i).

(i) Look up all the enthalpies of formation for the reactantsand products—make sure you use the value for the correct phase ofthe species. Calculate the sum of the enthalpies of formation (inkJ) for all of the reactants and all of the products, payingattention to the stoichiometric coefficients for each molecule fromthe balanced equation. (Enter unrounded values.)

Σ(Δ*H*_{f}, reactants)=kJΣ(Δ*H*_{f}, products)= ______kJ

(ii) Calculate the enthalpy of combustion, using Eqn. 2. Expressthe final answer as kJ/mol of butane. Pay attention to thestoichiometric coefficient of the fuel in the balanced chemicalequation. (Enter an unrounded value.)

———— kJ/mol of butane

Part B

The amount of heat that can be obtained from a reaction dependson the amount of reactant used or the amount of product made. Thequantity Δ*H*_{rxn} in kJ/mol can be used like anyother stoichiometric coefficient to relate the amount of heat tothe moles of reactant or product used to carry out a reaction. Theamount of enthalpy available per kg of fuel is called the*energy density* of the fuel, and is commonly used tocompare the energy content of different sources of energy.

Using your answers from **part A (a)**, answer thefollowing questions.

(a) For butane, C_{4}H_{10}, calculate theenergy released for the combustion of 1 kg of fuel. Express youranswer in the units MJ/kg and as the absolute value of the energy.(1 MJ = 1000 kJ.) (Enter an unrounded value.)

————— MJ/kg butane

(b) Calculate the kg of carbon dioxide produced per kilogram offuel for butane. Express your answer as kg CO_{2}/kg.(Enter an unrounded value.)

————— kg CO_{2}/kg butane

Part C

Diesel is a mixture of hydrocarbons with between 8 and 21 carbonatoms. The average empirical formula for the mixture that is dieselcorresponds to C_{12}H_{23}. Biodiesel is a fattyacid ester that can be synthesized from the fatty acids (stearicacid or linoleic acid) in plants or from used cooking oil, such ascanola oil or soybean oil. A typical component of biodiesel has theformula C_{19}H_{36}O_{2}.

(a) Write and balance the combustion reaction for diesel(C_{12}H_{23}) and for biodiesel(C_{19}H_{36}O_{2}). (*Hint*: Recallhow combustion engines work before answering this question. Includestates-of-matter under the given conditions in your answer. Use thelowest possible whole number coefficients.)

Dissel

4C_{12}H_{23}(*g*) +71O_{2}(*g*) →48CO_{2}(*g*)+46H_{2}O(*g*)

Biodiesel

C_{19}H_{36}O_{2}(*g*) +27O_{2}(*g*) →19CO_{2}(*g*)+18H_{2}O(*g*)

(b) Calculate the kg of carbon dioxide emitted per kg of dieseland biodiesel. (Enter unrounded values.)

(i) Diesel

________ kg CO_{2} / kg diesel

(ii) Biodiesel

________ kg CO_{2} / kg biodiesel

Please solve and show work for the questions with theblanks.

Answer:

2C_{4}H_{10} (g) + 13O_{2}(g) → 8CO_{2} (g)+ 10H_{2}O(g)

ΔH_{rxn} = Σ(bond energy of bonds broken) − Σ(bondenergy of bonds formed)Eqn. 1

ΔH_{rxn} = Σ(ΔH_{f}, products) −Σ(ΔH_{f}, reactants)Eqn. 2

Look up all the bond enthalpies for the reactants and products.Calculate the sum of the bond energies (in kJ) in all of thereactants and in all of the products, paying attention to thenumber of bonds in the molecules and the stoichiometriccoefficients for each molecule from the balanced chemical equation.(Enter unrounded values.)

Σ(bond energy of bonds broken)= 16406kJ

Σ(bond energy of bonds formed)= 22160 kJ

Calculate the enthalpy of combustion, using Eqn. 1. Express thefinal answer as kJ/mol of butane. Pay attention to thestoichiometric coefficient of the fuel in the balanced chemicalequation. (Enter an unrounded value.)

-2876.9 kj/mole of butane

b) Use enthalpies of formation to calculate the enthalpy ofcombustion for butane with the same balanced reaction written in(a)(i).

(i) Look up all the enthalpies of formation for the reactantsand products—make sure you use the value for the correct phase ofthe species. Calculate the sum of the enthalpies of formation (inkJ) for all of the reactants and all of the products, payingattention to the stoichiometric coefficients for each molecule fromthe balanced equation. (Enter unrounded values.)

Σ(ΔH_{f}, reactants)= 3131.1kJ Σ(ΔH_{f}, products)= 6008kJ

(ii) Calculate the enthalpy of combustion, using Eqn. 2. Expressthe final answer as kJ/mol of butane. Pay attention to thestoichiometric coefficient of the fuel in the balanced chemicalequation. (Enter an unrounded value.)

-2876.9kJ/mol of butane

Part B

The amount of heat that can be obtained from a reaction dependson the amount of reactant used or the amount of product made. Thequantity ΔH_{rxn} in kJ/mol can be used like any otherstoichiometric coefficient to relate the amount of heat to themoles of reactant or product used to carry out a reaction. Theamount of enthalpy available per kg of fuel is called the energydensity of the fuel, and is commonly used to compare the energycontent of different sources of energy.

Using your answers from **part A (a)**, answer thefollowing questions.

(a) For butane,C_{4}H_{10}, calculate the energy released for thecombustion of 1 kg of fuel. Express your answer in the units MJ/kgand as the absolute value of the energy. (1 MJ = 1000 kJ.) (Enteran unrounded value.)

2C_{4}H_{10} (g) +13O_{2} (g) → 8CO_{2} (g)+10H_{2}O (g)

116g——————-→2876.9Kj/mol

1000g——————-→24800.86kj

24800.86/1000= 24.8 MJ/mole

24.8 MJ/kg butane

(b) Calculate the kg of carbon dioxide produced per kilogram offuel for butane. Express your answer as kg CO_{2}/kg.(Enter an unrounded value.)

3.034 kg CO_{2}/kg butane

Part C

Diesel is a mixture of hydrocarbons with between 8 and 21 carbonatoms. The average empirical formula for the mixture that is dieselcorresponds to C_{12}H_{23}. Biodiesel is a fattyacid ester that can be synthesized from the fatty acids (stearicacid or linoleic acid) in plants or from used cooking oil, such ascanola oil or soybean oil. A typical component of biodiesel has theformula C_{19}H_{36}O_{2}.

(a) Write and balance the combustion reaction for diesel(C_{12}H_{23}) and for biodiesel(C_{19}H_{36}O_{2}). (Hint: Recall howcombustion engines work before answering this question. Includestates-of-matter under the given conditions in your answer. Use thelowest possible whole number coefficients.)

Dissel

4C_{12}H_{23}(g) + 71O_{2}(g) →48CO_{2}(g)+46H_{2}O(g)

668g———→2112g

1000g——–→ 3161g

Biodiesel

C_{19}H_{36}O_{2}(g) +27O_{2}(g) →19CO_{2}(g)+18H_{2}O(g)

296g——-→836g

1000g——-→2824g