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Chapter 8: Problem 71

Use bond energies to estimate \(\Delta H\) for the combustion of one mole of acetylene: $$ \mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$

Short Answer

Expert verified
The change in enthalpy (∆H) for the combustion of one mole of acetylene can be calculated using bond energies as follows: 1. Identify bonds in reactants and products 2. Determine bond energies (C≡C: 835 kJ/mol, C-H: 413 kJ/mol, O=O: 498 kJ/mol, C=O: 799 kJ/mol, O-H: 467 kJ/mol) 3. Calculate energy required to break bonds in reactants (4151 kJ/mol) 4. Calculate energy released when new bonds are formed in products (4130 kJ/mol) 5. Calculate ∆H = Energy released when bonds are formed - Energy required to break bonds in reactants = 4130 kJ/mol - 4151 kJ/mol = -21 kJ/mol Therefore, ∆H for the combustion of one mole of acetylene is -21 kJ/mol, indicating an exothermic reaction.

Step by step solution

01

Identify the bonds in reactants and products

First, we need to identify the types of bonds present in the reactants and products of the combustion reaction: Reactants: - One C≡C bond in acetylene (C₂H₂) - Two C-H bonds in acetylene (C₂H₂) - Five O=O bonds in oxygen molecules (O₂) Products: - Four C=O bonds in carbon dioxide (CO₂) - Two O-H bonds in water (H₂O)
02

Determine bond energies

Next, we need to find the bond energies for each type of bond. Bond energies are generally given in units of kJ/mol. Here are the bond energies for the bonds we identified: - C≡C: 835 kJ/mol - C-H: 413 kJ/mol - O=O: 498 kJ/mol - C=O: 799 kJ/mol - O-H: 467 kJ/mol
03

Calculate the energy required to break bonds in reactants

Now, we will multiply the bond energies by the number of each bond in the reactants to find the total energy required to break all bonds in the reactants: - Energy to break 1 C≡C bond: 1 × 835 kJ/mol = 835 kJ/mol - Energy to break 2 C-H bonds: 2 × 413 kJ/mol = 826 kJ/mol - Energy to break 5 O=O bonds: 5 × 498 kJ/mol = 2490 kJ/mol Total energy to break bonds in reactants = 835 + 826 + 2490 = 4151 kJ/mol
04

Calculate the energy released when new bonds are formed in the products

Similarly, we will multiply the bond energies by the number of each bond in the products to find the total energy released when new bonds are formed in the products: - Energy released by forming 4 C=O bonds: 4 × 799 kJ/mol = 3196 kJ/mol - Energy released by forming 2 O-H bonds: 2 × 467 kJ/mol = 934 kJ/mol Total energy released when new bonds are formed = 3196 + 934 = 4130 kJ/mol
05

Calculate the change in enthalpy (∆H) for the combustion of one mole of acetylene

Finally, we can calculate the change in enthalpy (∆H) for the combustion reaction by taking the difference between the energy required to break the bonds in the reactants and the energy released when new bonds are formed in the products: ∆H = Energy released when bonds are formed - Energy required to break bonds in reactants ∆H = 4130 kJ/mol - 4151 kJ/mol = -21 kJ/mol The change in enthalpy for the combustion of one mole of acetylene is -21 kJ/mol, which means that the reaction is exothermic and releases 21 kJ of energy per mole of acetylene combusted.

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Most popular questions from this chapter

Write Lewis structures that obey the octet rule for the following species. Assign the formal charge for each central atom. a. \(\mathrm{POCl}_{3}\) e. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) b. \(\mathrm{SO}_{4}^{2-}\) f. \(\mathrm{XeO}_{4}\) c. \(\mathrm{ClO}_{4}^{-}\) g. \(\mathrm{ClO}_{3}^{-}\) d. \(\mathrm{PO}_{4}^{3-}\) h. \(\mathrm{NO}_{4}^{3-}\)

Arrange the atoms and/or ions in the following groups in order of decreasing size. a. \(\mathrm{O}, \mathrm{O}^{-}, \mathrm{O}^{2-}\) b. \(\mathrm{Fe}^{2+}, \mathrm{Ni}^{2+}, \mathrm{Zn}^{2+}\) c. \(\mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{Cl}^{-}\)

Combustion reactions of fossil fuels provide most of the energy needs of the world. Why are combustion reactions of fossil fuels so exothermic?

Some plant fertilizer compounds are \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}, \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\), \(\mathrm{K}_{2} \mathrm{O}, \mathrm{P}_{2} \mathrm{O}_{5}\), and \(\mathrm{KCl}\). Which of these compounds contain both ionic and covalent bonds?

Use the following data (in \(\mathrm{kJ} / \mathrm{mol}\) ) to estimate \(\Delta H\) for the reaction \(\mathrm{S}^{-}(g)+\mathrm{e}^{-} \rightarrow \mathrm{S}^{2-}(g)\). Include an estimate of uncertainty. $$ \begin{array}{cl} \mathrm{S}(s) \longrightarrow \mathrm{S}(g) & \Delta H=277 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{S}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{S}^{-}(g) & \Delta H=-200 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ Assume that all values are known to \(\pm 1 \mathrm{~kJ} / \mathrm{mol}\).
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