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Chapter 1: Problem 11

\(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\) Based on the information given in the table below, what is \(\Delta H^{\circ}\) for the above reaction? \(\begin{array}{cc}{\text { Bond }} & {\text { Average bond energy }(\mathrm{kJ} / \mathrm{mol})} \\ {\mathrm{H}-\mathrm{H}} & {500} \\\ {\mathrm{O}=\mathrm{O}} & {500} \\ {\mathrm{O}-\mathrm{H}} & {500}\end{array}\) (A) \(-2,000 \mathrm{kJ}\) (B) \(-500 \mathrm{kJ}\) (C) \(+1,000 \mathrm{kJ}\) (D) \(+2,000 \mathrm{kJ}\)

Short Answer

Expert verified
(C) \(+1,000 \mathrm{kJ}\)

Step by step solution

01

Calculate the total energy required to break the bonds in the reactants

The reactants in the given reaction are \(2 \mathrm{H}_{2}(g)\) and \(\mathrm{O}_{2}(g)\). The average bond energies given in the table are 500 kJ/mol for the \(\mathrm{H}-\mathrm{H}\) bond and 500 kJ/mol for the \(\mathrm{O}=\mathrm{O}\) bond. Therefore, the total energy required to break the bonds in the reactants is \(2(2 \times 500) + 500 = 2500 \mathrm{kJ}\). The multiple of 2 in front of the bond energy for \(\mathrm{H}-\mathrm{H}\) is because there are two moles of \(\mathrm{H}_{2}\) in the reactants, and thus four \(\mathrm{H}-\mathrm{H}\) bonds.
02

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

The product of the reaction is \(2 \mathrm{H}_{2}\mathrm{O}(g)\), which involves \(\mathrm{O}-\mathrm{H}\) bonds. The average bond energy given in the table for an \(\mathrm{O}-\mathrm{H}\) bond is 500 kJ/mol. For each molecule of \(\mathrm{H}_{2}\mathrm{O}\), there are two \(\mathrm{O}-\mathrm{H}\) bonds, and thus four \(\mathrm{O}-\mathrm{H}\) bonds for two molecules. Therefore, the total energy released when new bonds are formed in the products is \(2 \times 2 \times 500 = 2000 \mathrm{kJ}\).
03

Find the enthalpy change \(\Delta H^{\circ}\) for the reaction

According to the first law of thermodynamics, the enthalpy change \(\Delta H^{\circ}\) for the reaction is 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. Therefore, \(\Delta H^{\circ} = 2500 \mathrm{kJ} - 2000 \mathrm{kJ} = +500 \mathrm{kJ}\). In exothermic reactions, the enthalpy change is negative because energy is released to the environment. However, in this case, the enthalpy change is positive, indicating that the reaction is endothermic, i.e., energy is absorbed from the environment.

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Most popular questions from this chapter

A sealed, rigid container contains three gases: 28.0 \(\mathrm{g}\) of nitrogen, 40.0 \(\mathrm{g}\) of argon, and 36.0 g of water vapor. If the total pressure exerted by the gases is \(2.0 \mathrm{atm},\) what is the partial pressure of the nitrogen? (A) 0.33 atm (B) 0.40 atm (C) 0.50 \(\mathrm{atm}\) (D) 2.0 \(\mathrm{atm}\)

Use the following information to answer questions 25-28. A voltaic cell is created using the following half-cells: $\begin{array}{ll}{\mathrm{Cr}^{3+}+3 e \rightarrow \mathrm{Cr}(s)} & {E^{\circ}=-0.41 \mathrm{V}} \\ {\mathrm{Pb}^{2+}+2 e \rightarrow \mathrm{Pb}(s)} & {E^{\circ}=-0.12 \mathrm{V}}\end{array}$ The concentrations of the solutions in each half-cell are 1.0 M. Which net ionic equation below represents a possible reaction that takes place when a strip of magnesium metal is oxidized by a solution of chromium (III) nitrate? (A) $\operatorname{Mg}(s)+\operatorname{Cr}\left(\mathrm{NO}_{3}\right)_{3}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cr}^{3+}(a q)+3 \mathrm{NO}_{3}^{-}(a q)$ (B) $3 \mathrm{Mg}(s)+2 \mathrm{Cr}^{3+} \rightarrow 3 \mathrm{Mg}^{2+}+2 \mathrm{Cr}(s)$ (C) $\mathrm{Mg}(s)+\mathrm{Cr}^{3+} \rightarrow \mathrm{Mg}^{2+}+\mathrm{Cr}(s)$ (D) $3 \mathrm{Mg}(s)+2 \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}(a q) \rightarrow 3 \mathrm{Mg}^{2+}(a q)+2 \mathrm{Cr}(s)+\mathrm{NO}_{3}^{-}(a q)$

Which of the following expressions is equal to the \(K_{\mathrm{sp}}\) of \(\mathrm{Ag}_{2} \mathrm{CO}_{3} ?\) (A) \(K_{s p}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{CO}_{3}^{2-}\right]\) (B) \(K_{s p}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{CO}_{3}^{2-}\right]^{2}\) (C) \(K_{s p}=\left[\mathrm{Ag}^{+}\right]^{2}\left[\mathrm{CO}_{3}^{2-}\right]\) (D) \(K_{s p}=\left[\mathrm{Ag}^{+}\right]^{2}\left[\mathrm{CO}_{3}^{2-}\right]^{2}\)

Nitrogen’s electronegativity value is between those of phosphorus and oxygen. Which of the following correctly describes the relationship between the three values? (A) The value for nitrogen is less than that of phosphorus because nitrogen is larger, but greater than that of oxygen because nitrogen has a greater effective nuclear charge. (B) The value for nitrogen is less than that of phosphorus because nitrogen has fewer protons, but greater than that of oxygen because nitrogen has fewer valence electrons. (C) The value for nitrogen is greater than that of phosphorus because nitrogen has fewer electrons, but less than that of oxygen because nitrogen is smaller. (D) The value for nitrogen is greater than that of phosphorus because nitrogen is smaller, but less than that of oxygen because nitrogen has a smaller effective nuclear charge.

$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{Cl}_{2}(g) \mapsto 2 \mathrm{NOCl}(g) \Delta G^{\circ}=132.6 \mathrm{kJ} / \mathrm{mol}$$ For the equilibrium above, what would happen to the value of \(\Delta G^{\circ}\) if the concentration of \(\mathrm{N}_{2}\) were to increase and why? (A) It would increase because the reaction would become more themodynamically favored. (B) It would increase because the reaction would shift right and create more products. (C) It would decrease because there are more reactants present. (D) It would stay the same because the value of \(K_{e q}\) would not change.
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