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Chapter 7: Problem 68

Use Hess's law to determine \(\Delta H^{\circ}\) for the reaction $$\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g}), \text { given that }$$ $$\begin{array}{l} \text { C(graphite) }+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}(\mathrm{g}) \\ &\left.\qquad \Delta H^{\circ}=-110.54 \mathrm{k} \mathrm{J}\right] \end{array}$$ $$\begin{aligned} &\text { C(graphite) }+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})\\\ &&\Delta H^{\circ}=-393.51 \mathrm{kJ} \end{aligned}$$

Short Answer

Expert verified
The standard enthalpy change for the reaction CO(g) + 1/2O2(g) -> CO2(g) is -86.215 kJ.

Step by step solution

01

Analyze the given reactions

First, let's identify the reactions that we are provided with: Reaction 1: C(graphite) +1/2 O2(g) -> CO(g) ΔH1 = -110.54 kJ Reaction 2: C(graphite) + O2(g) -> CO2(g) ΔH2 = -393.51 kJ. The given reactions involve the formation of CO and CO2 from their elements in their standard states, which are the standard enthalpy of formation reactions.
02

Rearrange the reactions

Next, let's manipulate the given reactions to match the target reaction (CO(g) + 1/2O2(g) -> CO2(g)). Notice that the CO2(g) is on the product side in the target reaction and the CO(g) is on the reactant side, opposite to the given reactions. We will make CO(g) from reaction 1 a reactant by reversing the reaction and for reaction 2, we'll keep it as is but divide by 2, to match the 1/2 O2 in the target reaction. So the new reactions are: - Reaction 1: CO(g) -> C(graphite) +1/2 O2(g), ΔH1' = -(ΔH1) = 110.54 kJ - Reaction 2: 1/2 [C(graphite) +O2(g) -> CO2(g)], ΔH2' = 1/2(ΔH2) = -196.755 kJ.
03

Add the reactions

To find the ΔH for the target reaction, simply add the ΔHs from step 2: ΔH = ΔH1' + ΔH2' = 110.54 kJ - 196.755 kJ = -86.215 kJ.

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Most popular questions from this chapter

We can determine the purity of solid materials by using calorimetry. A gold ring (for pure gold, specific heat \(=0.1291 \mathrm{Jg}^{-1} \mathrm{K}^{-1}\) ) with mass of \(10.5 \mathrm{g}\) is heated to \(78.3^{\circ} \mathrm{C}\) and immersed in \(50.0 \mathrm{g}\) of \(23.7^{\circ} \mathrm{C}\) water in a constant-pressure calorimeter. The final temperature of the water is \(31.0^{\circ} \mathrm{C}\). Is this a pure sample of gold?

Refer to Example \(7-3 .\) Based on the heat of combustion of sucrose established in the example, what should be the temperature change \((\Delta T)\) produced by the combustion of \(1.227 \mathrm{g} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) in a bomb calorimeter assembly with a heat capacity of \(3.87 \mathrm{kJ} /^{\circ} \mathrm{C} ?\)

Explain the important distinctions between each pair of terms: (a) system and surroundings; (b) heat and work; (c) specific heat and heat capacity; (d) endothermic and exothermic; (e) constant-volume process and constant-pressure process.

What is the change in internal energy of a system if the surroundings (a) transfer 235 J of heat and 128 J of work to the system; (b) absorb 145 J of heat from the system while doing \(98 \mathrm{J}\) of work on the system; (c) exchange no heat, but receive 1.07 kJ of work from the system?

Thermite mixtures are used for certain types of welding, and the thermite reaction is highly exothermic. $$\begin{array}{r} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Fe}(\mathrm{s}) \\ \Delta H^{\circ}=-852 \mathrm{kJ} \end{array}$$ \(1.00 \mathrm{mol}\) of granular \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(2.00 \mathrm{mol}\) of granular Al are mixed at room temperature \(\left(25^{\circ} \mathrm{C}\right),\) and a reaction is initiated. The liberated heat is retained within the products, whose combined specific heat over a broad temperature range is about \(0.8 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1} .\) (The melting point of iron is \(1530^{\circ} \mathrm{C} .\) ) Show that the quantity of heat liberated is more than sufficient to raise the temperature of the products to the melting point of iron.
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