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Chapter 5: Problem 97

Limestone stalactites and stalagmites are formed in caves by the following reaction: $$ \mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q) \longrightarrow \mathrm{CaCO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$ If \(1 \mathrm{~mol}\) of \(\mathrm{CaCO}_{3}\) forms at \(298 \mathrm{~K}\) under 1 atm pressure, the reaction performs \(2.47 \mathrm{~kJ}\) of \(P-V\) work, pushing back the atmosphere as the gaseous \(\mathrm{CO}_{2}\) forms. At the same time, \(38.95 \mathrm{~kJ}\) of heat is absorbed from the environment. What are the values of \(\Delta H\) and of \(\Delta E\) for this reaction?

Short Answer

Expert verified
The enthalpy change (ΔH) for the given reaction is \(41.42 \: \text{kJ}\) and the internal energy change (ΔE) is \(36.48 \: \text{kJ}\).

Step by step solution

01

Calculate ΔH

The enthalpy change (ΔH) is given by the equation: ΔH = q + PΔV, where q is the heat absorbed and PΔV is the work done on the system. We are given the values of q (38.95 kJ) and PΔV (2.47 kJ). Plug these values into the equation and calculate ΔH: ΔH = 38.95 kJ + 2.47 kJ = 41.42 kJ So, the enthalpy change for this reaction is 41.42 kJ.
02

Calculate ΔE

The internal energy change (ΔE) is given by the equation: ΔE = q + w, where w is the work done on the system. In this case, the work done (w) is -PΔV (as the work is done by the system, not on the system). We are given the values of q (38.95 kJ) and PΔV (2.47 kJ). Plug these values into the equation and calculate ΔE: ΔE = 38.95 kJ - 2.47 kJ = 36.48 kJ So, the internal energy change for this reaction is 36.48 kJ. In summary, the enthalpy change (ΔH) for the given reaction is 41.42 kJ and the internal energy change (ΔE) is 36.48 kJ.

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Most popular questions from this chapter

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing \(0.655 \mathrm{~kJ}\) of heat. It shrinks on cooling, and the atmosphere does \(382 \mathrm{~J}\) of work on the balloon. (b) A 100.0 -g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50{ }^{\circ} \mathrm{C}\) during which it absorbs \(322 \mathrm{~J}\) of heat. Assume the volume of the gold bar remains constant. (c) The surroundings do \(1.44 \mathrm{~kJ}\) of work compressing gas in a perfectly insulated cylinder.

(a) When a 4.25 -g sample of solid ammonium nitrate dissolves in \(60.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.18), the temperature drops from \(22.0^{\circ} \mathrm{C}\) to \(16.9^{\circ} \mathrm{C}\). Calculate \(\Delta H\left(\right.\) in \(\left.\mathrm{kJ} / \mathrm{mol} \mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) for the solution process $$ \mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) $$ Assume that the specific heat of the solution is the same as that of pure water. (b) Is this process endothermic or exothermic?

Two solid objects, \(A\) and \(B\), are placed in boiling water and allowed to come to temperature there. Each is then lifted out and placed in separate beakers containing \(1000 \mathrm{~g}\) water at \(10.0^{\circ} \mathrm{C}\). Object A increases the water temperature by \(3.50^{\circ} \mathrm{C}\); B increases the water temperature by \(2.60^{\circ} \mathrm{C}\). (a) Which object has the larger heat capacity? (b) What can you say about the specific heats of \(\mathrm{A}\) and \(\mathrm{B}\) ?

(a) Why are tables of standard enthalpies of formation so useful? (b) What is the value of the standard enthalpy of formation of an element in its most stable form? (c) Write the chemical equation for the reaction whose enthalpy change is the standard enthalpy of formation of sucrose (table sugar), \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s), \Delta H_{f}^{\circ}\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right]\)

Write balanced equations that describe the formation of the following compounds from elements in their standard states, and use Appendix \(\mathrm{C}\) to obtain the values of their standard enthalpies of formation: (a) \(\mathrm{H}_{2} \mathrm{O}_{2}(g)\) (b) \(\mathrm{CaCO}_{3}(s)\) (c) \(\mathrm{POCl}_{3}(l),(\mathbf{d}) \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\)
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