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Chapter 5: Problem 68

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

Short Answer

Expert verified
(a) The standard enthalpy of formation of an element in its most stable form is \(0 \, \text{kJ/mol}\). (b) The balanced chemical equation for the standard enthalpy of formation of sucrose is \(12 C(graphite) + 11 H_{2}(g) + 11 O_{2}(g) \rightarrow C_{12}H_{22}O_{11}(s)\).

Step by step solution

01

(a) Standard Enthalpy of Formation Definition

The standard enthalpy of formation, \(\Delta H_{f}^{\circ}\), is the change in enthalpy when one mole of a substance in its standard state is formed from its constituent elements in their standard states. For an element in its most stable form, it is already in its standard state; thus, no change in enthalpy occurs, and its standard enthalpy of formation is zero.
02

(a) Entropy of Formation Value for a Stable Element

Given the definition of standard enthalpy of formation, we conclude that the value of the standard enthalpy of formation of an element in its most stable form is \(0 \, \text{kJ/mol}\).
03

(b) Formation of Sucrose Chemical Equation

We are asked to write a balanced chemical equation representing the enthalpy change for the formation of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\). Sucrose is formed from its constituent elements, carbon (C), hydrogen (H), and oxygen (O), in their standard states (solid graphite, diatomic hydrogen gas, and diatomic oxygen gas, respectively). We will begin by writing the unbalanced chemical equation: \(C(graphite) + H_{2}(g) + O_{2}(g) \rightarrow C_{12}H_{22}O_{11}(s)\) Next, we will balance the equation by adjusting the coefficients to ensure that the number of atoms of each element on the reactant side equals the number on the product side.
04

(b) Balanced Chemical Equation for Sucrose Formation

After balancing the equation, we obtain: \(12 C(graphite) + 11 H_{2}(g) + 11 O_{2}(g) \rightarrow C_{12}H_{22}O_{11}(s)\) This balanced chemical equation represents the standard enthalpy of formation of sucrose, \(\Delta H_{f}^{\circ}\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\right]\).

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Most popular questions from this chapter

Consider the decomposition of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) to gaseous acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g) :\) $$\mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \quad \Delta H=+630 \mathrm{kJ}$$ (a) What is the enthalpy change for the reverse reaction? (b) What is \(\Delta H\) for the formation of 1 mol of acetylene? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) were consumed instead of \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

Consider the reaction \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \longrightarrow 2 \mathrm{HI}(g) .(\mathbf{a})\) Use the bond enthalpies in Table 5.4 to estimate \(\Delta H\) for this reaction, ignoring the fact that iodine is in the solid state. (b) Without doing a calculation, predict whether your estimate in part (a) is more negative or less negative than the true reaction enthalpy. (c) Use the enthalpies of formation in Appendix \(C\) to determine the true reaction enthalpy.

A 2.200 -g sample of quinone \(\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) is burned in a bomb calorimeter whose total heat capacity is 7.854 \(\mathrm{kJ} / \mathrm{c}\) . The temperature of the calorimeter increases from 23.44 to \(30.57^{\circ} \mathrm{C}\) . What is the heat of combustion per gram of quinone? Per mole of quinone?

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 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.

For each of the following compounds, write a balanced thermochemical equation depicting the formation of one mole of the compound from its elements in their standard states and then look up \(\Delta H^{\circ} f\) for each substance in Appendix C. (a) \(\mathrm{NO}_{2}(g),(\mathbf{b}) \mathrm{SO}_{3}(g),(\mathbf{c}) \mathrm{NaBr}(s),(\mathbf{d}) \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s) .\)
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