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Chapter 5: Problem 62

Consider the following hypothetical reactions: $$ \begin{array}{ll} \mathrm{A} \longrightarrow \mathrm{B} & \Delta H=+30 \mathrm{~kJ} \\ \mathrm{~B} \longrightarrow \mathrm{C} & \Delta H=+60 \mathrm{~kJ} \end{array} $$ (a) Use Hess's law to calculate the enthalpy change for the reaction \(\mathrm{A} \longrightarrow\) C. (b) Construct an enthalpy diagram for substances \(A, B,\) and \(C,\) and show how Hess's law applies.

Short Answer

Expert verified
(a) Using Hess's law, we find the enthalpy change for the reaction A → C is +90 kJ. (b) The enthalpy diagram shows the energy levels of A, B, and C, with B being 30 kJ above A and C being 60 kJ above B. The diagram visualizes how the sum of the individual enthalpy changes for A → B and B → C equals the total enthalpy change for A → C, which confirms our calculated value of +90 kJ.

Step by step solution

01

Identify the enthalpy changes for each step

The given enthalpy changes are: A → B: ΔH = +30 kJ B → C: ΔH = +60 kJ
02

Apply Hess's law

Hess's law states that the total enthalpy change for the reaction is the sum of the enthalpy changes for the individual steps. Therefore, we can calculate the enthalpy change for A → C by adding the enthalpy changes for A → B and B → C: ΔH(A → C) = ΔH(A → B) + ΔH(B → C) Substitute the given values: ΔH(A → C) = +30 kJ + 60 kJ
03

Calculate the enthalpy change for A → C

Add the values together: ΔH(A → C) = 90 kJ This means that the enthalpy change for the reaction A → C is +90 kJ. #b) Construct an enthalpy diagram for substances A, B, and C#
04

Draw the energy levels for A, B, and C

On the y-axis, represent the energy levels of A, B, and C. The energy level of B is 30 kJ above A (due to the enthalpy change of +30 kJ for A → B), and the energy level of C is 60 kJ above B (due to the enthalpy change of +60 kJ for B → C).
05

Draw the reaction pathways

Draw arrows to represent the reactions A → B and B → C, with the enthalpy changes written next to each arrow. The reaction A → C can be represented by a single arrow connecting A and C directly or by showing how the two separate steps add up to the overall reaction pathway.
06

Apply Hess's law to the enthalpy diagram

The enthalpy diagram visualizes Hess's law by showing the sum of the individual enthalpy changes for A → B and B → C equaling the total enthalpy change for A → C, which we calculated as +90 kJ. The completed enthalpy diagram should help visualize how Hess's law applies to this problem, confirming our calculated value.

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Most popular questions from this chapter

A 1.800 -g sample of phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) was burned in a bomb calorimeter whose total heat capacity is \(11.66 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter plus contents increased from \(21.36^{\circ} \mathrm{C}\) to \(26.37{ }^{\circ} \mathrm{C}\). (a) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol? Per mole of phenol?

Calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with water to form acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and \(\mathrm{Ca}(\mathrm{OH})_{2}\). From the following enthalpy of reaction data and data in Appendix C, calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{CaC}_{2}(s):\) $$ \begin{aligned} \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \\ \Delta H^{\circ}=-127.2 \mathrm{~kJ} \end{aligned} $$

(a) What is meant by the term fuel value? (b) Which is a greater source of energy as food, \(5 \mathrm{~g}\) of fat or \(9 \mathrm{~g}\) of carbohydrate? (c) The metabolism of glucose produces \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) How does the human body expel these reaction products?

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Methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) is used as a fuel in race cars. (a) Write a balanced equation for the combustion of liquid methanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming \(\mathrm{H}_{2} \mathrm{O}(g)\) as a product. (c) Calculate the heat produced by combustion per liter of methanol. Methanol has a density of \(0.791 \mathrm{~g} / \mathrm{mL}\). (d) Calculate the mass of \(\mathrm{CO}_{2}\) produced per kJ of heat emitted.
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