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Chapter 7: Problem 9

Hess's law is really just another statement of the first law of thermodynamics. Explain.

Short Answer

Expert verified
Hess's law and the first law of thermodynamics both focus on conservation principles, with Hess's law conserving enthalpy and the first law conserving energy. Enthalpy is related to internal energy, pressure, and volume, and under constant pressure conditions, the change in enthalpy represents the heat exchanged. Therefore, Hess's law is essentially stating that the total heat exchange in a reaction is constant, which aligns with the first law of thermodynamics' focus on energy conservation, making Hess's law another statement of the first law of thermodynamics.

Step by step solution

01

Understand the First Law of Thermodynamics

The first law of thermodynamics states that energy cannot be created or destroyed, but can only change from one form to another. In other words, the total energy of an isolated system is conserved. Mathematically, it can be expressed as: \(\Delta E = q + w\), where \(\Delta E\) is the change in internal energy, \(q\) is the heat exchanged, and \(w\) is the work done on/by the system.
02

Understand Hess's Law

Hess's law states that the enthalpy change for a given reaction is the same, regardless of the particular way the reaction is carried out. In other words, if a reaction can be expressed as a series of steps, the sum of the enthalpy changes for each step is equal to the enthalpy change for the overall reaction. This is true as long as the initial and final conditions are the same.
03

Compare the Principles of the First Law of Thermodynamics and Hess's Law

Both the first law of thermodynamics and Hess's law are based on the conservation of a certain property of a system. In the case of thermodynamics, it's the conservation of energy, whereas for Hess's law, it's the conservation of enthalpy. These two quantities, though not the same, both relate to the energy changes within a system.
04

Relate Enthalpy to Heat and Internal Energy

Enthalpy (\(H\)) is a state function that represents the total energy of a system. It is related to the internal energy (\(U\)), pressure (\(P\)), and volume (\(V\)) as follows: \(H = U + PV\). For an isobaric (constant pressure) process, the change in enthalpy is equal to the heat exchanged: \(\Delta H = q_p\). This links the concept of enthalpy to the heat term in the first law of thermodynamics equation.
05

Show that Hess's Law is a Reflection of the First Law of Thermodynamics

Since the enthalpy changes in a chemical reaction are equivalent to the heat exchanged in a constant pressure process, Hess's law is essentially stating that the sum of heat exchanges in a series of reactions is equal to the heat exchange in the overall reaction. This aligns with the first law of thermodynamics, which focuses on the conservation of energy in a system, including heat exchanges. Therefore, Hess's law can be considered another statement of the first law of thermodynamics.

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Most popular questions from this chapter

Consider the following reaction: $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-572 \mathrm{kJ}$$ a. How much heat is evolved for the production of 1.00 mole of \(\mathrm{H}_{2} \mathrm{O}(l) ?\) b. How much heat is evolved when 4.03 g hydrogen are reacted with excess oxygen? c. How much heat is evolved when \(186 \mathrm{g}\) oxygen are reacted with excess hydrogen?

In a coffee-cup calorimeter, \(50.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) and \(50.0 \mathrm{mL}\) of \(0.100 \mathrm{M}\) HCl are mixed to yield the following reaction: $$\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s)$$ The two solutions were initially at \(22.60^{\circ} \mathrm{C},\) and the final temperature is \(23.40^{\circ} \mathrm{C}\). Calculate the heat that accompanies this reaction in \(\mathrm{kJ} / \mathrm{mol}\) of \(\mathrm{AgCl}\) formed. Assume that the combined solution has a mass of \(100.0 \mathrm{g}\) and a specific heat capacity of \(4.18 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\).

Give the definition of the standard enthalpy of formation for a substance. Write separate reactions for the formation of NaCl, \(\mathrm{H}_{2} \mathrm{O}, \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) and \(\mathrm{PbSO}_{4}\) that have \(\Delta H^{\circ}\) values equal to \(\Delta H_{\mathrm{f}}^{\circ}\) for each compound.

The combustion of 0.1584 g benzoic acid increases the temperature of a bomb calorimeter by \(2.54^{\circ} \mathrm{C}\). Calculate the heat capacity of this calorimeter. (The energy released by combustion of benzoic acid is \(26.42 \mathrm{kJ} / \mathrm{g} .\) A 0.2130 -g sample of vanillin \(\left(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) is then burned in the same calorimeter, and the temperature increases by \(3.25^{\circ} \mathrm{C}\). What is the energy of combustion per gram of vanillin? Per mole of vanillin?

In a bomb calorimeter, the reaction vessel is surrounded by water that must be added for each experiment. since the amount of water is not constant from experiment to experiment, the mass of water must be measured in each case. The heat capacity of the calorimeter is broken down into two parts: the water and the calorimeter components. If a calorimeter contains \(1.00 \mathrm{kg}\) water and has a total heat capacity of \(10.84 \mathrm{kJ} /^{\circ} \mathrm{C},\) what is the heat capacity of the calorimeter components?
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