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Chapter 6: Problem 12

Explain what is meant by a state function. Give two examples of quantities that are state functions and two that are not.

Short Answer

Expert verified
A state function is a property that only depends on the current state of a system, not how the system achieved that state. Examples of state functions include internal energy and entropy. In contrast, non-state functions like work and heat depend on the path undertaken by the system to reach its current state.

Step by step solution

01

Understanding the Concept

A state function, in physics and thermodynamics, refers to a property that depends only on the current equilibrium state or condition of a system, and not on the path by which the system arrived at that state. This means that no matter how a system changes from one state to another, if those beginning and ending states are identical, the value of the state function for those two states will also be the same.
02

Examples of State Functions

Two examples of state functions are internal energy and entropy of a system: 1. Internal energy (\( E \)): It's a state function because it depends only on the state of the system at that moment and not how it got to that state. 2. Entropy (\( S \)): This thermodynamic property measures the level of disorder of a system and is also a state function. It doesn't matter how a system arrived at its current state; the level of disorder in that state will always be the same.
03

Examples of Non-State Functions

Two examples of quantities that are not state functions are work and heat: 1. Work (\( W \)): The work done on or by a system depends on the path taken and so it's not a state function. 2. Heat (\( Q \)): The amount of heat absorbed or released is not a state function as different paths (fast heating versus slow, for instance) can change the overall amount of heat exchanged.

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Most popular questions from this chapter

Describe how chemists use Hess's law to determine the \(\Delta H_{\mathrm{f}}^{\circ}\) of a compound by measuring its heat (enthalpy) of combustion.

Lime is a term that includes calcium oxide \((\mathrm{CaO}\) also called quicklime) and calcium hydroxide \(\left[\mathrm{Ca}(\mathrm{OH})_{2},\right.\) also called slaked lime \(] .\) It is used in the steel industry to remove acidic impurities, in airpollution control to remove acidic oxides such as \(\mathrm{SO}_{2}\), and in water treatment. Quicklime is made industrially by heating limestone \(\left(\mathrm{CaCO}_{3}\right)\) above \(2000^{\circ} \mathrm{C}\) : $$ \begin{aligned} \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \\ \Delta H^{\circ} &=177.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Slaked lime is produced by treating quicklime with water: $$ \begin{aligned} \mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s) \\ \Delta H^{\circ} &=-65.2 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ The exothermic reaction of quicklime with water and the rather small specific heats of both quicklime \(\left(0.946 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) and slaked lime \(\left(1.20 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) make it hazardous to store and transport lime in vessels made of wood. Wooden sailing ships carrying lime would occasionally catch fire when water leaked into the hold. (a) If a 500 -g sample of water reacts with an equimolar amount of \(\mathrm{CaO}\) (both at an initial temperature of \(\left.25^{\circ} \mathrm{C}\right)\), what is the final temperature of the product, \(\mathrm{Ca}(\mathrm{OH})_{2} ?\) Assume that the product absorbs all of the heat released in the reaction. (b) Given that the standard enthalpies of formation of \(\mathrm{CaO}\) and \(\mathrm{H}_{2} \mathrm{O}\) are \(-635.6 \mathrm{~kJ} / \mathrm{mol}\) and \(-285.8 \mathrm{~kJ} / \mathrm{mol}\), respectively, cal- culate the standard enthalpy of formation of \(\mathrm{Ca}(\mathrm{OH})_{2}\).

Consider these changes. (a) \(\operatorname{Hg}(l) \longrightarrow \operatorname{Hg}(g)\) (b) \(3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}_{3}(g)\) (c) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)\) At constant pressure, in which of the reactions is work done by the system on the surroundings? By the surroundings on the system? In which of them is no work done?

Which is the more negative quantity at \(25^{\circ} \mathrm{C}: \Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{H}_{2} \mathrm{O}(l)\) or \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{H}_{2} \mathrm{O}(g) ?\)

Consider this reaction: $$ \begin{aligned} 2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow & 4 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{CO}_{2}(g) \\ \Delta H &=-1452.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ What is the value of \(\Delta H\) if (a) the equation is multiplied throughout by \(2,\) (b) the direction of the reaction is reversed so that the products become the reactants and vice versa, (c) water vapor instead of liquid water is formed as the product?
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