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Chapter 6: Problem 18

The enthalpy change for a reaction is a state function and it is an extensive property. Explain.

Short Answer

Expert verified
The enthalpy change (\(ΔH\)) for a reaction is a state function because it depends only on the initial and final states of the system and is independent of the path taken during the reaction process. It can be demonstrated by Hess's Law, which states that the overall enthalpy change of a reaction is the same, regardless of the individual steps or reactions involved. Additionally, enthalpy change is an extensive property because it depends on the quantity of matter in the system. When the amount of reactants changes, the overall enthalpy change will also change, making it directly proportional to the quantity of matter involved.

Step by step solution

01

Definition of State Function

A state function is a property of a system that depends only on its current state and is independent of the path taken to reach that state. This means that the value of a state function is determined by the initial and final states of a chemical reaction and not on the specific steps taken during the reaction process.
02

Definition of Extensive Property

An extensive property is a property of a system that depends on the quantity of matter in the system. This means that an extensive property is directly proportional to the size or amount of the substances involved in a reaction. Examples of extensive properties include mass, volume, and enthalpy.
03

Enthalpy Change as a State Function

Enthalpy change (\(ΔH\)) is the amount of heat absorbed or released during a chemical reaction under constant pressure conditions. \(ΔH\) is a state function because it only depends on the initial and final states of the system and not on the specific path taken during the reaction. This can be demonstrated by using Hess's Law, which states that the overall enthalpy change of a reaction is the same, regardless of the individual steps or reactions involved in the process. The enthalpy change only depends on the enthalpy values of the reactants and products and not on the intermediate steps of the reaction.
04

Enthalpy Change as an Extensive Property

Enthalpy change is an extensive property because it depends on the amount of reactants and products in the system. When the quantity of reactants changes, the overall enthalpy change of the reaction will also change. For example, if the amount of reactants in a reaction is doubled, the enthalpy change (\(ΔH\)) of the reaction will also double, making it directly proportional to the quantity of matter in the system. To summarize, the enthalpy change for a reaction is a state function because it depends only on the initial and final states of the system, and it is an extensive property because it depends on the quantity of matter in the system.

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Most popular questions from this chapter

A \(5.00-\mathrm{g}\) sample of aluminum pellets (specific heat capacity \(=\) \(0.89 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) ) and a \(10.00-\mathrm{g}\) sample of iron pellets (specific heat capacity \(=0.45 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) ) are heated to \(100.0^{\circ} \mathrm{C}\). The mixture of hot iron and aluminum is then dropped into \(97.3 \mathrm{~g}\) water at \(22.0^{\circ} \mathrm{C}\). Calculate the final temperature of the metal and water mixture, assuming no heat loss to the surroundings.

For the reaction \(\mathrm{HgO}(s) \rightarrow \mathrm{Hg}(l)+\frac{1}{2} \mathrm{O}_{2}(g), \Delta H=+90.7 \mathrm{~kJ}:\) a. What quantity of heat is required to produce \(1 \mathrm{~mol}\) of mercury by this reaction? b. What quantity of heat is required to produce \(1 \mathrm{~mol}\) of oxygen gas by this reaction? c. What quantity of heat would be released in the following reaction as written? $$ 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{HgO}(s) $$

In a coffee-cup calorimeter, \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) and \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\) 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 \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\).

The standard enthalpy of formation of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(298 \mathrm{~K}\) is \(-285.8\) \(\mathrm{kJ} / \mathrm{mol} .\) Calculate the change in internal energy for the following process at \(298 \mathrm{~K}\) and 1 atm: $$ \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta E^{\circ}=? $$ (Hint: Using the ideal gas equation, derive an expression for work in terms of \(n, R\), and \(T\).)

The enthalpy of combustion of \(\mathrm{CH}_{4}(\mathrm{~g})\) when \(\mathrm{H}_{2} \mathrm{O}(l)\) is formed is \(-891 \mathrm{~kJ} / \mathrm{mol}\) and the enthalpy of combustion of \(\mathrm{CH}_{4}(\mathrm{~g})\) when \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is formed is \(-803 \mathrm{~kJ} / \mathrm{mol} .\) Use these data and Hess's law to determine the enthalpy of vaporization for water.
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