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Chapter 19: Problem 41

Predict the sign of the entropy change of the system for each of the following reactions: (a) $\mathrm{CO}(g)+\mathrm{H}_{2}(g) \longrightarrow C(s)+\mathrm{H}_{2} \mathrm{O}(g)$ (b) $2 \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$ (c) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{HCl}(g)+\mathrm{NH}_{3}(g)$ (d) $2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(g)$

Short Answer

Expert verified
(a) \(\Delta S < 0\) (negative entropy change) (b) \(\Delta S < 0\) (negative entropy change) (c) \(\Delta S > 0\) (positive entropy change) (d) \(\Delta S < 0\) (negative entropy change)

Step by step solution

01

Identify the change in the number of gas particles

In this reaction, we have 2 moles of gas as reactants (CO and H2) and 1 mole of gas as the product (H2O). The product also includes C(s), a solid.
02

Determine the entropy change

The reaction involves a decrease in the number of gas particles and the appearance of a solid. This means the disorder of the system decreases. Therefore, the entropy change for this reaction will be negative. (b) \(2 \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2\mathrm{NO}_{2}(g)\)
03

Identify the change in the number of gas particles

In this reaction, we have 3 moles of gas as reactants (2 moles O2 and 1 mole N2) and 2 moles of gas as products (2 moles NO2).
04

Determine the entropy change

The reaction involves a decrease in the number of gas particles. This means the disorder of the system decreases. Therefore, the entropy change for this reaction will be negative. (c) \(\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow\mathrm{HCl}(g)+\mathrm{NH}_{3}(g)\)
05

Identify the change in the number of gas particles

In this reaction, we have no moles of gas as reactants (only solid NH4Cl) and 2 moles of gas as products (HCl and NH3).
06

Determine the entropy change

The reaction involves an increase in the number of gas particles. This means the disorder of the system increases. Therefore, the entropy change for this reaction will be positive. (d) \(2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(g)\)
07

Identify the change in the number of gas particles

In this reaction, we have 3 moles of gas as reactants (2 moles C2H4 and 1 mole O2) and 2 moles of gas as products (2 moles C2H4O).
08

Determine the entropy change

The reaction involves a decrease in the number of gas particles. This means the disorder of the system decreases. Therefore, the entropy change for this reaction will be negative.

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Most popular questions from this chapter

A standard air conditioner involves a \(r\) frigerant that is typically now a fluorinated hydrocarbon, such as \(\mathrm{CH}_{2} \mathrm{~F}_{2}\). An air- conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram). During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (a) What is the sign of \(q\) for the expansion? (b) What is the sign of \(q\) for the compression? (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why? (d) Imagine that a sample of liquid refrigerant undergoes expansion followed by compression, so that it is back to its original state. Would you expect that to be a reversible process? (e) Suppose that a house and its exterior are both initially at $31^{\circ} \mathrm{C}$. Some time after the air conditioner is turned on, the house is cooled to \(24^{\circ} \mathrm{C}\). Is this process spontaneous of nonspontaneous?

Acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\), is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .(\mathbf{b})\) How much heat is produced in burning \(1 \mathrm{~mol}\) of $\mathrm{C}_{2} \mathrm{H}_{2}$ under standard conditions if both reactants and products are brought to \(298 \mathrm{~K} ?\) (c) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to $25^{\circ} \mathrm{C} .$ (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\).

Indicate whether each statement is true or false. (a) \(\Delta S\) depends on whether the process is reversible or irreversible. \((\mathbf{b})\) If a system undergoes an irreversible change, the entropy of the universe increases. (c) Only if the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings, the system undergoes a reversible process. (d) If the entropy change of the system is zero, the system undergoes a reversible process.

Indicate whether each of the following statements is trueor false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of $\Delta H\( for the process \)\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.
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