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Chapter 17: Problem 3

Gas \(A_{2}\) reacts with gas \(B_{2}\) to form gas AB at a constant temperature. The bond energy of \(A B\) is much greater than that of either reactant. What can be said about the sign of \(\Delta H ? \Delta S_{\mathrm{surr}} ?\) $\Delta S$? Explain how potential energy changes for this process. Explain how random kinetic energy changes during the process.

Short Answer

Expert verified
In the reaction where gas A₂ reacts with gas B₂ to form gas AB, ΔH is negative as it is an exothermic reaction, releasing energy. ΔSsurr is positive because the released heat increases the entropy of the surroundings. However, ΔS will be negative as the number of gaseous particles decreases, reducing the system's entropy. The potential energy decreases during the reaction due to the formation of stronger AB bonds, and the random kinetic energy increases because of the heat transfer, leading to higher particle motion and randomness.

Step by step solution

01

Analyze the bond energy information

Since the bond energy of AB is much greater than that of either reactant, we can infer that the formation of the AB bond is energetically favorable. This means that energy is released when the AB bond is formed.
02

Determine the sign of ΔH

As energy is released during the formation of the AB bond, the reaction is exothermic. Therefore, the enthalpy change, ΔH, would be negative.
03

Determine the sign of ΔS_surr

An exothermic reaction, like the one described, releases heat into the surroundings, increasing the randomness (entropy) of the surroundings. Thus, the entropy change of the surroundings, ΔSsurr, would be positive.
04

Determine the sign of ΔS

In this reaction, two gaseous reactants (A₂ and B₂) combine to form one gaseous product (AB). As the number of gaseous particles decreases, the randomness (entropy) of the system decreases. Therefore, the entropy change, ΔS, would be negative.
05

Explain the change in potential energy

The potential energy decreases during the reaction, since energy is released when the more stable AB bond is formed. The potential energy largely resides in the chemical bonds; so, when stronger bonds are formed, the potential energy is lowered.
06

Explain the change in random kinetic energy

The random kinetic energy, associated with the motion of particles, increases during the reaction. As the reaction is exothermic, heat is released into the surroundings. This heat transfer increases the kinetic energy and the motion of the particles in the system and surroundings, leading to a higher degree of randomness. In conclusion, the given reaction has a negative ΔH, a positive ΔSsurr, and a negative ΔS. The potential energy decreases, and the random kinetic energy increases during the process.

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Most popular questions from this chapter

For ammonia \(\left(\mathrm{NH}_{3}\right),\) the enthalpy of fusion is 5.65 \(\mathrm{kJ} / \mathrm{mol}\) and the entropy of fusion is 28.9 $\mathrm{J} / \mathrm{K} \cdot$ mol. a. Will \(\mathrm{NH}_{3}(s)\) spontaneously melt at \(200 . \mathrm{K}\) ? b. What is the approximate melting point of ammonia?

For the reaction $$\mathrm{CS}_{2}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{SO}_{2}(g)$$ \(\Delta S^{\circ}\) is equal to \(-143 \mathrm{JK}\) . Use this value and data from Appendix 4 to calculate the value of \(S^{\circ}\) for $\mathrm{CS}_{2}(g) .$

Predict the sign of \(\Delta S^{\circ}\) and then calculate \(\Delta S^{\circ}\) for each of the following reactions. a. $2 \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{SO}_{2}(g) \longrightarrow 3 \mathrm{S}_{\text { rhombic}}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)$ b. $2 \mathrm{SO}_{3}(g) \longrightarrow 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$ c. $\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)$

What information can be determined from \(\Delta G\) for a reaction? Does one get the same information from \(\Delta G^{\circ},\) the standard free energy change? \(\Delta G^{\circ}\) allows determination of the equilibrium constant \(K\) for a reaction. How? How can one estimate the value of \(K\) at temperatures other than \(25^{\circ} \mathrm{C}\) for a reaction? How can one estimate the temperature where \(K=1\) for a reaction? Do all reactions have a specific temperature where \(K=1 ?\)

Which of the following processes are spontaneous? a. Salt dissolves in \(\mathrm{H}_{2} \mathrm{O}\) . b. A clear solution becomes a uniform color after a few drops of dye are added. c. Iron rusts. d. You clean your bedroom.
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