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Chapter 19: Problem 53

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\) , the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

Short Answer

Expert verified
(a) The change in Gibbs free energy at constant temperature depends on both the enthalpy change (\(\Delta H\)) and entropy change (\(\Delta S\)) of the system, as given by the equation \(\Delta G = \Delta H - T\Delta S\). (b) If \(\Delta G\) is positive for a process occurring at constant \(T\) and \(P\), the process is non-spontaneous. (c) A large value of \(\Delta G\) does not directly imply a fast reaction rate, as the rate depends on activation energy (\(E_a\)) and the Arrhenius equation, not the Gibbs free energy change.

Step by step solution

01

(a) Gibbs free energy dependence on enthalpy and entropy change

Using the definition of Gibbs free energy change (\(\Delta G\)) at constant temperature and pressure, we can write the equation: \[ \Delta G = \Delta H - T\Delta S, \] where \(\Delta H\) is the enthalpy change, \(T\) is the temperature, and \(\Delta S\) is the entropy change. From this equation, we can see that the change in Gibbs free energy at constant temperature depends on the changes in both the enthalpy and entropy of the system.
02

(b) Spontaneity of the process

For a process to be spontaneous, \(\Delta G\) must be negative. In this case, \(\Delta G\) is given as positive, which implies that the process is non-spontaneous.
03

(c) Relationship between \(\Delta G\) and reaction rate

The magnitude of \(\Delta G\) is related to the thermodynamic feasibility of a process, so a large value of \(\Delta G\) does not directly imply that the process occurs at a fast rate. It is important to note that the reaction rate is determined by the activation energy (\(E_a\)) and the Arrhenius equation, not the Gibbs free energy change. The large value of \(\Delta G\) could indicate that the process is thermodynamically favorable, but it does not provide information about how fast the process occurs.

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Most popular questions from this chapter

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0,\) and \(w=0 .\) (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. (c) What is the "driving force" for the expansion of the gas: enthalpy or entropy?

Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (a) increase in temperature, (b) decrease in volume, (c) change of state from liquid to gas?

The element gallium (Ga) freezes at \(29.8^{\circ} \mathrm{C},\) and its molar enthalpy of fusion is \(\Delta H_{\text { fus }}=5.59 \mathrm{k} \mathrm{k} / \mathrm{mol}\) . (a) When molten gallium solidifies to Ga(s) at its normal melting point, is \(\Delta S\) positive or negative? (b) Calculate the value of \(\Delta S\) when 60.0 g of Ga(l) solidifies at \(29.8^{\circ} \mathrm{C}\) .

Consider the decomposition of barium carbonate: $$ \mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g) $$ Using data from Appendix \(\mathrm{C}\) , calculate the equilibrium pressure of \(\mathrm{CO}_{2}\) at (a) 298 \(\mathrm{K}\) and \((\mathbf{b}) 1100 \mathrm{K} .\)

As shown here, one type of computer keyboard cleaner contains liquefied \(1,1\) -difluoroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{F}_{2}\right),\) which is a gas at atmospheric pressure. When the nozzle is squeezed, the \(1,1\) -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects. (a) Based on your experience, is the vaporization a spontaneous process at room temperature? (b) Defining the \(1,1\) -difluoroethane as the system, do you expect \(q_{s y s}\) for the process to be positive or negative? (c) Predict whether \DeltaS is positive or negative for this process. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on enthalpy or entropy? [Sections 19.1 and 19.2\(]\)
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