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Chapter 19: Problem 46

Why is \(\Delta G^{\circ}\) such an important property of a chemical reaction, even though the reaction is generally carried out under nonstandard conditions?

Short Answer

Expert verified
\(\Delta G^{\circ}\) is an important property as it provides insights about whether a reaction will occur spontaneously even if the reaction is under non-standard conditions. It serves as a reference point for other conditions by applying the \(\Delta G = \Delta G^{\circ} + RT \ln Q\) equation.

Step by step solution

01

Understanding Gibbs Free Energy

\(\Delta G^{\circ}\) (standard Gibbs free energy change) is the difference in Gibbs free energy of reactants and products at standard temperature and pressure(298 K and 1 atm respectively). It provides an idea of whether a reaction will proceed spontaneously under standard conditions. A negative \(\Delta G^{\circ}\) signifies a spontaneous reaction while a positive \(\Delta G^{\circ}\) indicates a non-spontaneous one.
02

The role of \(\Delta G^{\circ}\) under non-standard conditions

The \(\Delta G^{\circ}\) value calculated under standard conditions can be related to the free energy change \(\Delta G\) at any other temperature or pressure (non-standard conditions) using the equation \(\Delta G = \Delta G^{\circ} + RT \ln Q\), where R is the ideal gas constant, T is the temperature in Kelvin, and Q is the reaction quotient. Even under non-standard conditions, the \(\Delta G^{\circ}\) serves as a reference point to calculate the \(\Delta G\) at those conditions. Hence, \(\Delta G^{\circ}\) remains an important property.
03

Its Contribution to reaction feasibility

Whether under standard or non-standard conditions, knowing the value of \(\Delta G^{\circ}\) provides insights about whether a reaction will occur spontaneously. Hence, even if reactions don't always occur under standard conditions, knowing \(\Delta G^{\circ}\) is still important.

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Most popular questions from this chapter

The standard Gibbs energy change for the reaction $$\mathrm{NH}_{3}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1) \rightleftharpoons \mathrm{NH}_{4}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})$$ is \(29.05 \mathrm{kJ} \mathrm{mol}^{-1}\) at \(298 \mathrm{K}\). Use this thermodynamic quantity to decide in which direction the reaction is spontaneous when the concentrations of \(\mathrm{NH}_{3}(\mathrm{aq})\) \(\mathrm{NH}_{4}^{+}(\mathrm{aq}),\) and \(\mathrm{OH}^{-}(\mathrm{aq})\) are \(0.10 \mathrm{M}, 1.0 \times 10^{-3} \mathrm{M}\) and \(1.0 \times 10^{-3} \mathrm{M},\) respectively.

Calculate the equilibrium constant and Gibbs energy for the reaction \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})\) at \(483 \mathrm{K}\) by using the data tables from Appendix D. Are the values determined here different from or the same as those in exercise \(35 ?\) Explain.

Sodium carbonate, an important chemical used in the production of glass, is made from sodium hydrogen carbonate by the reaction \(2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) Data for the temperature variation of \(K_{\mathrm{p}}\) for this reaction are \(K_{\mathrm{p}}=1.66 \times 10^{-5}\) at \(30^{\circ} \mathrm{C} ; 3.90 \times 10^{-4} \mathrm{at}\) \(50^{\circ} \mathrm{C} ; 6.27 \times 10^{-3}\) at \(70^{\circ} \mathrm{C} ;\) and \(2.31 \times 10^{-1}\) at \(100^{\circ} \mathrm{C}\) (a) Plot a graph similar to Figure \(19-12,\) and determine \(\Delta H^{\circ}\) for the reaction. (b) Calculate the temperature at which the total gas pressure above a mixture of \(\mathrm{NaHCO}_{3}(\mathrm{s})\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})\) is \(2.00 \mathrm{atm}\).

The reaction, \(2 \mathrm{Cl}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \Delta H=\) \(-161 \mathrm{kJ},\) is expected to be (a) spontaneous at all temperatures; (b) spontaneous at low temperatures, but nonspontaneous at high temperatures; (c) nonspontaneous at all temperatures; (d) spontaneous at high temperatures only.

The Gibbs energy change of a reaction can be used to assess (a) how much heat is absorbed from the surroundings; (b) how much work the system does on the surroundings; (c) the net direction in which the reaction occurs to reach equilibrium; (d) the proportion of the heat evolved in an exothermic reaction that can be converted to various forms of work.
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