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Chapter 17: Problem 79

Describe two ways that you could measure \(\Delta G^{\circ}\) of a reaction.

Short Answer

Expert verified
The two methods for measuring standard change in Gibbs free energy (\(\Delta G^{\circ}\)) of a reaction are direct measurement, which can be done in reactions where the products and reactants are at equilibrium under standard conditions, and indirect measurement done via Hess's Law, which is done by writing the desired reaction as the sum of other reactions for which \(\Delta G^{\circ}\) is already known.

Step by step solution

01

Method 1: Direct Measurement

The \(\Delta G^{\circ}\) can be measured directly in reactions where the reactants and products are at equilibrium under standard conditions. At this point we know that \(\Delta G = 0\), hence we can calculate \(\Delta G^{\circ}\) using the formula \(\Delta G^{\circ} = -RTlnK\), where \(R\) is the gas constant, \(T\) is the temperature in Kelvin and \(K\) is the equilibrium constant.
02

Method 2: Indirect Measurement via Hess's Law

If the reaction isn't under standard conditions or isn't at equilibrium, we can use the laws of thermodynamics to measure it indirectly. One such law is Hess's Law, which states that the total enthalpy change of a reaction is the sum of the enthalpy changes for each step in the reaction, even if the total final reaction isn't the same reaction. Since the \(\Delta G^{\circ}\) for many reactions have been measured and tabulated, if you can write your reaction as the sum of other reactions for which you know the \(\Delta G^{\circ}\), then you can calculate your \(\Delta G^{\circ}\) even if you can't measure it directly.

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Most popular questions from this chapter

Entropy has sometimes been described as "time's arrow" because it is the property that determines the forward direction of time. Explain.

(a) Over the years there have been numerous claims about "perpetual motion machines," machines that will produce useful work with no input of energy. Explain why the first law of thermodynamics prohibits the possibility of such a machine existing. (b) Another kind of machine, sometimes called a "perpetual motion of the second kind," operates as follows. Suppose an ocean liner sails by scooping up water from the ocean and then extracting heat from the water, converting the heat to electric power to run the ship, and dumping the water back into the ocean. This process does not violate the first law of thermodynamics, for no energy is created - energy from the ocean is just converted to electrical energy. Show that the second law of thermodynamics prohibits the existence of such a machine.

The reaction \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) proceeds spontaneously at \(25^{\circ} \mathrm{C}\) even though there is a decrease in the number of microstates of the system (gases are converted to a solid). Explain.

Consider two carboxylic acids (acids that contain the \(-\mathrm{COOH}\) group \(): \mathrm{CH}_{3} \mathrm{COOH}\) (acetic acid, \(\left.K_{\mathrm{a}}=1.8 \times 10^{-5}\right)\) and \(\mathrm{CH}_{2} \mathrm{ClCOOH}\) (chloroacetic acid, \(K_{\mathrm{a}}=1.4 \times 10^{-3}\) ). (a) Calculate \(\Delta G^{\circ}\) for the ionization of these acids at \(25^{\circ} \mathrm{C}\). (b) From the equation \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ},\) we see that the contributions to the \(\Delta G^{\circ}\) term are an enthalpy term \(\left(\Delta H^{\circ}\right)\) and a temperature times entropy term \(\left(T \Delta S^{\circ}\right) .\) These contributions are listed below for the two acids: $$ \begin{array}{lcc} \hline & \Delta H^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) & T \Delta S^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) \\ \hline \mathrm{CH}_{3} \mathrm{COOH} & -0.57 & -27.6 \\ \mathrm{CH}_{2} \mathrm{ClCOOH} & -4.7 & -21.1 \\ \hline \end{array} $$ Which is the dominant term in determining the value of \(\Delta G^{\circ}\) (and hence \(K_{\mathrm{a}}\) of the acid)? (c) What processes contribute to \(\Delta H^{\circ} ?\) (Consider the ionization of the acids as a Brønsted acid-base reaction.) (d) Explain why the \(T \Delta S^{\circ}\) term is more negative for \(\mathrm{CH}_{3} \mathrm{COOH}\)

Which of the following is not accompanied by an increase in the entropy of the system: (a) mixing of two gases at the same temperature and pressure, (b) mixing of ethanol and water, (c) discharging a battery, (d) expansion of a gas followed by compression to its original temperature, pressure, and volume?
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