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Chapter 17: Problem 4

What types of experiments can be carried out to determine whether a reaction is spontaneous? Does spontaneity have any relationship to the final equilibrium position of a reaction? Explain.

Short Answer

Expert verified
A spontaneous reaction occurs without external energy input and is influenced by enthalpy change (鈭咹) and entropy change (鈭哠). To determine spontaneity, calculate the Gibbs free energy change (鈭咷) using the formula 鈭咷 = 鈭咹 - T鈭哠, where T is the absolute temperature in Kelvin. If 鈭咷 is negative, the reaction is spontaneous, and if 鈭咷 is positive, it is non-spontaneous. Spontaneity is related to the final equilibrium position of a reaction, as a reaction mixture reaches equilibrium by following the lowest free energy path, determined by the relative values of 鈭咹, 鈭哠, and T.

Step by step solution

01

Defining spontaneous reactions

A spontaneous reaction is a reaction that occurs without the input of external energy. This means that the reaction will proceed on its own under certain conditions (temperature, pressure, etc.). The spontaneity of a reaction is mainly governed by two factors: enthalpy change (鈭咹) and entropy change (鈭哠). The Gibbs free energy change (鈭咷) is the determining factor for the spontaneity of a reaction, and it can be calculated by the formula 鈭咷 = 鈭咹 - T鈭哠, where T is the absolute temperature in Kelvin.
02

Measuring enthalpy change

One way to measure enthalpy change (鈭咹) experimentally is to use a calorimeter. A calorimeter measures the heat evolved or absorbed during a reaction, which is related to the enthalpy change. By measuring the temperature change and using the specific heat capacity of the reaction mixture, we can determine the enthalpy change for the reaction.
03

Measuring entropy change

To measure the entropy change (鈭哠) experimentally, we usually look at the difference in the number of moles of gas particles in the reactants and products. An increase in the number of moles of gas particles usually leads to a positive entropy change, whereas a decrease leads to a negative entropy change.
04

Determining the spontaneity of a reaction through Gibbs free energy

To determine whether a reaction is spontaneous, calculate the Gibbs free energy change (鈭咷) by applying the formula 鈭咷 = 鈭咹 - T鈭哠. If 鈭咷 is negative, the reaction is spontaneous. If 鈭咷 is positive, the reaction is non-spontaneous and will not occur. If 鈭咷 is zero, the reaction is in equilibrium and will proceed at an infinitely slow rate.
05

Spontaneity and equilibrium position

Spontaneity has a relationship with the final equilibrium position of a reaction. A spontaneous reaction proceeds in the direction where the free energy decreases and reaches an equilibrium position where the free energy is at its lowest possible value for that reaction mixture. At equilibrium, 鈭咷 is zero, and the reaction will cease to proceed any further. This means that a reaction mixture will reach its final equilibrium position by following the path of spontaneity, which is determined by the relative values of 鈭咹, 鈭哠, and T for the reaction.

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Most popular questions from this chapter

Given the values of \(\Delta H\) and \(\Delta S,\) which of the following changes will be spontaneous at constant \(T\) and \(P ?\) a. \(\Delta H=+25 \mathrm{kJ}, \Delta S=+5.0 \mathrm{J} / \mathrm{K}, T=300 . \mathrm{K}\) b. \(\Delta H=+25 \mathrm{kJ}, \Delta S=+100 . \mathrm{J} / \mathrm{K}, T=300 . \mathrm{K}\) c. \(\Delta H=-10 . \mathrm{kJ}, \Delta S=+5.0 \mathrm{J} / \mathrm{K}, T=298 \mathrm{K}\) d. \(\Delta H=-10 . \mathrm{kJ}, \Delta S=-40 . \mathrm{J} / \mathrm{K}, T=200 . \mathrm{K}\)

Predict the sign of \(\Delta S^{\circ}\) and then calculate \(\Delta S^{\circ}\) for each of the following reactions. a. \(\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) b. \(2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{HCl}(g) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Cl}^{-}(a q)\)

Describe how the following changes affect the positional probability of a substance. a. increase in volume of a gas at constant T b. increase in temperature of a gas at constant V c. increase in pressure of a gas at constant T

Using the free energy profile for a simple one-step reaction, show that at equilibrium \(K=k_{f} / k_{\mathrm{r}},\) where \(k_{\mathrm{f}}\) and \(k_{\mathrm{r}}\) are the rate constants for the forward and reverse reactions. Hint: Use the relationship \(\Delta G^{\circ}=-R T \ln (K)\) and represent \(k_{\mathrm{f}}\) and \(k_{\mathrm{r}}\) using the Arrhenius equation \(\left(k=A e^{-E_{2} / R T}\right)\) b. Why is the following statement false? "A catalyst can increase the rate of a forward reaction but not the rate of the reverse reaction."

Predict the sign of \(\Delta S\) for each of the following and explain. a. the evaporation of alcohol b. the freezing of water c. compressing an ideal gas at constant temperature d. dissolving NaCl in water
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