Spontaneity & Entropy

**Spontaneity **

A spontaneous process is one that, *once started*, continues on its own without input of energy. ** **A non-spontaneous process needs a continual input of energy.

**The application of spontaneity with respect to equilibrium is as follows:**

A reaction will never spontaneously move away from equilibrium and will always move spontaneously towards equilibrium.

**Determination of Spontaneity: **

Although spontaneous reactions are often exothermic, this is not a criteria for spontaneity. The best indicator of spontaneity in a reaction is the change in **Entropy (S or ****DS). **

The **Second Law of Thermodynamics** states that for a reaction to be spontaneous, there must be an increase in entropy.

Entropy is often defined as a measure of the disorder of a system, this is not a very accurate definition. **Entropy change measures the dispersal of energy: how ****much ****energy is spread out in a particular process, or how ****widely ****spread out it becomes **(at a specific temperature). This is reflected in the idea that a spontaneous change always results in the dispersal (spreading out) of energy (and also matter). You see now how hot pans cooling and chemical reactions belong to the ‘how much' category where energy is being transferred. Coffee in cream and gas expansion and perfume in air are ‘how widely' processes where the initial energy of the molecules stay the same but the volume occupied by the molecules increases. You have probably heard the phrase “the ever expanding Universe”, although this phrase is often taken to mean our ever increasing knowledge of our Universe, it also is quite true that our Universe is expanding and this effect is entropic in nature.

The **Third Law of Thermodynamics** is usually stated as a definition: **the entropy of a perfect crystal of an element at the absolute zero of temperature is zero. 0 Kelvin or absolute zero is the temperature at which atoms stop moving. This point is simply used as a starting point for the measurement of entropy. **

** **

**Entropy is then measured by determining the energy (heat) required to raise the temperature of a element from absolute zero to whatever temperature and conditions are prescribed. The change must be reversible and is calculated as:**

** **

**DS =q _{REV}/T **

** **

Since heat is added to the system, all entropy values are positive at temperatures above 0K.

Standard entropy values are indicated as S° and are for substances at 1 bar pressure and 1 molal solution concentration. The units for entropy are in J/K^{.}mol.

DS^{o} is calculated as the

** **

** **Some general (practical) guidelines for determining Entropy:

**The entropy of a given system depends on its state and temperature. **

**For a sample: S _{solid} < S_{liquid}: Solids are generally more ordered than liquids **

**S _{liquid} < S_{gas}: Liquids are more ordered than gases **

**S increases as T increases **

**Problems:**

** **

**Which substance has the higher entropy in each of the following pairs? Explain your answers.**

**CO**_{2}(at -78^{o}C) or CO_{2}at 0^{o}C?**Liquid water at 50**^{o}C or 25^{o}C?**A sample of pure silica or a contaminated sample of silica?****HF, HCl or HBr****C**_{2}H_{4}or N_{2}

** **

** **

**Calculate the entropy change ****DS ^{o} for the following:**

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**CS**_{2}+ 3O_{2}(g) ---> CO_{2}(g) + 2SO_{2}(g)

- Check to make sure the equation is balanced.
- Look up the Standard Molar Entropy for CO
_{2}(g) in the Thermodynamic Properties table found in your text and multiply it by its coefficient in the balanced equation (1).

1 mole (213.7 J/mole-K) = 213.7 J/K = Standard Entropy for one mole of CO_{2}

- Look up the Standard Molar Entropy for SO
_{2}and multiply it by its coefficient(2)

2 moles(248.1 J/mole-K) = 496.2 J/K = Standard Entropy for 2 moles of SO_{2}

- Add the result of steps 2 and 3 to get the Summ of the Entropies of the products

(+213.7 J/K) + (+496.2 J/K) = +709.9 J/K = Sum of Entropies of products

- Look up the Standard Molar Entropy of CS
_{2}(l) and multiply by its coeff (1)

1 mole ( +151 J/mole-K) = +151 J/K = Standard Entropy of one mole of CS_{2}(l)

- Look up the Standard Molar Entropy of O
_{2}(g) and multiply by its coefficient(3)

3 mole(+205 J/mole-K) = +615 J/K = Standard Entropy for 3 moles O_{2}

- Add results of steps 5 and 6 to get the Sum of the Standard Entropies for the Reactants

(+151 J/K) + (+615 J/K) = +766 J/K = Sum of Standard Entropies for Reactants

- Subtract the result of step 7 from step 4 to get the Standard Change in Entropy for the reaction

709.9 J/K - (+766 J/K) = -56.1 J/K = Delta S_{rx}

** **

**CS**_{2}(g) + 4H_{2}(g) ---> CH_{4}(g) + 2H_{2}S(g)

- Check to make sure the equation is balanced.
- Look up the Standard Molar Entropy of CH
_{4}(g) and multiply by its coefficient(1)

1 mole ( +186.3 J/mole-K) = +186.3 J/K = Standard Entropy of one mole of CH_{4}

- Look up the Standard Molar Entropy of H
_{2}S(g) and multiply by its coefficient(2)

2 mole(205.6 J/mole-K) = +411.2 J/K = Standard Entropy of 2 moles H_{2}S

- Add the results of steps 2 and 3 for the Sum of the Standard Entropies of the products

(+186.3 J/K) + (+411.2 J/K) = +597.5 J/K = Sum of the Standard Entropies for the Products

- Look up the Standard Molar Entropy of CS
_{2}(g) and multiply it by its coefficient(1)

1 mole( +151 J/mole-K) = +151 J/K = Standard Entropy for one mole of H_{2}S(g)

- Look up the Standard Molar Entropy of H
_{2}(g) and multiply by its coefficient(4)

4 moles (130.6 J/mole-K) = +522.4 J/K = Standard Entropy for 4 moles of H2

- Add the results of steps 5 and 6 for the Sum of the Standard Entropies for the Reactants

(+151 J/K) + (+522.4 J/K) = +673.4 J/K = Sum of Standard Entropies of Reactants

- Subtract the results of step 7 from the results of step 5 to get the Standard Entropy Change for the reaction, Delta S
_{rx}

597.5 J/K - ( +673.4 J/K) = -75.9 J/K = Delta S_{rx}

** **

**Name of Species Delta Hf(kJ/mole) Delta Gf(kJ/mole) S(J/mole-K)**

**CO _{2}(g) -393.5 -394.4 213.7**

**Cl _{2}(g) 0 0 223**

**H _{2}O(g) -241.8 -228.6 188.7**

**H _{2}O(l) -285.8 -237.2 69.9**

**O _{2}(g) 0 0 205**

**CS _{2}(g) 151**

**H _{2}(g) 0 0 130.6**

**H _{2}S(g) -20.17 -33.01 205.6**

**SO _{2}(g) 248.1**

**NH _{4}Cl(s) -314.55 -203.08 94.85**

**NH _{4}Cl(aq) -299.66 -210.57 169.9 **