## Sunday, October 21, 2007

### Study Guide Ch. 6 ENERGETICS

JEE Syllabus

Energetics:
First law of thermodynamics;
Internal energy, work and heat,
pressure-volume work;
Enthalpy,
Hess's law;
Heat of reaction, fusion and vapourization;
Second law of thermodynamics;
Entropy;
Free energy;
Criterion of spontaneity.
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Main Topics in TMH Book Chapter

FIRST LAW THERMODYNAMICS
INTERNAL ENERGY AND ENTHALPY
ENTHALPY CHANGE OF A CHEMICAL EQUATION
MOLAR ENHTALPIES OF FORMATIONS
HESS'S LAW OF CONSTANT HEAT SUMMATION
TYPES OF REACTIONS
RELATION BETWEEN DELTA H AND DELTA U OF A CHEMICAL EQUATION
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Enthalpy Change, ∆H, With Temperature and State Change

Enthalpy, represented by the symbol H, is essentially a chemistry term for heat, and a term for total kinetic energy of particle motion in a sample. If the reaction is exothermic, the energy contained in the substances is reduced so ∆H has a negative value. On the other hand, if the reaction is endothermic, the substances absorb energy and ∆H is positive.

Temperature is a measure of the average kinetic energy of the particles in a sample.

The faster the molecules in a sample of water the higher the temperature.

Changing temperature of a sample requires a change in enthalpy

It makes sense that you have to add heat to increase temperature, and as a sample cools it gives off heat. The amount of heat required to change the temperature of a sample depends on two factors:

# Mass. The bigger the sample the more heat needed to change its temperature.

# Specific heat capacity of the substance it is made of. This is the energy needed to change the temperature of a 1 gram sample 1 Celsius and it is different for different materials. Its symbol is Cp.

When you go to the beach on a hot summer day, you may have noticed that dry sand can get really hot, while wet sand stays cooler, though the air over them is obviously the same temperature and they are getting the same sunlight. How about dry pavement versus wet pavement? Metal versus tile?

The difference is the specific heat capacity of the different materials. Substances with low specific heat capacities will get very hot very fast, while those with large specific heat capacities warm up much slower since more energy is required to change their temperature. In fact, liquid water has about the highest specific heat of any common substance, so it tends to "heat up" and 'cool down' very slowly compared to most other substances. Ice and steam have lower heat capacities than liquid water.

Some people who prize their outdoor plants set gallon jugs of water around their plants. How does this help the plants? During the heat of the day, that water absorbs energy from the air around it, leaving the air cooler. During the cold night, that water releases that energy as it slowly cools, warming the air around it. This is known as a heat sink.

To find the energy required to change the temperature of a sample use Changing temperature of a sample requires a change in enthalpy

It makes sense that you have to add heat to increase temperature, and as a sample cools it gives off heat. The amount of heat required to change the temperature of a sample depends on two factors:

? Mass. The bigger the sample the more heat needed to change its temperature.

? Specific heat capacity of the substance it is made of. This is the energy needed to change the temperature of a 1 gram sample 1? Celsius and it is different for different materials. For some reason its symbol is Cp. Sorry.

When you go to the beach on a hot summer day, you may have noticed that dry sand can get really hot, while wet sand stays cooler, though the air over them is obviously the same temperature and they are getting the same sunlight. How about dry pavement versus wet pavement? Metal versus tile?

The difference is the specific heat capacity of the different materials. Substances with low specific heat capacities will get very hot very fast, while those with large specific heat capacities warm up much slower since more energy is required to change their temperature. In fact, liquid water has about the highest specific heat of any common substance, so it tends to "heat up" and 'cool down' very slowly compared to most other substances. Ice and steam have lower heat capacities than liquid water.

Some people who prize their outdoor plants set gallon jugs of water around their plants. How does this help the plants? During the heat of the day, that water absorbs energy from the air around it, leaving the air cooler. During the cold night, that water releases that energy as it slowly cools, warming the air around it. This is known as a heat sink.

In Chicago, which sits on the shores of Lake Michigan, the weather near the lake is warmer in winter and cooler in summer than the weather farther inland. This is known as the lake effect. The lake functions as a giant heat sink.

To find the energy required to change the temperature of a sample use ∆H = (m)(∆T)(Cp)

Stoichiometry with Energy

Enthalpy values can be included as part of balanced chemical equations. In exothermic reactions, ∆H is negative, but energy is listed as a positive value on the product side of the equation. In endothermic reactions, ∆H is positive and energy is required and is listed on the reactant side of the equation.

The number part of the energy value (as opposed to the unit) can act as a coefficient of a mole ratio, just as any other coefficient would. This way you can convert energy information to information about any substance in a balanced equation and vice versa.

2H-2 + O-2 → 2 H-2O + 561.6 kJ

Enthalpy changes of different types have different names.

The enthalpy change when something dissolves is heat of solution (∆H sol) The enthalpy change during a chemical reaction is heat of reaction (∆Hrxn). The enthalpy change during a comustion reaction is heat of combustion (∆Hcomb). The enthalpy change during a reaction in which a compound is formed from its elements is heat of formation (∆Hf).

Heat of Formation is an important concept.

Heat of Formation Problems.

The enthalpy change can be calculated by taking the total enthalpy of the products - the total enthalpy of the reactants. The formula is...

DHrxn = (the sum of ∆Hf products ) - (the sum of the ∆Hf reactants )

To do this, multiply the number of moles, or coefficient from the balanced equation, of each substance by its heat of formation), and add them up for the products, then do the same for the reactants. Then subtract. Heats of formation are given in kJ / mol, but ∆H is in kJ, since the moles cancel out.

Hess's Law

Hess's Law states that the enthalpy change for a reaction that occurs in many steps is the same as if it occurred in one step. Another way to put this is if several reactions add up to some total reaction, then their enthalpy changes will add up to the enthalpy change for the total reaction.

DHtotal = ∆Hrxn 1 + ∆Hrxn 2 + ∆Hrxn 3 + etc.

Hess's law problems usually give you two or three reactions with their enthalpy change information, then ask you to find the enthalpy change for some target reaction. You must figure out how to make the given reactions add up to the target. This can mean reversing the reactions (and reversing the sign on the enthalpy change), or using them multiple times, or both.

Entropy

Entropy (S) is a measure of the amount of disorder in a substance Gases with their rapid random motion are high in entropy, and solids with their ordered crystalline lattice are low in entropy.

The change in entropy (∆S) is determined just like a heat of formation problem, only use entropy values instead.

∆Srxn = (the sum of ∆Sproducts ) - (the sum of the ∆Sreactants )

Note that the units for entropy are given in J / mol K. ∆S is in J / K, since the moles cancel out.

K stands for Kelvins, the temperature unit on the absolute scale. Also called the Kelvin scale, it is named for Lord Kelvin, who developed it, so the units should be capitalized.

Entropy is temperature affected. It is large at high temperatures, and small at low temperatures. Enthalpy is not temperature affected.

How Enthalpy and Entropy Drive Change

If a reaction will occur spontaneously, it will occur so the products are said to be favored. If a reaction will not occur spontaneously, then the reverse reaction will(in a reversible reaction), so the reactants are said to be favored.

Exothermic changes, those with negative enthalpy changes, are favored to occur spontaneously. So if ∆H is negative, a reaction is more likely than if it is not.

On the other hand, changes that involve an increase in disorder, or entropy, are favored to occur spontaneously. So if ∆S is positive, a reaction is more likely than if it is not.

If ∆H is negative and ∆S is positive, a reaction will certainly occur, no matter what the temperature. If ∆H is positive and ∆S is negative, there will not be a reaction at any temperature, since both indicators say it wont.

The trouble is that often the two indicators disagree. When they do, the enthalpy tends to win out at low temperatures, and the entropy (since it is temperature affected) tends to win out at high temperatures.

For example, if the enthalpy and entropy change values are both negative, the enthalpy indicates the reaction will occur, and it will at low temperatures. The entropy indicates that there will be no reaction, and at high temperatures there wont. The reverse is true for positive enthalpy and entropy changes. These reactions are more likely to occur at high, but not at low temperatures.

Gibbs Free Energy (∆G) determines for sure whether a reaction will be favored to occur. It is simply a formula that compares ∆H to ∆S in a special way.

∆G = ∆H - T∆S

Temperature must be in Kelvins. If ∆G has a negative value, the reaction will occur spontaneously. If ∆G has a positive value, it will not occur

One complication in calculating the free energy change is that the enthalpy values are typically given in kilojoules (kJ), while entropy values are given in J / K, so you must convert so that both use Joules, or both use kilojoules. It doesn't matter which.

Sometimes you may be asked to find the temperature above which a reaction will or wont occur. This is the temperature at which ∆G is between negative and positive, or when it equals zero.

∆G = 0 so 0 = ∆H - T∆S

Rearrange the equation to solve for T, and you will find that...

T = ∆H/∆S

Above that temperature entropy change determines whether a reaction occurs, and below that temperature, enthalpy change determines whether a reaction occurs.

∆G = 0 means there will be equilibrium in a reversible reaction.
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JEE Question 2007 paper II

For the process (water becoming steam) H-2O(l)(1 bar, 373 K) --> H-2O(g)(1 bar, 373 K), the correct set of thermodynamic parameters is

(A) ∆G=0,∆S= + ve
(B)∆G=0,∆S= -ve
(C)∆G=+ve,∆S=0
(D)∆G=-ve, ∆S= + ve

Solution: A

The answer is A because, because at 100 degree C, the steam and water mixture is at equilibrium. Hence ΔG = 0(G = H - TS), and ΔS is positive. Why? when liquid becomes gas, there is more disorder. More entropy.
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