11-as-givengenchem.bu.edu/ch131-summer-1-2020/lectures/11-as-given.pdfThis means that adding energy...

Lecture 11 CH131 Summer 1 2020 6/11/2020 12:12 PM

Lecture 11 CH131 Summer 1Thursday, June 11, 2020

• Standard enthalpy of formation of X, Δf𝐻° X• Example thermochemistry problems.

Begin ch13: Spontaneous Processes• The essence of change: Blind chance and dumb luck• Arrangements particles entropy• Heat energy flow entropy change

Next lecture: Complete ch13

Standard enthalpy of formation, ΔfH°, of XForm one mole of X …

… from the elements it contains, …… each in their standard state.

The standard state of an element is its most stable form.

ΔfH° of glucose, C6H12O6(s)Form one mole of glucose …

C6H12O6 𝑠… from the elements it contains, …

C, H, and O… each in their standard state,

C 𝑠 , H2 𝑔 , and O2 𝑔

ΔfH° of glucose, C6H12O6(s)The standard enthalpy of formation of glucose is defined as the enthalpy change when one mole of sugar is formed from its elements, each in their standard states.

Lecture 11 CH131 Summer 1 2020

ΔfH° of glucose, C6H12O6(s)Task: Write down the balanced chemical equation whose enthalpy change is the standard enthalpy of formation of sugar, C6H12O6 𝑠

The enthalpy change of the chemical reaction6 C 𝑠 6 H2 𝑔 3 O2 𝑔 C6H12O6 𝑠

is the standard enthalpy of formation of sugar.

ΔfH° of water, H2O(l)Task: Write down the balanced chemical equation whose enthalpy change is the standard enthalpy of formation of water, H2O 𝑙

The enthalpy change of the chemical reaction

H2 𝑔 O2 𝑔 H2O 𝑙

is the standard enthalpy of formation of water.

ΔfH° of steam, H2O(g)Task: Write down the balanced chemical equation whose enthalpy change is the standard enthalpy of formation of steam, H2O 𝑔 .

The enthalpy change of the chemical reaction

H2 𝑔 O2 𝑔 H2O 𝑔

is the standard enthalpy of formation of steam.

ΔfH° of water and steamIs the standard enthalpy of formation of water 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 as that of steam?

The enthalpy changes of the chemical reactions

H2 𝑔 O2 𝑔 H2O 𝑙

H2 𝑔 O2 𝑔 H2O 𝑔

are different, since …H2O 𝑙 H2O 𝑔 requires energy.

Example thermochemistry problems

Heat of combustionCalculate ∆𝐻° for the combustion of methane, CH 𝑔 .

Heat of combustionCalculate ∆𝐻° for the combustion of glucose, C H O 𝑔 .

Problem 7e & 8e: 12.39Lecture 11 CH131 Summer 1 2020

TP The enthalpy diagram shows changes associated with the reaction Na2 𝑔 Br2 𝑔 2 NaBr 𝑔 .

The uppermost line corresponds to the species …

1. 2 Na 𝑠 Br2 𝑙2. 2 Na 𝑔 2 Br 𝑔3. Na2 𝑔 Br2 𝑔

Chapter 13: Spontaneous Processes

The essence of spontaneous changeWhy does a drop of ink in water disperse?

Why do salt water and fresh water mix?

The essence of spontaneous change“things happen simply because they can happen

and because they are statisticallymost likely to happen.”

Michael Munowitz, "Principles of Chemistry," W. W. Norton, 2000

A gas fills its containerLecture 11 CH131 Summer 1 2020

A gas fills its container

Gas all on left of container

A gas fills its container

Gas evenly distributed throughout container

moveable barrier

𝑃 proportional to 𝑛/𝑉 “lattice gas”𝑃 higher on the right

Pressure in a gas is uniform

𝑃 proportional to 𝑛/𝑉 “lattice gas”𝑃 the same on the left and right

moveable barrier

One gas on left, another on right

permeable barrier

Equal amounts throughout

permeable barrier

The essence of spontaneous changeThe essential similarity in all of these behaviors…

gas particles spontaneously spread uniformly thought their container, so that pressure is everywhere the same;an ink drop spontaneously disperses throughout water;gases spontaneously mix uniformly, so that their partial pressures are everywhere the same; …

The essence of spontaneous changeThe essential similarity in all of these behaviors…

is that all spontaneous change results in the possible arrangements 𝑊 of particles that is as large as it can be:

𝑊 → 𝑊 𝑊

The essence of spontaneous changeSpontaneous change always results in the possible arrangements 𝑊 of particles that is as large as it can be.For example,

gas particles spontaneously spread uniformly thought their container, so that pressure is everywhere the same .

𝑊 1

𝑊 !! !

The essence of spontaneous change“things happen simply because they can happen

and because they are statisticallymost likely to happen.”

Michael Munowitz, "Principles of Chemistry," W. W. Norton, 2000

All spontaneous change results in the possible arrangements 𝑊 of particles that is as large as it can be:

𝑊 → 𝑊 𝑊

Arrangements → entropy𝑆 𝑘 ln 𝑊

𝑘B 1.4 10 23 J/K

S = kB ln(W )Why natural log?

So that doubling the size of the system double the value of the spontaneity measure:

𝑊 ⟶ 𝑊 𝑊 𝑊

𝑆 → 𝑘 ln 𝑊 2𝑘 ln 𝑊 2𝑆, so …

Boltzmann’s definition in terms of natural log makes 𝑆 extensive …S scales with size of system

The essence of spontaneous changeGas particles spontaneously spread uniformly thought their container, so that pressure is everywhere the same:

𝑊 1

𝑊 !! !

TP What is the value of ∆ for 𝑊 1 → 𝑊 84?

1. 12. 4.43. 834. 845. Something else

The essence of spontaneous changeGas particles spontaneously spread uniformly thought their container, so that pressure is everywhere the same:

𝑊 1

𝑊 !! !

Δ𝑆 𝑆 – 𝑆 𝑘B ln 𝑘B ln 𝑘 4.4 0

TP Boltzmann’s definition of entropy is proportional to the natural logarithm of the number of arrangements, 𝑆~ln 𝑊 . Could Boltzmann’s definition of entropy just as well be defined in terms of base-10 logarithm, 𝑆~ log 𝑊 ?

1. Yes2. No3. Not sure

S = kB ln(W )The extensive property of entropy is true for any logarithm base.

For example, if base-10 logarithm were used, the only change needed would be the numerical value of the proportionality constant.

𝑆 𝑘 ln 𝑊 𝑘 2.303 log 𝑊

Heat (energy) flow entropy changeAdding energy increases the units of energy in the system.

More units of energy mean more arrangements of energy 𝑊

This means that adding energy increases entropy, 𝑆 𝑘 ln 𝑊 .

Does the entropy increase depend on how much energy is initially present?

TP How does ∆𝑆 for adding 10 J to 1 mol at 300 K

compare with ∆𝑆 for adding 10 J to 1 mol at 600 K?

1. ∆𝑆 ∆𝑆2. ∆𝑆 ∆𝑆3. ∆𝑆 ∆𝑆

Heat (energy) flow entropy changeΔ𝑆 is larger the less energy already present

Δ𝑆 is larger the lower 𝑇 at which the energy is added.

∆𝑆~

11-as-givengenchem.bu.edu/ch131-summer-1-2020/lectures/11-as-given.pdfThis means that adding energy...

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