Thermochemistry: (calorimetry)

Chapter 5 Sections 1-5 [Brown/LeMay]

The Nature of Energy

Thermodynamics

Thermodynamics is the study of energy and its interconversions

Energy

Everything is energy, there is nothing that is not energy.

However, for our purposes, Energy is the capacity to do work or to produce heat.

The SI unit of energy is the Joule (J).

1 J = 1 kg m2/s2

A common conversion

1 cal = 4.184 J      (exact)

Kinetic Energy

Kinetic energy is the energy of motion and depends upon an objects mass and velocity through the equation

Ek = (1/2)mv2

When mass is kg and velocity is m/s, then energy is J.

Potential Energy

Potential energy is energy do to position or composition.

For particles with electrical charges (such as electrons and nucleus's), the electrostatic potential energy is:

Eel = kQ1Q2
            d

Where k = 8.99 x 109 Jm/C2

C refers to coulomb, a unit of electrical charge.

Q1 and Q2 are the charge of particles.

The charge of an electron is -1.60 x 10-19 C.

When Q1 and Q2 have the same sign Eel is positive and pushes the particles apart.

When Q1 and Q2 have opposite signs Eel is negative and pulls the particles together.

Chemical Energy (a form of Potential Energy)

Chemical systems hold potential energy, which can be released (as heat and work) through chemical reactions.

Examples: burning methane for heat, burning gasoline for the work of moving a car, and producing hydrogen to store energy.

Law of Conservation of Energy (1st Law of Thermodynamics)

Energy cannot be created or destroyed.

Energy is conserved.

DEuniverse = DEsystem + DEsurroundings = 0

Note: Energy can be converted from one form to another.

Note:  Matter is a form of condensed energy, and energy and matter can be interconverted.

System

The system is the part of the universe we are examining. In this case, usually a chemical reaction.

Surroundings

The surroundings are the part of the universe not in the system.

Closed System

A closed system can exchange energy with the surroundings, but not matter.

Heat

Heat is energy in transit due to a temperature difference between the source and sink.

Heat flows from hotter objects to cooler objects.

Notice that a temperature difference can be tapped to produce work in addition to heat flow.

Work

Work is energy in transit defined as force acting over a distance.

Or, Work is the energy used to cause an object to move against a force.

The force can be overcoming friction, gravity, inertia or other obstacle/force.

Force is mass times acceleration; and work is force times distance, so:

F = m · a    in units of kg m/s2

w = F · d in units of (kg m/s2) m = kg m2/s2 = = J

Heat and work are the two ways to transfer energy.

Force

That influence on a body which causes it to accelerate
or
quantitatively, a vector equal to the body's time rate of change of momentum

Exothermic

When a reaction (system) releases heat (to the surroundings), it is termed exothermic. The heat is flowing out of the system into the surroundings.

Chemical potential energy is converted to heat.

Endothermic

Reactions (system) that absorb heat from the surroundings are endothermic.

Heat is converted into chemical potential energy.

Internal Energy, E, heat, and Work

The internal energy, E, of a system is the sum of all the kinetic and potential energies of all the particles of the system. This is hard to define. It is easier to define the energy flow into or out of a system.

DE = Efinal – Einitial

DE = q + w

Where DE represents the change in the system's internal energy;  q represents heat;
and w represents work.

These terms consist of a value (magnitude) and a sign, representing direction of flow. The sign represents the systems point of view.

An exothermic process releases energy to the environment, the systems energy is decreasing, so the value of q is negative. ( DE and w have similar sign conventions)

An endothermic process absorbs energy from the environment, the system energy is increasing, so the value of q is positive. ( DE and w have similar sign conventions)

Doing work on the system has a positive w and E.

Having the system do work on the surroundings has a negative w and E.

Any change in the energy of the system is accompanied by an opposite change of energy in the surroundings.

State Function (State Property)

A state function (property) depends only on the present state (does not depend upon the past or future).

A change in a state function (property) does not depend upon the pathway taken between the two states.

Work and heat are not state functions.

Energy is a state function.

Enthalpy is a state function.

Pathway

The pathway is the condition between two states. The pathway determines the partitioning of energy between heat and work.

PV Work

Work can be done through the expansion or compression of gases, called pressure-volume work (PV work). This is the process in the internal combustion engine and the steam engine, where heated gases are used to expand in a chamber. This expansion acts on the piston which transfers the work to other components.

When pressure is constant.

w = -PDV

P is the external pressure, the pressure that causes compression or resists expansion.

As a gas expands, DV is positive, but work is expended on the environment (work is negative).

For an ideal gas, the volume has to change for work to occur.

Enthalpy

Enthalpy is heat flow at constant pressure

DH = qp

H = E + PV

Enthalpy is known as the heat content of a system.

Absolute enthalpy cannot be measured; only change in enthalpy can be measured.

DH = DE + PDV

These (pressure, volume, internal energy, and enthalpy) are all state functions.

The change of enthalpy of a system is equal to heat flow at constant pressure (with only PV work allowed).

Enthalpies of Reaction

For chemical reactions

DH = Hproducts – Hreactants   (Hfinal – Hinitial)

This is a state function and does not depend on reaction path, just initial and final states.

Exothermic: DH is negative

Endothermic: DH is positive

·        Enthalpy is an extensive property; it depends on amount of material reacting.

·        The enthalpy of reaction is equal in magnitude but opposite in sign for the reverse reaction.

·        The enthalpy of reaction depends on the physical state of reactants and products.

Some Special Types of Enthalpy of Reactions

Heat of formation (DHf): The enthalpy of forming a compound from its elements in their standard (normal) states at 25°C and 1 atm.

2Ag (s) + S(s) à Ag2S(s)        DH = DHf

Heat of fusion (DHfus): The enthalpy of melting a solid into a liquid.

Cs(s) à Cs(l)                          DH = DHfus

Heat of vaporization (DHvap): The enthalpy of vaporizing a liquid into a gas.

HCl(l) à HCl(g)                      DH = DHvap

Heat of combustion (DHcomb): The enthalpy of burning a substance with O2.

C4H8 + 6O2 à 4CO2 + 4H2O

Stoichiometry and Enthalpy

Sign: The sign of the enthalpy of a reaction is the opposite for the reverse reaction.

4CuO(s) à 2Cu2O(s) + O2(g)                                                 DH° = 288 kJ

2Cu2O(s) + O2(g) à 4CuO(s)                                                 DH° = -288 kJ

Magnitude (1): The enthalpy of a reaction is written without reference to an amount of substance. The amount of substance is determined from the equation depending on what substance is referenced

4CuO(s) à 2Cu2O(s) + O2(g)                                                 DH° = 288 kJ

The enthalpy of this reaction is 288 kJ/4 mol CuO = 72 kJ/mol CuO;
or 288 kJ/2 mol Cu2O = 144 kJ/mol Cu2O;
or 288 kJ/mol O2

Magnitude (2): If a reaction is rewritten using a factor to change the stoichiometric ratios, the enthalpy is changed by the same amount.

4CuO(s) à 2Cu2O(s) + O2(g)                                                 DH° = 288 kJ

CuO(s) à (1/2)Cu2O(s) + (1/4)O2(g)                                      DH° = 72 kJ

Hess's Law of Heat Summation

The enthalpy change of an overall process is the sum of the enthalpy changes of its individual steps.

This rule allows us to get the enthalpy of reaction by summing the enthalpy of other reactions that add up to the reaction that we desire.

We commonly use heats of formation to derive the heat of a reaction.

If we want the enthalpy of the reaction:

2NaHCO3(s) à Na2CO3(s) + CO2(g) + H2O(g)

We look for formation reactions or other reactions that can add up to this reaction

Na(s) + (1/2)H2(g) + C(s,graphite) + (3/2)O2(g) à NaHCO3(s)           DHf = -947.7 kJ

so

2NaHCO3(s) à 2Na(s) + H2(g) + 2C(s,graphite) + 3O2(g)                  DH = 1895.4 kJ

For sodium carbonate, carbon dioxide, and water:

2Na(s) + C(s,graphite) + (3/2)O2(g) à Na2CO3(s)                              DHf = -1130.8 kJ

C(s) + O2(g) à CO2(g)                                                                       DHf = -393.7 kJ

H2(g) + (1/2)O2(g) à H2O(g)                                                              DHf = -241.8 kJ

These last four equations add up to the desired equation, so we add up the last four enthalpies to get the enthalpy of reaction:

DHrxn = 1895.4 kJ – 1130.8 kJ – 393.7 kJ – 241.8 kJ = 129 1 kJ (an endothermic reaction)

Heat of Reaction from Heats of Formation

If we examine the above example, we see that we get the answer using the formula:

DHrxn = nDHf(products) - nDHf(reactants)

Where n is the coefficients from the balanced equation.

This works for all reactions.

Standard Heats of Reaction

The heats of reaction depend upon physical states of reactants and products along with pressures of gases and concentrations of solutions. To make comparisons of reactions possible, we use standard heats of reactions, where all the reactants and products are in their standard states. Standard states are:

·        For a gas, the standard state is 1 atm
(recently changed to 1 bar, a minor change [1 atm = 1.013 bar])

·        For a substance in aqueous solution, the standard state is 1 M concentration.

·        For a pure substance, the standard state is the most stable form at 1 atm and 25°C (298 K)

Calorimetry

Calorimetry is the science of measuring heat flow. This is done by measuring temperature changes when heat is absorbed or released.

Calorimeter

A Calorimeter is a heat isolating device used to measure temperature and heat changes. The calorimeter isolates the system from the surroundings.

Heat Capacity

Heat capacity, C, is a measure of how fast temperature changes with a change in heat energy. Heat capacity is defined as:

C = heat exchanged/change in temperature

C = q/DT

DT will be either °C or K.

This term will be dependent upon amount of material present.

Specific Heat Capacity

Specific Heat Capacity is heat capacity per gram of material.

The units are J/K g or J/°C g

Specific Heat Capacity = q/(mass DT)

s = q/(m DT)

Also:

q = smDT

·        A larger heat capacity (s) results in a lower change in temperature for the same heat applied.

·        A smaller heat capacity (s) results in a larger change in temperature for the same heat applied.

Molar Heat Capacity

The Molar Heat Capacity is heat capacity per mole of material.

The units are J/K mol or J/°C mol

Sample specific heat capacities (Liquid water is the only one to know)

Substance

Specific Heat Capacity (J/K g)

H2O(l)

4.18

H2O(s)

2.03

Al(s)

0.89

C(s)

0.71

Fe(s)

0.45

Hg(l)

0.14

Metals (lower specific heat) change their temperature much faster than water in response to heat.

Constant-Pressure Calorimeter

A Constant-Pressure Calorimeter measures changes in enthalpy (heat of reaction). This is simple for reactions in solution using a simple calorimeter at constant atmospheric pressure.

Measures Enthalpy

DH = qp

For a reaction in solution, the heat produced by a reaction (qrxn) is absorbed by the solution (qsoln); however the sign is different so:

qsoln = -qrxn

With qsoln usually be calculated using the heat capacity of the solution and temperature increase.

qsoln = smDT

Constant Volume Calorimetry (Bomb Calorimeter)

Constant Volume Calorimetry prevents work from being done, so what is measured is Internal Energy, DE, instead of enthalpy.

DE = q + w = qv

This type of calorimetry is done in a bomb calorimeter because if it isn't designed will, it is a literal bomb.

The heat capacity of the calorimeter (Ccal) must be known and the temperature change measured precisely.

DE = qrxn = -Ccal DT

For most reactions the difference between DH and DE are very small.

Thermochemistry: (calorimetry) Equations

Ek = (1/2)mv2

Eel = kQ1Q2
            d

Where k = 8.99 x 109 Jm/C2

DE = q + w

w = -PDV

DH = DE + PDV

C = q/DT

s = q/(m DT)

q = smDT

 

Relationships

1 J = 1 kg m2/s2

1 cal = 4.184 J      (exact)

The charge of an electron is -1.60 x 10-19 C.