Internal Energy, Heat, Enthalpy, and Calorimetry

The Relationships Between …

Recap of Last Class

Last class, we began our discussion about energy changes that accompany chemical reactions

Chapter 5 discusses: Thermodynamics

The study of energy transformations

Thermochemistry

Study of energy transformations specific the field to chemical reactions

Recall that energy is often defined as the ability to do work or produce heat

The sum of all potential energy and kinetic energy in a system is known as the internal energy of the system

We call it E

Internal Energy

Internal Energy

By definition, the change in internal energy, E, is the final energy of the system minus the initial energy of the system:

E = Efinal − Einitial

Changes in Internal Energy

If E > 0, Efinal > Einitial Therefore, the system absorbed energy from the surroundings

This energy change is called endergonic

Changes in Internal Energy

If E < 0, Efinal < Einitial Therefore, the system released energy to the surroundings.

This energy change is called exergonic

When energy is exchanged between the system and the surroundings, it is exchanged as either heat (q) or work (w) Mathematically, this can be represented by:

E = q + w

Changes in Internal Energy

Sign Conventions for q, w, and ∆E

For q + means heat absorbed by system

- means heat released by system

For w + means work done ON system

- means work done BY the system

For ∆E + means net gain of energy by system

- means net loss of energy by system

When related to gases, work is a function of pressure

Pressure is defined as force per unit area

So when the volume is changed:

Work was done ON the gas

Compression (decrease in volume)

+w

OR work was done BY the gas

Expansion (increase in volume)

-w

Relation of Work to Gases

Work and Gases

Usually in an open container the only work done is by a gas pushing on the surroundings (or by the surroundings pushing on the gas)

Work and Gases

We can measure the work done by the gas if the reaction is done in a vessel that has been fitted with a piston:

w = −PV

State Functions

Usually we have no way of knowing the internal energy of a system

Finding that value is simply too complex a problem

However, we do know that the internal energy of a system is independent of the path by which the system achieved that state

Called a state function

A state function is formally defined as a property of the system that depends only on its present state

Does not depend in any way on the system’s past (or future)

A change in this function in going from one state to another state is independent of the particular pathway taken between the two states

Internal energy, pressure, and volume are all state functions

Example

In the system below, the water could have reached room temperature from either direction

Examples of State Functions

Illustration of a State Function

Examples

Energy

Enthalpy

Elevation (non-scientific analogy)

Non-examples

Work

Heat

Distance travelled (non-scientific analogy)

If a process takes place at constant pressure (as the majority of processes we study do) and the only work done is this pressure–volume work, we can account for heat flow during the process by measuring the enthalpy of the system

Enthalpy is a thermodynamic function that is mathematically defined as:

H = E + PV

What is Enthalpy and How Does it Relate to Internal Energy (E)?

Enthalpy

When the system changes at constant pressure, the change in enthalpy, H, is

H = (E + PV)

This can be written

H = E + PV

Enthalpy

Since E = q + w and w = −PV, we can substitute these into the enthalpy expression:

H = E + PV

H = (q + w) − w

H = q

So, at constant pressure, the change in enthalpy is the heat gained or lost

The change in enthalpy is better defined as the heat content of a substance at constant atmospheric pressure

Since ∆H is derived from E, P, and V – all of which are state functions - then ∆H is also a state function

Enthalpy and State Functions

The Truth about Enthalpy

1. Enthalpy is an extensive property

This means that ΔH depends directly on amount of substance

2. H for a reaction in the forward direction is equal in size, but opposite in sign, to H for the reverse reaction

3. H for a reaction depends on the state of the products and the state of the reactants

ΔHrxn (in kJ/ molrxn) Heat absorbed (+) or released (-) by a chemical reaction

ΔHcomb (in kJ/ molrxn) Heat absorbed or released when ONE mole of a substance is completely

burned in oxygen, O2

ΔHf (in kJ/ molrxn) Heat absorbed or released when ONE mole of a compound is formed from

elements in their standard states

ΔHfus (in kJ/ molrxn) Heat absorbed to melt ONE mole of solid to liquid at melting point

ΔHvap (in kJ/ molrxn) Heat absorbed to change ONE mole of a liquid to a gas at boiling point

Various Depictions of Enthalpy

Enthalpy can be calculated from several sources including:

Stoichiometry

Calorimetry

Heats of formation (∆Hf)

Hess’ Law

Bond energies

How do We Calculate ∆H?

Chemical Reactions and ∆H

Most chemical reactions involve a change in enthalpy Endothermic reaction

Net ABSORPTION of energy (heat) by the system

Enthalpy of products is greater than enthalpy of reactants ΔH is positive

Energy is considered a reactant

Chemical Reactions and ∆H

Exothermic reaction Net RELEASE of

energy (heat) by the system

Enthalpy of products is less than enthalpy of reactants

ΔH is negative

Energy is considered a product

As stated before: ΔH depends on the amount of substance present ΔH can be represented as a product or a reactant in a balanced

chemical equation

When ΔH is included in a chemical equation, it is called a thermochemical equation

KOH (s) → KOH (aq) + 43 kJ/mol

You would read the above equation as:

“43 kJ are released for every 1 mole of potassium hydroxide that is decomposed at 250C and 1 atm”

Determining ∆H using Stoichiometry

But, what if you don’t have the amounts of substance as described in the balanced equation? How much energy would be transferred?

Use stoichiometry!

Practice!

# 2 on page 157

Determining ∆H using Stoichiometry

Since we cannot know the exact enthalpy of the reactants and products, we measure H through calorimetry, the measurement of heat flow

Specifically, calorimetry is the process of measuring heat based on observing the temperature change when a body absorbs or releases energy as heat energy

Based on First Law of Thermodynamics

qsystem + qsurroundings = 0

Determining ΔH using Calorimetry

Some Terms to Know when Using Calorimetry

Heat capacity (C) Energy required to raise temperature

by 1 degree

Units are J/°C or J/K

Specific heat capacity (Cp) Energy required to raise temperature of

1 gram of substance by 1 degree

Units are J/g ∙°C or J/g ∙ K

Specific heat of water is 4.184 J/g ∙°C or 1.00 cal /g ∙°C

Molar heat capacity Energy required to raise temperature of

1 mole of substance by 1 degree

Units are J/mol∙K or J/mol ∙°C

Specific heat, then, is represented mathematically by the following equation:

Specific heat capacity Cp

=quantity of heat transferred

(g of material)(degrees of temperature change)

More on Specific Heat

Calorimetry is done using a calorimeter!

A device used to measure heat flow

Coffee-cup calorimeter

Experiment is done at constant pressure

Bomb calorimeter

Experiment is done at constant volume

Determination of ΔH using Calorimetry

Calorimetry at Constant Pressure Coffee-Cup Calorimetry

Constant-pressure calorimetry is used in determining the changes in enthalpy (∆Hrxn) for reactions occurring in solution

By carrying out a reaction in aqueous solution in a simple calorimeter, the heat change for the system can be found by measuring the heat change for the water in the calorimeter

Recall that under constant pressure, the change in enthalpy equals heat

Also recall that enthalpy follows the First Law of Thermodynamics

Thus,

∆H = q at constant pressure qsystem + qsurroundings = 0

−qsystem = qsurroundings

In other words,

Energy (heat) released by the reaction = Energy (heat) absorbed by the solution

Assume that the calorimeter does not absorb or leak any heat and that the solution can be treated as if it were pure water with a density of 1.0 g/mL

So,

Energy (heat) released by substance = Energy (heat) gained by water

Coffee-Cup Calorimetry

#7 on page

Practice!

Since the change in enthalpy is dependent on amount of substance, the energy exchanged during a reaction is expressed as:

∆H = q= specific heat capacity × mass of solution × increase in tempearture

∆H = q = mC∆T Where:

q = heat

m = mass (g)

C = Specific heat capacity (J/g∙°C)

T = °C

Quantifying Energy Exchanges using Constant-Pressure Calorimetry

#8 on page

Practice!

Remember, enthalpies of reactions are often expressed in terms of energy per moles of reacting substances or moles of produced substances

Divide calculated energy by amount of substance

May need to use stoichiometry to find amount of substance

Quantifying Energy Exchanges using Constant-Pressure Calorimetry

Bomb Calorimeters and Constant-Volume Calorimetry

Bomb calorimeters are used to measure heats of combustion

The steel jacket isolates the system so that the heat produced by the combustion is taken up by calorimeter

−qrxn = qcalorimeter

qrxn = – Ccal × ∆T

Bomb Calorimetry

Because the volume in the bomb calorimeter is constant, what is measured is really the change in internal energy, E, not H

For most reactions, the difference is very small

−∆Erxn= Ccal∆T

# 11 on page

Practice!