Thermochemistry

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Enthalpy and Calorimetry

Thermochemistry

© 2009, Prentice-Hall, Inc.

Enthalpy (H)• Chemicals commonly react at constant

external pressure—often at atmospheric pressure.

• Consider the mathematics below:E = q + w

E = q + (-PV)Efinal – Einitial = q + [(-PVfinal) - (-PVinitial)]q = (Efinal + PVfinal) - (Einitial + PVinitial)

• The term enthalpy (H) is used to represent E + PV, which occurs at constant external pressure.

Thermochemistry

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Enthalpy

• 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 the internal energy plus the product of pressure and volume:

H = E + PV

Thermochemistry

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Enthalpy & Calorimetry:

• Enthalpy = H = E + PV– E is the internal energy of the system– P is the pressure of the system– V is the volume of the system

• Enthalpy is a state function– A change in enthalpy does not depend on

the pathway between the two states.

Thermochemistry

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Change in enthalpy (H)

• Will represent the exchange of heat between a system and its surroundings at constant external pressure.

H = E + PV

• Enthalpy change is then equal to heat exchanged at constant external pressure:

H = q constant pressure

Thermochemistry

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For chemical reactions, H can be calculated theoretically and

measured directly.

• Often PV is small– even when there is a gas involved– even when there is a change in volume.

• Theoretically, therefore, work is done by or on the system.

• If PV is sufficiently small, it can be ignored from calculations– change in internal energy can be assumed to be

the same as the change in enthalpy H = E

Thermochemistry

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At Constant Pressure• W = -PV (only work allowed is press.-vol. work)

E = qp + w E = qp - PV

• Or qp = E + PV

• qp is the heat at constant pressure (change in enthalpy)

• Change in H = Change in E + Change in PV

H = E + (PV)

Thermochemistry

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At Constant Pressure

• Since P is constant, the change in PV is due only to a change in volume

(PV) = PV H = E + PV• qp = E + PV H = qp

• At constant pressure (where only PV work is allowed), the change in enthalpy H of the system is equal to the energy flow as heat

Thermochemistry

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Enthalpy

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

H = (E + PV)

• This can be written

H = E + PV

Thermochemistry

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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.

Thermochemistry

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Heat Capacity and Specific Heat

The amount of energy required to raise the temperature of a substance by 1 K (1C) is its heat capacity.

Thermochemistry

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Heat Capacity and Specific Heat

We define specific heat capacity (or simply specific heat) as the amount of energy required to raise the temperature of 1 g of a substance by 1 K.

Thermochemistry

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Heat Capacity and Specific Heat

Specific heat, then, is

Specific heat =heat transferred

mass temperature change

s =q

m T

Thermochemistry

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Heats of Reaction:

• In thermodynamics, a reaction is “complete” when no further changes take place and substances have returned to their original temperature—usually room temperature.

• The total heat absorbed or released in a complete reaction is called the heat of reaction (q reaction).

Thermochemistry

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Heats of Reaction:

• If the heat of reaction occurs at constant external pressure, the heat of reaction is the same as the enthalpy change (H).

• The value of H depends upon the specific reaction, amounts of substances, and the temperature.

• As a result, H is expressed in terms of quantity of heat (joules) per quantity of substance (usually moles), at a specifi c temperature.

• The unit for H is usually joules/mole or kilojoules/mole.

Thermochemistry

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Heats of Reaction:

H for a reaction is given as heat released or absorbed in the reaction according to the molar amounts of reactants and products in the balanced equation.

• This is referred to as a thermochemical equation and includes the value for H.

2HgO(s) + heat 2Hg(l) +O2(g) H = +181.67 kJ (endothermic)

K2O(s) + CO2(g) K2CO3(s) H = -391.1 kJ (exothermic)

Thermochemistry

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Thermochemical equations

• Can also be expressed as heat of reaction per mole of reactant or product.

• This may require fractional coefficients.

Example: HgO(s) + heat Hg(l) + 1/2 O2(g) H = 90.84 kJ

• Since H in a thermochemical equation is always molar amounts in the balanced equation, the unit kJ/mol is unnecessary.

• If the amount of reactants changes, the heat of reaction will change proportionally.

Thermochemistry

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Standard Enthalpies of

Formation

Thermochemistry

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Common Definitions of Standard States

• For a compound– Standard state of a gaseous substance is a

pressure of exactly 1 atm.

– For a pure substance in a condensed state (liquid or solid), the standard state is the pure liquid or solid

– For a substance present in a solution, the standard state is a concentration of exactly 1M.

Thermochemistry

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Common Definitions of Standard States

• For an element– The standard state of an element in the

form in which the element exists under condition of 1 atm and 25 °C.

• The standard state for oxygen is O2 (g) at a pressure of 1 atm

• The standard state for sodium is Na(s)

• The standard state for mercury is Hg(l), and so on.

Thermochemistry

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Standard Enthalpies of Formation

• Every reaction does not occur under conditions of constant pressure – (reaction may occur very slowly)

• Calorimeter can not be used to obtain the enthalpy change

• Standard enthalpy of formation (H°f) = the change in enthalpy that accompanies the formation of one mole of a compound from its elements with all substances in their standard states.

Thermochemistry

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Standard Enthalpies of Formation

• The degree symbol indicates that the corresponding process has been carried out under standard condition.

• Standard State = a reference state

Thermochemistry

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Standard Enthalpies of Formation

Standard enthalpies of formation, Hf°, are measured under standard conditions (25 °C and 1.00 atm pressure).

Thermochemistry

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Change in Enthalpy

• Can be calculated from enthalpies of formation of reactants and products.

Hrxn = npHf(products) - nrHf(reactants)

Thermochemistry

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Enthalpy of Reaction

The change in enthalpy, H, is the enthalpy of the products minus the enthalpy of the reactants:

H = Hproducts − Hreactants

Thermochemistry

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H = Hproducts - Hreactants

• For a reaction studied at constant press., the flow of heat is a measure of the change in enthalpy for the system.

• “Heat of reaction” and “Change in enthalpy” are used interchangeably for reaction studied at constant press.

Thermochemistry

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H = Hproducts - Hreactants

• At constant pressure:

– Endothermic means H is positive

– Exothermic means H is negative

Thermochemistry

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The Truth about Enthalpy

1. Enthalpy is an extensive property.

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.

Thermochemistry

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Calculating overall enthalpy changes

• There are a variety of methods for that an AP Chemistry student should be familiar with.

• The three most common– Law of Hess– Heats of Formation– Bond Energies.

Thermochemistry

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The Law of Hess or Hess’s Law of Heat Summation.

• When a reaction may be expressed as the algebraic sum of other reactions, the enthalpy change of the reaction is the algebraic sum of the enthalpy changes for the combined reactions.

Thermochemistry

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Hess’s Law

H is well known for many reactions, and it is inconvenient to measure H for every reaction in which we are interested.

• However, we can estimate H using published H values and the properties of enthalpy.

Thermochemistry

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Hess’s Law

Hess’s law states that “[i]f a reaction is carried out in a series of steps, H for the overall reaction will be equal to the sum of the enthalpy changes for the individual steps.”

Thermochemistry

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Hess’s Law

Because H is a state function, the total enthalpy change depends only on the initial state of the reactants and the final state of the products.

Thermochemistry

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Calculation of H

We can use Hess’s law in this way:

H = nHf°products – mHf° reactants

where n and m are the stoichiometric coefficients.

Thermochemistry

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H = [3(-393.5 kJ) + 4(-285.8 kJ)] – [1(-103.85 kJ) + 5(0 kJ)]

= [(-1180.5 kJ) + (-1143.2 kJ)] – [(-103.85 kJ) + (0 kJ)]= (-2323.7 kJ) – (-103.85 kJ) = -2219.9 kJ

C3H8 (g) + 5 O2 (g) 3 CO2 (g) + 4 H2O (l)

Calculation of H

Thermochemistry

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Hess’s Law

• Coffee cup calorimeters are often used to develop an understanding of Hess’s Law.

• The heats of reaction of two or more different reactions are determined.

• The sum of these enthalpies is equal to the heat of reaction for a target reaction, whose equation is the sum of the equations of the two or more reactions studied.

Thermochemistry

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Calorimetry

• The device used experimentally to determine the heat associated with a chemical reaction is a calorimeter.

• Calorimetry is the science of measuring heat by observing the temperature change when a body absorbs or discharges energy as heat.

Thermochemistry

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Calorimetry

• Heat capacity (C) = a measure of how much energy is needed to raise its temp. by one degree.

• C = heat absorbed/ increase in temp.

Thermochemistry

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Calorimetry• In defining the heat capacity of a substance, the

amount of the substance must be specified. [See table 6.1]

• Specific heat capacity = the energy required to raise the temp. of one gram of a substance by one degree Celsius.– J/C * g or J/K *g– Cp = q/mT

• Molar Heat Capacity = the energy required to raise the temperature of one mole of a substance by one degree Celsius– J/C * mol or J/K* mol

Thermochemistry

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Calorimetry• Constant-Pressure

Calorimetry

– Used in determining the changes in enthalpy for reaction occurring in solution.

– Exo = warm– Endo = cool

• Constant-Volume Calorimetry– No work is done because

the vol must change for press-vol work to be performed.

– Energy change is measured by the increase in the temp. of the water and other calorimeter parts.

E = q+w=q=qv

Thermochemistry

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Calorimetry

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

Thermochemistry

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A Coffee Cup Calorimeter Made of Two Styrofoam Cups

Thermochemistry

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Constant Pressure Calorimetry

By carrying out a reaction in aqueous solution in a simple calorimeter such as this one, one can indirectly measure the heat change for the system by measuring the heat change for the water in the calorimeter.

Thermochemistry

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Constant Pressure Calorimetry

Because the specific heat for water is well known (4.184 J/g-K), we can measure H for the reaction with this equation:

q = m s T

Thermochemistry

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Bomb Calorimetry

• Reactions can be carried out in a sealed “bomb” such as this one.

• The heat absorbed (or released) by the water is a very good approximation of the enthalpy change for the reaction.

Thermochemistry

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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.

Thermochemistry

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Using Heats of Formation:

• Heats of formation reactions for each of the compounds involved in a chemical change may be rearranged, using the Law of Hess to calculate the overall enthalpy change for the process.

Thermochemistry

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Bond Energy Calculations:

• Bond energy is defined as the energy required to break a bond.

• bond breaking requires energy, while the formation of bonds releases energy

Thermochemistry

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Energy in FoodsMost of the fuel in the food we eat comes from carbohydrates and fats.