# Enthalpy and Calorimetry

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Enthalpy and Calorimetry

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. © 2009, Prentice-Hall, Inc.

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 © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

Change in enthalpy (H) Will represent the exchange of heat between a system and its surroundings at constant external pressure. H =  E + PV Enthalpy change is then equal to heat exchanged at constant external pressure: H = q constant pressure © 2009, Prentice-Hall, Inc.

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 © 2009, Prentice-Hall, Inc.

At Constant Pressure W = -PV (only work allowed is press.-vol. work)
E = qp + w  E = qp - PV Or qp = E + PV qp is the heat at constant pressure (change in enthalpy) Change in H = Change in E Change in PV H = E (PV) © 2009, Prentice-Hall, Inc.

At Constant Pressure Since P is constant, the change in PV is due only to a change in volume (PV) = PV H = E + PV qp = E + PV 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 © 2009, Prentice-Hall, Inc.

Enthalpy When the system changes at constant pressure, the change in enthalpy, H, is H = (E + PV) This can be written H = E + PV © 2009, Prentice-Hall, Inc.

Enthalpy Since E = q + w and w = -PV, we can substitute these into the enthalpy expression: H = E + PV H = (q+w) − w H = q So, at constant pressure, the change in enthalpy is the heat gained or lost. © 2009, Prentice-Hall, Inc.

Heat Capacity and Specific Heat
The amount of energy required to raise the temperature of a substance by 1 K (1C) is its heat capacity. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

Heat Capacity and Specific Heat
Specific heat, then, is Specific heat = heat transferred mass  temperature change s = q m  T © 2009, Prentice-Hall, Inc.

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). © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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 = kJ (endothermic) K2O(s) + CO2(g)  K2CO3(s)  H = kJ (exothermic) © 2009, Prentice-Hall, Inc.

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 = 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. © 2009, Prentice-Hall, Inc.

Standard Enthalpies of Formation

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

Standard Enthalpies of Formation
The degree symbol indicates that the corresponding process has been carried out under standard condition. Standard State = a reference state © 2009, Prentice-Hall, Inc.

Standard Enthalpies of Formation
Standard enthalpies of formation, Hf°, are measured under standard conditions (25 °C and 1.00 atm pressure). © 2009, Prentice-Hall, Inc.

Hrxn = npHf(products) - nrHf(reactants)
Change in Enthalpy Can be calculated from enthalpies of formation of reactants and products. Hrxn = npHf(products) - nrHf(reactants) © 2009, Prentice-Hall, Inc.

Enthalpy of Reaction The change in enthalpy, H, is the enthalpy of the products minus the enthalpy of the reactants: H = Hproducts − Hreactants © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

H = Hproducts - Hreactants
At constant pressure: Endothermic means H is positive Exothermic means H is negative © 2009, Prentice-Hall, Inc.

Enthalpy is an extensive property. H for a reaction in the forward direction is equal in size, but opposite in sign, to H for the reverse reaction. H for a reaction depends on the state of the products and the state of the reactants. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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.” © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

Calculation of H We can use Hess’s law in this way:
H = nHf°products – mHf° reactants where n and m are the stoichiometric coefficients. © 2009, Prentice-Hall, Inc.

Calculation of H C3H8 (g) + 5 O2 (g)  3 CO2 (g) + 4 H2O (l)
H = [3( kJ) + 4( kJ)] – [1( kJ) + 5(0 kJ)] = [( kJ) + ( kJ)] – [( kJ) + (0 kJ)] = ( kJ) – ( kJ) = kJ © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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/mT 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 © 2009, Prentice-Hall, Inc.

Calorimetry Constant-Volume Calorimetry Constant-Pressure 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 Constant-Pressure Calorimetry Used in determining the changes in enthalpy for reaction occurring in solution. Exo = warm Endo = cool © 2009, Prentice-Hall, Inc.

Calorimetry Since we cannot know the exact enthalpy of the reactants and products, we measure H through calorimetry, the measurement of heat flow. © 2009, Prentice-Hall, Inc.

A Coffee Cup Calorimeter Made of Two Styrofoam Cups

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. © 2009, Prentice-Hall, Inc.

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 © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

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 © 2009, Prentice-Hall, Inc.

Energy in Foods Most of the fuel in the food we eat comes from carbohydrates and fats. © 2009, Prentice-Hall, Inc.

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