Chapter 6 – Energy

Types of Systems

Energy First Law of thermodynamics: The energy of the universe is constant (i.e. energy is neither created nor destroyed) Energy (E) The capacity to do work or transfer heat. Kinetic Energy The energy of motion. Potential Energy Energy due to condition, position, or composition. Internal Energy The sum of all kinetic & potential energy contained in a system

Calorie (cal) The quantity of heat required to change the temperature of one gram of water by one degree Celsius. Joule (J) SI unit for heat 1 cal = J (exactly) Energy Units

q = Heat The transfer of energy due to temperature changes Heat and temperature are not the same w = Work Force acting through a distance. ΔE = q + w Internal Energy Changes Energy can be transferred between a system and its surroundings as a result of a temperature difference (q) and/or work being done (w).

The sign of q and w are from the system’s point of view Internal Energy Changes In an endothermic process, heat flows into a system - ΔE is positive In an exothermic process, heat flows out of a system - ΔE is negative

Calculate Δ E for a system undergoing an endothermic process in which 15.6 kJ of heat flows and where 1.4 kJ of work is done on the system.

The expansion/compression of the system against the external atmosphere is pressure–volume work. Pressure – Volume Work

Calculating Energy Changes ( Δ E) When a reaction is run, the internal energy (kinetic, potential) can be transferred as heat and/or pressure-volume work: ΔE = q + w = q – PΔV

How much work is associated with the expansion of a gas from 46L to 64L at a constant pressure of 15 atm?

Filling (and heating) a hot air balloon takes 1.3X10 8 J of heat. At the same time, the volume changes from 4.00X10 6 L to 4.5X10 6 L. Assuming a constant pressure of 1 atm, what is the energy change for the process?

Heat capacity, C Amount of heat needed to raise the temperature of the system by one degree Kelvin Heat Capacities

Heat capacity, C Amount of heat needed to raise the temperature of the system by one degree Kelvin Molar heat capacity, C System = one mole of substance. Specific heat capacity, c System = one gram of substance q =CΔTCΔT mcΔT Heat Capacities

If we add 500 J of heat to 25g of water initially at 25 °C, what is the final temperature of the water? (the specific heat of water = J/g°C)

If substances at two different temperatures are mixed and allowed to come to a constant temperature: Heat Capacity and Conservation of Energy q a = –q b

What is the final temperature when 125 g of iron at 92.3 °C is dropped into 50.0 g of water at 27.7 °C? The specific heat of iron is J/g°C and the specific heat of water is J/g°C. (Assume an isolated system)

A gram sample of metal at 75.0 °C is added to 150.0g of water at 15.0 °C. The temperature of the water rises to 23.0 °C. What is the specific heat of the metal? (Assume an isolated system)

q rxn = –q cal = –CΔT As long as we know the calorimeter (C): q cal = CΔT heat Reaction (Bomb) Calorimetry Well insulated – considered isolated If we run a reaction in an isolated system (a calorimeter), we can very accurately measure the heat transferred as a result of the reaction. Note that this is a constant volume process.

ΔE = q – PΔV In a system at constant volume, no pressure-volume work is done: ΔE = q + 0 = q v Reactions at Constant Volume PΔV = P(0) = 0 Therefore, at constant volume, the internal energy change is equal to the heat of reaction:

Well insulated – considered isolated q rxn = -q cal A Coffee Cup (Simple) Calorimeter Note that this is a constant pressure process.

50.0 mL each of 1.0M HCl and 1.0M NaOH at 25 °C at mixed in a calorimeter. After reaction, the temperature of the calorimeter is 31.9 °C. What is the heat generated for the reaction? (We will estimate that the specific heat of the solution/calorimeter is about the same as that of water = J/g°C)

State Functions Any property that has a unique value for a specified state of a system is said to be a State Function. Water at 293 K and 1.00 atm is in a specified state. In this state, the density of water is g/mL This density is a unique function of the state. It does not matter how the state was established. Capitalized letters are used to identify State functions

ΔE has a unique value between two states Internal Energy – A State Function

In a system at constant volume, no pressure-volume work is done: ΔE = q v Reactions at Constant Volume PΔV = P(0) = 0 Therefore, at constant volume, the internal energy change is equal to the heat of reaction:

At constant pressure, both heat and pressure-volume work results from energy changes: Reactions at Constant Pressure Normally, reactions are run at constant pressure (and changing volume).

Because we are usually only interested in the heat of reaction at constant pressure, we will define a new state function: ΔE = q P - PΔVq P = ΔE + PΔV Let H = E + PV q P = ΔH = ΔE + PΔV Enthalpy Change ΔH, the enthalpy change, is the measurement we will generally use to describe thermal changes in a chemical system.

Note: Enthalpy change is an extensive property – it is directly proportional to the amount of substances in the system Negative ΔH = an exothermic reaction Positive ΔH = an endothermic reaction Exothermic and Endothermic Reactions

How Does a “Hand Warmer” Work?

How much energy is needed to heat the water used in a 5 minute shower on Colby’s campus? (Assume Colby showers are set to 2 gal/min)

Heat (Enthalpy) of Reaction All reactions will have an accompanying enthalpy change: ΔH rxn = ΔH products - ΔH reactants For any reaction, the enthalpy change is the sum of the product enthalpies minus the sum of the starting material enthalpies. ΔH rxn = H final - H initial

Why Do We Use These Energy Sources?

How much natural gas must we burn to produce the heat (4435 kJ) needed for a single 5 minute hot shower on Colby’s campus?

Changes in States of Matter Why doesn’t a pot of (boiling) water at 100 °C all become steam at once? Why do we have to continually apply heat?

Changes in States of Matter Any change of state will cause an enthalpy change : Unless stated otherwise, ΔH values are assumed to be per mole

Changes in States of Matter Any change of state will cause an enthalpy change : How much energy is required to convert 5 g of ice at 0 °C to water at 50 °C? To steam at 100 °C?

Changes in States of Matter Any change of state will cause an enthalpy change : Which will cause a more damaging burn: skin exposed to 1 g of water at 100 °C or skin exposed to 1 g of steam at 100 °C?

Manipulating Reaction Enthalpies The “reverse” of any reaction will have an equal enthalpy change of opposite sign.

Standard States and Standard Enthalpy Changes First we must define a particular state as a standard state ΔH ° is the standard enthalpy of reaction –The enthalpy change of a reaction in which all reactants and products are in their standard states The Standard States are defined as: –The pure element or compound at a pressure of 1 bar (approximately 1 atm) and at the temperature “of interest” (usually 25 °C).

ΔH f °, the standard enthalpy of formation, is the enthalpy change that occurs in the formation of one mole of a substance in the standard state from the reference (most common) forms of the elements in their standard states. The standard enthalpy of formation of a pure element in its standard state is 0. Standard Enthalpies of Formation

ΔH f ° for CH 2 O = – kJ/mol. ΔH f ° for Al 2 O 3 = – 1670 kJ/mol. ΔH f ° for Fe 2 O 3 = – 822 kJ/mol. What reactions do these heats of formation represent?

Standard Enthalpies of Formation

Reaction Summation – Hess’s Law Hess’s law: If a process occurs in stages or steps (even hypothetically), then the enthalpy change for an overall process is the sum of the enthalpy changes for the individual steps.

Manipulating ΔH – Hess’s Law The enthalpy change of a chemical transformation is directly proportional to the amounts of substances: The reverse of a chemical reaction has an equal but opposite  H:

What is the standard enthalpy of reaction for the thermite reaction? How can we use a table of standard heats of formation to determine this? ΔH f ° for Al 2 O 3 = – 1670 kJ/mol. ΔH f ° for Fe 2 O 3 = – 822 kJ/mol.

What is the standard enthalpy of reaction for the reaction below? How can we use a table of standard heats of formation to determine this?

ΔH rxn = ΣΔH f ° products - ΣΔH f ° reactants What is the standard enthalpy of reaction for the reaction below? How can we use a table of standard heats of formation to determine this?

What is the standard enthalpy of reaction for the formation of N 2 O 5 as shown below?