The Concept of Energy

The concept of energy  the usual definition of energy: the ability to do work or produce heat o work is moving an object against an opposing force o work = distance × opposing force o SI unit of work or energy: the joule (J)  two basic forms of energy o potential energy: energy of position and composition . examples . boulder on a ledge . cations and anions . composition: types of atoms, number and types of bonds and arrangement o kinetic energy: energy of motion . examples (external and internal kinetic energy . pool balls . molecules  why is the concept of energy useful? o if something is isolated from everything else, its total energy never changes o this allows seemingly unrelated behaviors of the system to be connected o example: the pendulum  Two things energy is NOT o some sort of invisible fluid o something which can be measured directly

Thermal energy  definition: energy due to chaotic molecular motions  three factors affecting thermal energy o temperature: higher temperature leads to higher thermal energy o sample size: a cup of hot coffee has more energy than a teaspoon of coffee, all other things being equal. o composition : E(solid) < E(liquid) < E(gas), all other things being equal  anything that changes temperature, sample size and/or composition of an object can change its thermal energy

Heat  definition: transfer of thermal energy due to a temperature difference  thermal energy isn't measurable, but heat is  Three factors affect how much heat an object absorbs or loses o mass of object o temperature change of object (K or °C ) . final temperature - initial temperature . if there is no change in temperature, no heat flows o composition of object . specific heat: heat required to raise the temperature of 1 g of material by 1 K o different materials have different specific heats o heat capacity: heat required to raise the temperature of an object by 1 K Calorimetry

Experimentally, we can determine the heat flow (∆Hrxn) associated with a chemical reaction by measuring the temperature change it produces.  The measurement of heat flow is called calorimetry  An apparatus that measures heat flow is called a calorimeter Heat capacity and specific heat The temperature change experienced by an object when it absorbs a certain amount of energy is determined by its heat capacity.  The heat capacity of an object is defined as the amount of heat energy required to raise its temperature by 1 K (or °C )  The greater the heat capacity of an object, the more heat energy is required to raise the temperature of the object For pure substances the heat capacity is usually given for a specified amount of the substance  The heat capacity of 1 mol of a substance is called its molar heat capacity  The heat capacity of 1 gram of a substance is called its specific heat The specific heat of a substance can be determined experimentally by measuring the temperature change (∆T) that a known mass (m) of the substance undergoes when it gains or loses a specific quantity of heat (q):

material at 298 K and 1 atm specific heat (J/g K) ice 2.09 water 4.18 steam 1.86 sodium 1.23 aluminum 0.9 iron 0.45

 computing heat o heat = mass x specific heat x temperature change = heat capacity x temperature change o examples . 100.0 g of water cools from 30.10°C to 25.05 °C. How much heat is released?

. 100.0 g of water at 25.00 °C absorbs 100 J of heat. What is its final temperature?

. A stone weighing 2.0 g absorbs 5.0 J of heat and warms by 3.0 °C. What is the specific heat of the stone? What is the heat capacity of the stone? Thermochemical equations are just like other balanced equations except they also specify the heat flow for the reaction. The heat flow is listed to the right of the equation using the symbol ΔH. The most common units are kilojoules, kJ. Here are two thermochemical equations:

H2 (g) + ½ O2 (g) → H2O (l); ΔH = -285.8 kJ

HgO (s) → Hg (l) + ½ O2 (g); ΔH = +90.7 kJ

When you write thermochemical equations, be sure to keep the following points in mind:

1. Coefficients refer to the number of moles. Thus, for the first equation, -282.8 kJ is the ΔH when 1 mol of

H2O (l) is formed from 1 mol H2 (g) and ½ mol O2. 2. Enthalpy changes for a phase change, so the enthalpy of a substance depends on whether is it is a solid, liquid, or gas. Be sure to specify the phase of the reactants and products using (s), (l), or (g) and be sure to look up the correct ΔH from heat of formation tables. The symbol (aq) is used for species in water (aqueous) solution. 3. The enthalpy of a substance depends upon temperature. Ideally, you should specify the temperature at which a reaction is carried out. When you look at a table of heats of formation, notice that the temperature of the ΔH is given. For homework problems, and unless otherwise specified, temperature is assumed to be 25°C. In the real world, temperature may different and thermochemical calculations can be more difficult.

Certain laws or rules apply when using thermochemical equations:

1. ΔH is directly proportional to the quantity of a substance that reacts or is produced by a reaction.

Enthalpy is directly proportional to mass. Therefore, if you double the coefficients in an equation, then the value of ΔH is multiplied by two. For example:

H2 (g) + ½ O2 (g) → H2O (l); ΔH = -285.8 kJ

2 H2 (g) + O2 (g) → 2 H2O (l); ΔH = -571.6 kJ

2. ΔH for a reaction is equal in magnitude but opposite in sign to ΔH for the reverse reaction. For example:

HgO (s) → Hg (l) + ½ O2 (g); ΔH = +90.7 kJ

Hg (l) + ½ O2 (l) → HgO (s); ΔH = -90.7 kJ

This law is commonly applied to phase changes, although it is true when you reverse any thermochemical reaction.

3. ΔH is independent of the number of steps involved. This rule is called Hess's Law. It states that ΔH for a reaction is the same whether it occurs in one step or in a series of steps. Another way to look at it is to remember that ΔH is a state property, so it must be independent of the path of a reaction.

If Reaction (1) + Reaction (2) = Reaction (3), then ΔH3 = ΔH1 + ΔH2 Heat and Enthalpy Changes

When a chemical reaction occurs in an open container most of the energy gained or lost is in the form of heat. Almost no work is done (i.e. nothing is being moved).

Heat flows between the system and surroundings until the two are at the same temperature.

 When a chemical reaction occurs in which the system absorbs heat, the process is endothermic (it feels cold)  When a chemical reaction occurs in which the system produces heat it is exothermic (it feels hot)

Enthalpy

Under conditions of constant pressure (e.g. most biological processes under constant atmospheric pressure) the heat absorbed or released is termed enthalpy (or "heat content").

We do not measure enthalpy directly, rather we are concerned about the heat added or lost by the system, which is the change in enthalpy (or ∆H).

In formal terms: The change in enthalpy, ∆H, equals the heat, qp, added to or lost by the system when the process occurs under constant pressure:

H=qp

DH represents the difference between the enthalpy of the system at the beginning of the reaction compared to what it is at the end of the reaction:

H = Hfinal - Hinitial

We are considering the enthalpic state of the system. Thus:

 if the system has higher enthalpy at the end of the reaction, then it absorbed heat from the surroundings (endothermic reaction)  if the system has a lower enthalpy at the end of the reaction, then it gave off heat during the reaction (exothermic reaction)

Therefore:

 For endothermic reactions Hfinal > Hinitial and H is positive (+H)

 For exothermic reactions Hfinal < Hinitial and H is negative (-H)

Enthalpies of Reaction

Because the enthalpy change for a reaction is described by the final and initial enthalpies: H = Hfinal - Hinitial we can also describe H for a reaction by comparing the enthalpies of the products and the reactants:

H = H(products) - H(reactants)

The enthalpy change that accompanies a reaction is called the enthalpy of reaction (Hrxn).

It is sometimes convenient to provide the value for Hrxn along with the balanced chemical equation for a reaction (also known as a thermochemical equation):

2H2(g) + O2(g) -> 2H2O(g) H = -483.6 kJ

Note the following:

 H is negative, indicating that this reaction results in the release of heat (exothermic)  The reaction gives of 483.6 kilo Joules of energy when 2 moles of H2 combine with 1 mole of O2 to produce 2 moles of H2O.

The relative enthalpies of the reactants and products can also be shown on an energy diagram:

Properties of enthalpy:

1. Enthalpy is an extensive property. The magnitude of H is dependent upon the amounts of reactants consumed. Doubling the reactants, doubles the amount of enthalpy. 2. Reversing a chemical reaction results in the same magnitude of enthalpy but of the opposite sign. For example, splitting two moles of water to produce 2 moles of H2 and 1 mole of O2 gas requires the input of +483.6 kJ of energy. 3. The enthalpy change for a reaction depends upon the state of the reactants and products. The states (i.e. g, l, s or aq) must be specified.

CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g) H = -802 kJ Given the above thermochemical equation for the combustion of methane, how much heat energy is released when 4.5 grams of methane is burned (in a constant pressure system)?

The negative sign (exothermic) indicates that 225.5 kJ of energy are given off by the system into the surroundings. Enthalpy

 enthalpy change: heat absorbed or released by a process running at constant pressure o symbol: H = final enthalpy - initial enthalpy . note: enthalpy changes depend only on initial and final states, not on the route between them! . state function: a quantity that depends only on the present state (properties) of the system, not on the process used to arrive at that state. o enthalpy changes are slightly different from thermal energy changes . constant pressure processes must use a little energy to push back the atmosphere . enthalpy change is thermal energy change, minus work against atmosphere, for a constant pressure process

Comparing Thermochemical Quantities

definition SI units type temperature hotness/coldness property that controls direction of heat flows K intensive property thermal energy energy due to molecular motions J extensive property heat transfer of thermal energy due to a temperature difference J process enthalpy adjusted thermal energy J extensive property

Calorimetry

 calorimetry is the experimental measurement of heat flows  bomb calorimetry  constant pressure calorimetry: heat generated by a constant pressure process  strategy for solving calorimetry problems 1. identify all q's by deciding which parts of the system absorb or release significant amounds of heat 2. set up an energy conservation equation. set the sum of all heat flows to zero. 3. introduce T's. replace experimental q's with temperature changes, using q = mc T or q = C T. 4. solve the equation for the desired quantity.

Enthalpy of Reaction

 chemical reactions usually absorb or release heat o energy must be absorbed to break a chemical bond o energy is released when a chemical bond forms  exothermic vs. endothermic reactions

Reaction type: exothermic endothermic heat is: released absorbed reaction vessel temperature: rises falls enthalpy change is negative positive net bond: formation breaking

Thermochemical equations

 example: spacecraft reentry o shockwave processes involve bond breaking

N2(g) 2N(g) H = +941 kJ

O2(g) 2O(g) H = +502 kJ

N2(g) + O2(g) 2NO(g) H = + 168 kJ o heat shield processes involve bond making

2N(g) N2(g) H = -941 kJ

2O(g) O2(g) H = -502 kJ N(g) + O(g) NO(g) H = -638 kJ  these are thermochemical equations: stoichiometric equations with reaction enthalpy o whatever you do to the stoichiometric equation, do also to the reaction enthalpy! . reversing the reaction reverses the sign on the reaction enthalpy . scaling the reaction scales the reaction enthalpy . adding reactions adds reaction enthalpies o How to combine 'step' thermochemical equations to get a 'target' equation:

1. write the step reactions. 2. write the target reaction. 3. reverse step reactions so products/reactants match the target reaction. 4. scale step reactions so products/reactants that don't appear in the target reaction will cancel out. 5. add the step reactions. 6. scale the resulting reaction so it matches the target reaction.  H depends on pressures, concentrations, and temperatures of reactants and products! o to keep things simple, define standard conditions:

. all solution concentrations are 1 M . all gases have a partial pressure of 1 atm . all liquids and solids are under an external pressure of 1 atm . reaction occurs at 25°C o write H° when the reaction is run under standard conditions  special reaction enthalpies o the following are often tabulated for use as 'step' reactions: definition symbol sign

enthalpy of enthalpy of formation of one mole of compound from its elements in Hf + or - formation their most stable forms

enthalpy of enthalpy of complete combustion of one mole of compound Hc always - combustion o use the same procedure we outlined earlier to combine formation or combustion reactions to get a target reaction

Enthalpies of phase changes

definition symbol sign

enthalpy of Heat to melt 1 mole of solid to liquid Hfus always + fusion

enthalpy of Heat to evaporate 1 mol of liquid Hvap always + vaporization

enthalpy of Heat to vaporize 1 mol of solid Hsub always + sublimation

 heating & cooling curves o obtain heat capacities from slopes of curve where temperature changes o plateaus are regions where melting or boiling is occuring . temperatures at plateaus indicate melting and boiling points . length of plateau is enthalpy of phase change . mixtures give curves without flat plateaus

Molecular view of enthalpy changes

 bond enthalpy: enthalpy change per mole when a bond is broken in the gas phase for a particular substance.  average bond enthalpy: average enthalpy change per mole when the same type of bond is broken in the gas phase for many similar substances.

Average Bond Enthalpies in kJ/mol. = denotes a double bond; denotes a triple bond.

Cl S F O N C H H 432 368 563 463 391 415 436 C 328 259 441 351 292 348 477 = 728 = 615 = 615 = 890 N 200 270 175 161 638 418 = 941 O 203 185 139 502 = F 251 310 158 S 277 266 Cl 243  bond enthalpies are always positive: bond breaking is endothermic  estimating H from bond enthalpies o strategy: imagine reaction as a) dissociation of reactants into atoms, b) recombination of atoms into products. 1. Add enthalpies for all product bonds 2. Add enthalpies for all reactant bonds 3. H is approximately the difference between the product and reactant bond enthalpies o limitations

. procedure doesn't account for molecular attractions/repulsions, so doesn't work well for liquid/solid phase reactions . bonds interact with each other within molecules, so bond enthalpies really aren't additive