Chem U3

Le Châtelier's principle

The French chemist Henri Le Châtelier (1850-1936) studied how the equilibrium position shifts as a result of changing conditions. He proposed what has come to be called Le Châtelier's principle: If a stress is applied to a system in dynamic equilibrium, the system changes in a way that relieves the stress. Stresses that upset the equilibrium of a chemical system include changes in the concentration of reactants or products, changes in temperature, and changes in pressure. The following examples of applications of Le Châtelier's principle all involve reversible reactions. For simplicity and clarity, the components to the left of the reaction arrow will be considered the reactants and the components to the right of the reaction arrow will be considered the products. Blue arrows indicate the shifts resulting from additions to or removals from the system. The arrows always point in the direction of the resulting shift in the equilibrium position—that is, toward the favored side.

molar heat of vaporization

The amount of heat necessary to vaporize one mole of a given liquid is called its molar heat of vaporization (ΔHvap)

heat capacity

The amount of heat needed to increase the temperature of an object exactly 1°C is the heat capacity of that object. The heat capacity of an object depends on both its mass and its chemical composition. The greater the mass of the object, the greater its heat capacity.

law of disorder

The concept that physical and chemical systems attain the lowest possible energy has a companion idea called the law of disorder, which states that the natural tendency is for systems to move in the direction of maximum disorder or randomness. You already know something about this natural tendency toward disorder. Maybe the photographs in Figure 18.23 look familiar to you. More than likely, your bedroom is neat and clean at the beginning of the week. But unless you put energy (work) into maintaining it, your room becomes messy by the end of the week. The law of disorder (entropy change) also operates at the level of atoms and molecules and so it is a factor in determining the direction of chemical reactions. An increase in entropy favors the spontaneous chemical reaction; a decrease favors the nonspontaneous reaction. Figure 18.24 on the following page illustrates some generalities that will help you to predict the course of many reactions.

Hess's Law

The enthalpy change accompanying a chemical change is independent of the route by which the chemical change occurs. Hess's Law is saying that if you convert reactants A into products B, the overall enthalpy change will be exactly the same whether you do it in one step or two steps or however many steps.

molar heat of solution

The enthalpy change caused by dissolution of one mole of substance is the molar heat of solution (ΔHsoln)

equilibrium constant

The equilibrium constant (Keq) (Keq) is the ratio of product concentrations to reactant concentrations at equilibrium, with each concentration raised to a power equal to the number of moles of that substance in the balanced chemical equation. The expression for the equilibrium constant can be written this way. K=([C]^c [D]^d)/([A]^a [B]^b) The exponents in the equilibrium-constant expression are the coefficients in the balanced chemical equation. The square brackets indicate the concentrations of substances in moles per liter (mol/L). The value of Keq depends on the temperature of the reaction. If the temperature changes, the value of Keq also changes. The size of the equilibrium constant shows whether products or reactants are favored at equilibrium. A value of Keq greater than 1 means that products are favored over reactants; a value of Keq less than 1 means that reactants are favored over products. Keq > 1, products favored at equilibrium Keq < 1, reactants favored at equilibrium When the numerical value of an equilibrium constant is calculated, the cancellation of units may or may not lead to a unit for the constant. Chemists have agreed to report all equilibrium constants without stated units. Sample Problem 18.1 shows how to calculate the equilibrium constant for the reaction illustrated in Figure 18.14.

molar heat of fusion

The heat absorbed by one mole of a solid substance as it melts to a liquid at a constant temperature is the molar heat of fusion (ΔHfus).

enthalpy

The heat content of a system at constant pressure is the same as a property called the enthalpy (H) (H) of the system. The heat released or absorbed by a reaction at constant pressure is the same as the change in enthalpy, symbolized as ΔH. Because the reactions presented in this textbook occur at constant pressure, the terms heat and enthalpy change are used interchangeably. In other words, q = ΔH. Because you know the initial and final temperatures and the heat capacity of water, you can calculate the heat absorbed by the surroundings (qsurr) using the formula for specific heat. qsurr = m × C × ΔT In this expression, m is the mass of the water; C is the specific heat of water; and ΔT = Tf − Ti. Because the heat absorbed by the surroundings is equal to, but has the opposite sign of, the heat released by the system, the enthalpy change for the reaction (ΔH) can be written as follows. qsys = ΔH = −qsurr = −m × C × ΔT

heat of reaction

The heat of reaction is the enthalpy change for the chemical equation exactly as it is written. You will usually see heats of reaction reported as ΔH, which is equal to the heat flow at constant pressure. The physical state of the reactants and products must also be given. The standard conditions are that the reaction is carried out at 101.3 kPa (1 atmosphere) and that the reactants and products are in their usual physical states at 25°C. The heat of reaction, or ΔH, in the above example is −65.2 kJ. Each mole of calcium oxide and water that react to form calcium hydroxide produces 65.2 kJ of heat. CaO(s) + H2O(l) → Ca(OH)2(s) ΔH = −65.2 kJ Other reactions absorb heat from the surroundings. For example, baking soda (sodium bicarbonate) decomposes when it is heated. The carbon dioxide released in the reaction causes a cake to rise while baking. This process is endothermic. 2NaHCO3(s) + 129 kJ → Na2CO3(s) + H2O(g) + CO2(g) Remember that ΔH is positive for endothermic reactions. Therefore, you can write the reaction as follows. 2NaHCO3(s) → Na2CO3(s) + H2O(g) + CO2(g) ΔH = 129 kJ Figure 17.7b shows the enthalpy diagram for this reaction. Chemistry problems involving enthalpy changes are similar to stoichiometry problems. The amount of heat released or absorbed during a reaction depends on the number of moles of the reactants involved. The decomposition of 2 mol of sodium bicarbonate, for example, requires 129 kJ of heat. Therefore, the decomposition of 4 mol of the same substance would require twice as much heat, or 258 kJ. In this and other endothermic processes, the potential energy of the product(s) is higher than the potential energy of the reactant(s).

calorimeter

The insulated device used to measure the absorption or release of heat in chemical or physical processes is called a calorimeter.

joule

The joule is the SI unit of energy. One joule of heat raises the temperature of 1 g of pure water 0.2390°C. You can convert between calories and joules using the following relationships. 1 J = 0.2390 cal 4.184 J = 1 cal

law of conservation of energy

The law of conservation of energy states that in any chemical or physical process, energy is neither created nor destroyed. If the energy of the system decreases during that process, the energy of the surroundings must increase by the same amount so that the total energy of the universe remains unchanged.

transition state

The lifetime of an activated complex is typically about 10−13 s. Its brief existence ends with the re-formation of the reactants or with the formation of products. The two outcomes are equally likely. Thus the activated complex is sometimes called the transition state. Collision theory explains why some naturally occurring reactions are immeasurably slow at room temperature. Carbon and oxygen react when charcoal burns, but this reaction has a high activation energy. At room temperature, the collisions of oxygen and carbon molecules are not energetic enough to break the O—O and C—C bonds. These bonds must be broken to form the activated complex. Thus the reaction rate of carbon with oxygen at room temperature is essentially zero.

common ion effect

The lowering of the solubility of an ionic compound as a result of the addition of a common ion is called the common ion effect. Adding sodium chromate to the solution of PbCrO4 would also produce the common ion effect. The additional chromate ion, a different common ion, would similarly cause the solubility equilibrium to shift to the left and produce more PbCrO4.

activation energy

The minimum energy that colliding particles must have in order to react is called the activation energy. In a sense, the activation energy for a chemical reaction is a barrier that reactants must cross to be converted to products. You can see in the energy diagram in Figure 18.5 that when two reactant particles with the necessary activation energy collide, a new entity called the activated complex may form.

equilibrium position

The relative concentrations of the reactants and products at equilibrium constitute the equilibrium position of a reaction. The equilibrium position indicates whether the reactants or products are favored in a reversible reaction. If A reacts to give B and the equilibrium mixture contains significantly more of B—say 1% A and 99% B—then the formation of B is said to be favored. On the other hand, if the mixture contains 99% A and 1% B at equilibrium, then the formation of A is favored. Notice that the equilibrium arrows are not of equal length; the longer of the two arrows indicates the favored direction of a reaction. In principle, almost all reactions are reversible to some extent under the right conditions. In practice, one set of components is often so favored at equilibrium that the other set cannot be detected. If one set of components (reactants) is completely converted to new substances (products), you can say that the reaction has gone to completion, or is irreversible. When you mix chemicals expecting to get a reaction but no products can be detected, you can say that there is no reaction. Reversible reactions occupy a middle ground between the theoretical extremes of irreversibility and no reaction. A catalyst speeds up both the forward and the reverse reactions equally because the reverse reaction is exactly the opposite of the forward reaction. The catalyst lowers the activation energy of the reaction by the same amount in both the forward and reverse directions. Catalysts do not affect the amounts of reactants and products present at equilibrium; they simply decrease the time it takes to establish equilibrium.

specific heat (C)

The specific heat capacity, or simply the specific heat, of a substance is the amount of heat it takes to raise the temperature of 1 g of the substance 1°C. To calculate the specific heat (C) of a substance, you divide the heat input by the temperature change times the mass of the substance. C= g/m•🔼T = heat(joules or calories)/mass(g)•change temp(ºC) In the equation above, q is heat and m is mass. The symbol ΔT (read "delta T") represents the change in temperature. ΔT is calculated from the equation ΔT = Tf − Ti, where Tf is the final temperature and Ti is the initial temperature. As you can see from the equation, specific heat may be expressed in terms of joules or calories. Therefore, the units of specific heat are either J/(g•°C) or cal/(g•°C).

standard heat of formation

The standard heat of formation (ΔHf0) of a compound is the change in enthalpy that accompanies the formation of one mole of a compound from its elements with all substances in their standard states at 25°C. The ΔHf0 of a free element in its standard state is arbitrarily set at zero. Thus, ΔHf0 = 0 for the diatomic molecules H2(g), N2(g), O2(g), F2(g), Cl2(g), Br2(l), and I2(s). Similarly, ΔHf0 = 0 for the graphite form of carbon, C(s, graphite). Enthalpy changes generally depend on conditions of the process. In order to compare enthalpy changes, scientists specify a common set of conditions as a reference point. These conditions, called the standard state, refer to the stable form of a substance at 25°C and 101.3 kPa. Standard heats of formation provide an alternative to Hess's law in determining heats of reaction indirectly. For a reaction that occurs at standard conditions, you can calculate the heat of reaction by using standard heats of formation. Such an enthalpy change is called the standard heat of reaction (ΔH0). The standard heat of reaction is the difference between the standard heats of formation of all the reactants and products. ΔH0=ΔHf0(products)-ΔHf0(reactants)

surroundings

The surroundings include everything else in the universe. In thermochemical experiments, you can consider the region in the immediate vicinity of the system as the surroundings. Together, the system and its surroundings make up the universe. A major goal of thermochemistry is to examine the flow of heat between the system and its surroundings.

Gibbs free-energy change

This energy, called the Gibbs free-energy change (ΔG), is the maximum amount of energy that can be coupled to another process to do useful work. The change in Gibbs free energy is related to the change in entropy (ΔS) and the change in enthalpy (ΔH) of the system by the free-energy equation. ΔG = ΔH − TΔS The temperature (T) is in kelvins. All spontaneous processes release free energy. The numerical value of ΔG is negative in spontaneous processes because the system loses free energy. Nonspontaneous processes require that work be expended to make them go forward at the specified conditions. Therefore, the numerical value of ΔG is positive for a nonspontaneous process. However, a reaction that is nonspontaneous under one set of conditions may be spontaneous under another set of conditions.

solubility product constant

This new constant, called the solubility product constant (Ksp) (Ksp), equals the product of the concentrations of the ions each raised to a power equal to the coefficient of the ion in the dissociation equation. The coefficients for the dissociation of silver chloride are each 1. The value of Ksp for silver chloride at 25°C is 1.8 × 10−10. What does the size of the solubility product constant tell you about the solubility of the compound? The smaller the numerical value of the solubility product constant, the lower the solubility of the compound. The solubility product constants for some common sparingly soluble salts are given in Table 18.2 on the next page. The mineral deposits around sink drains, such as the one shown in Figure 18.17, are composed of compounds such as calcium carbonate (Ksp = 4.5 × 10−9). The low solubility of such compounds makes them difficult to remove. The solubility product (Ksp) can be used to predict whether a precipitate will form when solutions are mixed. If the product of the concentrations of two ions in the mixture is greater than the Ksp of the compound formed from the ions, a precipitate will form. After precipitation, the solution will be saturated with the precipitated compound. If the product of the concentrations is less than the Ksp, no precipitate will form and the solution is unsaturated.

molar heat of condensation

When a vapor condenses, heat is released. The amount of heat released when 1 mol of vapor condenses at the normal boiling point is called its molar heat of condensation (ΔHcond). This value is numerically the same as the corresponding molar heat of vaporization, however the value has the opposite sign. The quantity of heat absorbed by a vaporizing liquid is exactly the same as the quantity of heat released when the vapor condenses; that is, ΔHvap = −ΔHcond.

chemical equilibrium

When the rates of the forward and reverse reactions are equal, the reaction has reached a state of balance called chemical equilibrium. Changes in concentrations of the three components during the course of the reaction are shown in the graphs in Figure 18.10. The graph on the left shows the progress of a reaction that starts with specific concentrations of SO2 and O2, but with zero concentration of SO3. The graph on the right shows concentrations for a reaction that begins with an initial concentration of SO3 and zero concentrations for SO2 and O2. Notice that after a certain time, all concentrations remain constant. At chemical equilibrium, no net change occurs in the actual amounts of the components of the system. The amount of SO3 in the equilibrium mixture is the maximum amount that can be produced by this reaction under the conditions of the reaction.

nonspontaneous reaction

a reaction that does not favor the formation of products at the specified conditions. Nonspontaneous reactions do not give substantial amounts of products at equilibrium. Nonspontaneous reactions, those in which the products are not favored, can have enthalpy changes, entropy changes, or both working against them. For example, a reaction might be highly endothermic with a large decrease in entropy. In that case, both changes work against the formation of products and the reaction is nonspontaneous. In another case, a reaction may be exothermic but involve a decrease in entropy large enough to offset the favorable enthalpy change. This reaction will also be nonspontaneous. Alternatively, an endothermic reaction could have an increase in entropy too small to overcome the unfavorable enthalpy change

activated complex. transition state.

activated complex. transition state. An intermediate structure formed in the conversion of reactants to products. The activated complex is the structure at the maximum energy point along the reaction path; the activation energy* is the difference between the energies of the activated complex and the reactants.

collision theory

atoms, ions, and molecules can react to form products when they collide with one another, provided that the colliding particles have enough kinetic energy. Particles lacking the necessary kinetic energy to react bounce apart unchanged when they collide.

heat of combustion

he heat of combustion is the heat of reaction for the complete burning of one mole of a substance. The combustion of natural gas, which is mostly methane, is an exothermic reaction used to heat many homes around the country. CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) + 890 kJ You can also write this equation as follows. CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) ΔH = −890 kJ Burning 1 mol of methane releases 890 kJ of heat. The heat of combustion (ΔH) for this reaction is −890 kJ per mole of carbon burned. Like other heats of reaction, heats of combustion are reported as the enthalpy changes when the reactions are carried out at 101.3 kPa of pressure and the reactants and products are in their physical states at 25°C.

rate

is a measure of the speed of any change that occurs within an interval of time. The interval of time may range from fractions of a second to centuries. Figure 18.2 shows some familiar examples of rates of change. If one half of a 1-molar piece of iron turns to rust in one year, the rate at which iron rusts might be expressed as 0.5 mol/yr. In chemistry, the rate of chemical change or the reaction rate is usually expressed as the amount of reactant changing per unit time. Every chemical reaction proceeds at its own rate. Some reactions are naturally fast and some are naturally slow under the same conditions. However, by varying the conditions of the reaction, the rate of almost any reaction can be modified. The rate of a chemical reaction depends upon temperature, concentration, particle size, and the use of a catalyst. Collision theory helps explain why changing one or more of these factors may affect the rate of a chemical reaction.

activated complex

is an unstable arrangement of atoms that forms momentarily at the peak of the activation-energy barrier. An activated complex forms only if the colliding particles have sufficient energy and if the atoms are oriented properly.

reversible reaction

is one in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously. One example of a reversible reaction is the following: Forward reaction: 2SO2(g) + O2(g) → 2SO3(g) Reverse reaction: 2SO2(g) + O2(g) ←2SO3(g) In the first reaction, which is read from left to right, sulfur dioxide and oxygen produce sulfur trioxide. In the second reaction, which is read from right to left, sulfur trioxide decomposes into oxygen and sulfur dioxide. The first reaction is called the forward reaction. The second is called the reverse reaction. The two equations can be combined into one using a double arrow. The double arrow tells you that this reaction is reversible.

molar heat of solidification

molar heat of solidification (ΔHsolid) is the heat lost when one mole of a liquid solidifies at a constant temperature. The quantity of heat absorbed by a melting solid is exactly the same as the quantity of heat released when the liquid solidifies; that is, ΔHfus = −ΔHsolid.

spontaneous reaction

occurs naturally and favors the formation of products at the specified conditions. Spontaneous reactions produce substantial amounts of products at equilibrium and release free energy.

heat

represented by q,, is energy that transfers from one object to another because of a temperature difference between them. One of the effects of adding heat to an object is an increase in its temperature. It is the radiant heat of the sun's rays that makes a summer day hot. In this example, the air is the object that absorbs heat and increases in temperature. Heat always flows from a warmer object to a cooler object. If two objects remain in contact, heat will flow from the warmer object to the cooler object until the temperature of both objects is the same.

Hess's law of heat summation

states that if you add two or more thermochemical equations to give a final equation, then you can also add the heats of reaction to give the final heat of reaction. Hess's law allows you to determine the heat of reaction indirectly. Sometimes it is hard to measure the enthalpy change for a reaction. For example, the reaction might take place too slowly to actually measure the enthalpy change. Or, the reaction might be an intermediate step in a series of reactions. Or, as mentioned above, you might not want to destroy the material that undergoes the reaction. Fortunately, it is possible to measure a heat of reaction indirectly. a. C(s, graphite) + O2(g) → CO2(g) ΔH = −393.5 kJ b. C(s, diamond) + O2(g) → CO2(g) ΔH = −395.4 kJ Write equation a in reverse to give: c. CO2(g) → C(s, graphite) + O2(g) ΔH = 393.5 kJ When you write a reverse reaction, you must also change the sign of ΔH. If you now add equations b and c, you get the equation for the conversion of diamond to graphite. The CO2(g) and O2(g) terms on both sides of the summed equations cancel, just as they do in algebra. Now if you also add the values of ΔH for equations b and c, you get the heat of reaction for this conversion. Another case in which Hess's law is useful is when reactions yield products in addition to the product of interest. Suppose you want to determine the enthalpy change for the formation of carbon monoxide from its elements. You can write the following equation for this reaction.

thermochemistry

the study of energy changes that occur during chemical reactions and changes in state.

calorie (cal)

A calorie (cal) is defined as the quantity of heat needed to raise the temperature of 1 g of pure water 1°C. The word calorie is written with a small c except when referring to the energy contained in food. The dietary Calorie, written with a capital C, always refers to the energy in food. One dietary Calorie is actually equal to one kilocalorie, or 1000 calories. 1 Calorie = 1 kilocalorie = 1000 calories

common ion

A common ion is an ion that is found in both salts in a solution. Adding lead nitrate to a saturated solution of PbCrO4 causes the solubility of PbCrO4 to decrease.

bomb calorimeter

A device called a bomb calorimeter is used in calorimetry experiments. It can be used to measure the change in enthalpy, which is the heat released or absorbed during a reaction at constant pressure. Changes in enthalpy are often measured in Joules per mole or Joules per gram. One familiar reaction is the combustion of food, or the amount of heat released when a particular amount of a specific food is burned. It is commonly measured in calories. A bomb calorimeter is a strong, sealed, insulated, container where a combustion reaction takes place surrounded by water. When the combustion reaction occurs, heat is released. The heat flows through the walls of the sealed container to the water. The temperature change of the water is then measured. A simpler device, called a calorimeter cup, can provide similar though less precise information. This consists of an insulated, covered cup containing water with a thermometer and stirrer inserted. The reaction occurs in the water and the change in temperature is noted.

endothermic process

An endothermic process is one that absorbs heat from the surroundings. In an endothermic process, the system gains heat as the surroundings cool down. In Figure 17.2a, the system (the person) gains heat from its surroundings (the fire). Heat flowing into a system from its surroundings is defined as positive; q has a positive value.

exothermic process

An exothermic process is one that releases heat to its surroundings. In an exothermic process, the system loses heat as the surroundings heat up. In Figure 17.2b, the system (the body) loses heat to the surroundings (the perspiration on the skin, and the air). Heat flowing out of a system into its surroundings is defined as negative; q has a negative value because the system is losing heat.

inhibitor

An inhibitor is a substance that interferes with the action of a catalyst. Some inhibitor molecules work by reacting with, or "poisoning," the catalyst itself. Thus the inhibitor reduces the amount of functional catalyst available. Reactions slow or even stop when a catalyst is poisoned.

units of heat

Describing the amount of heat flow requires units different than those used to describe temperature. Heat flow is measured in two common units, the calorie and the joule.

entropy

Entropy (S) is a measure of the disorder of a system. The size and direction of enthalpy changes and entropy changes together determine whether a reaction is spontaneous; that is, whether it favors products and releases free energy. An exothermic reaction accompanied by an increase in entropy is definitely spontaneous because both factors are favorable. A reaction is also spontaneous if a decrease in entropy is offset by a large release of heat. Similarly, an endothermic, or heat-absorbing, reaction is spontaneous if an entropy increase offsets the heat absorption.

chemical potential energy

Every substance has a certain amount of energy stored inside it. The energy stored in the chemical bonds of a substance is called chemical potential energy. The kinds of atoms and their arrangement in the substance determine the amount of energy stored in the substance.

free energy

Free energy is energy that is available to do work. Just because free energy is available to do work, however, does not mean that it can be used efficiently. Even in living things, which are among the most efficient users of free energy, processes are seldom more than 70% efficient.

calorimetry

Heat that is released or absorbed during many chemical reactions can be measured by a technique called calorimetry. Calorimetry is the precise measurement of the heat flow into or out of a system for chemical and physical processes. In calorimetry, the heat released by the system is equal to the heat absorbed by its surroundings. Conversely, the heat absorbed by a system is equal to the heat released by its surroundings. depends on the law of conservation of energy.

thermochemical equation

In a chemical equation, the enthalpy change for the reaction can be written as either a reactant or a product. In the equation describing the exothermic reaction of calcium oxide and water, the enthalpy change can be considered a product. CaO(s) + H2O(l) → Ca(OH)2(s) + 65.2 kJ This equation is presented visually in Figure 17.7a. A chemical equation that includes the enthalpy change is called a thermochemical equation.

system

In studying energy changes, you can define a system as the part of the universe on which you focus your attention.

catalyst

Increasing the temperature is not always the best way to increase the rate of a reaction. A catalyst is often better. Recall that a catalyst is a substance that increases the rate of a reaction without being used up during the reaction. Catalysts permit reactions to proceed along a lower energy path, as Figure 18.8 shows. Notice that the activation energy barrier for the catalyzed reaction is lower than that of the uncatalyzed reaction. With a lower activation-energy barrier, more reactants have the energy to form products within a given time. For instance, the rate of the combination reaction of hydrogen and oxygen at room temperature is negligible, but with a trace of finely divided platinum (Pt) as a catalyst, the reaction is rapid. Because a catalyst is not consumed during a reaction, it does not appear as a reactant or product in the chemical equation. Instead, the catalyst is often written above the yield arrow, as in the equation above. Catalysts are crucial for many life processes. Your body temperature is only 37°C and cannot be raised significantly without danger. Without catalysts, few reactions in the body would proceed fast enough. Enzymes are biological catalysts that increase the rates of biological reactions. When you eat a meal containing protein, enzymes in your digestive tract break down the protein molecules in a few hours. Without enzymes, the digestion of protein at 37°C would take many years!