Plot the step response for using MATLAB. From your plots, find the time constant, rise time, and settling time.
CHEM 1040 YNGARD REVIEW EXAM 2 Highlight = Important Principle Highlight = Important Concept Highlight = Key Term Chapter 15.1 The Concept of Equilibrium - By our deﬁnition of a chemical reaction, reactants are consumed and products are produced. This is known as the forward reaction. - A reversible process is one in which the products can also be consumed to produce reactants, a process known as the reverse reactions. - Equilibrium is the condition where the forward and reverse reactions are occurring at the same rate and there si no net change in the reactant and product concentrations over time. - In theory, equilibrium can be established starting with just reactants, with just products, or with a combination or reactants and products. - Equilibrium is a dynamic state: both forward and reverse reactions continue to occur. Chapter 15.2 The Equilibrium Constant - The reaction quotient is the product of the product concentrations over the product of the reactant concentrations, with each concentration raised to a power equal to the corresponding stoichiometric coefﬁcient in the balanced chemical equation. [This is known as the Law of Mass Action] - At equilibrium, the reaction quotient is equal to a constant whole value, the equilibrium constant (Kc) - At equilibrium, concentrations in the reaction quotient are equilibrium concentrations and the quotient is called the equilibrium expression. - Because each concentration is in the units of mol/L both Kc and Qc are unitless. - Kc is constante at constant temperature. The value of Kc can be calculated b plugging equilibrium concentrations into the equilibrium expression. - A large equilibrium constant indicates that product are favored at equilibrium. [“lie to the right”] - A small equilibrium constant indicates that reactants are favored at equilibrium. [“lie to the left”] - If Kc is neither small nor large, the equilibrium mixture will contain comparable amounts of both reactants and products; therefore, neither one is favored over the other. Chapter 15.3 Equilibrium Expressions - Solids and Liquids do not appear in the equilibrium expression for heterogeneous reaction - When chemical equations that represent equilibria are reversed, multiplied, combined with other equation, or any combination of the processes, the corresponding changes must be made to the equilibrium constants. - Equilibrium expressions that contain only gasses can be written either as Kc expressions or as Kp expressions. Kp expressions have the same form as Kc expressions but contain partial pressures rather than molar concentrations. The reaction quotient, Q, can also be expressed in terms of the pressures of products and reactants. In this case it is labeled Qp. - If the equation is reversed, invert the equilibrium constant. - If the coefﬁcients in the reaction are multiplied by a factor, Kc1, is raised to a power equal to that same factor. - The equilibrium constant for a reaction made up of two or more reactions is the product of the equilibrium constants for the individual reactions. - Kc and Kp are not usually equal. The values are te same only when the reactions results in no net change in the number of moles of gas. Gaseous Equilibria Kp = pressure at equilibrium Pa, Pb = partial pressures at equilibrium Chapter 15.4 The Concept of Equilibrium - The free-energy change (∆G) is determined using the standard free-energy change (∆G ) and o the reaction quotient (Q). - We can predict in which direction a reaction must proceed to achieve equilibrium by comparing the values of Qc and Kc (or of Qp and Kp). - The sign of ∆G tells us where the reaction is spontaneous under the conditions described. - o ∆G is related to toe equilibrium constant, - A negative ∆G corresponds to a large K - A positive ∆G corresponds to a small K - If Qc is greater than Kc; products are favored - If Qc is smaller than Kc; reactants are favored - If Q > K, the reaction procedes from right to left until equilibrium is reached - If Q < K, the reaction procedes from left to right until equilibrium is reached. - If Q = K, the reaction is a equilibrium - When a reaction is not at equilibrium the spontaneity of a reaction is dependent upon the concentration of the reactants and products (Q) - Reaction at equilibrium: ∆G= 0 and Q = K Chapter 15.5 Calculating Equilibrium Concentrations - Starting concentrations can be used along with the equilibrium expression and equilibrium constant, to determine equilibrium concentrations. - How to calculate Equilibrium Concentrations: 1. Use of initial reactant concentrations to determine equilibrium concentrations 2. Use initial concentrations to calculate the reaction quotient, Q, and compare Q to K to determine the direction in which the reaction will proceed. 3. Deﬁne x as the amount of a particular species consumed, and use the stoichiometry of the reaction to deﬁne (in terms of x) the amount of other species consumed or produced. 4. For each species in the equilibrium, add the change in concentration to the initial concentration to get the equilibrium concentration. 5. Use the equilibrium concentrations and the equilibrium expression to solve for x. 6. Using the calculated value of x, determine the concentrations of all species at equilibrium. 7. Check your work by plugging the calculated equilibrium concentrations into the equilibrium expression. The result should be very close to the K staced in the problem. Chapter 15.6 Le Chatelier’s Principle: Factors that Affect Equilibrium - According to Le Chatelier’s Principle, a system at equilibrium will react to stress by shifting in the direction that will partially offset the effects of the stress. - The stresses that can be applied to a system at equilibrium include: - The addition or removal of a substance - Changes in the volume of the reaction vessel - Changes in the temperature - An equilibrium that shifts to the right is one in which more products are produced by the forward reaction. - An equilibrium that shifts to the left is one in which more reactants are produced by the reverse reaction. - Inert Gas: a gas that does not react or inﬂuence the other gases in the reactants or products - When volume is decreased, the equilibrium is driven toward the side with the smallest number of moles of gas - Pressure increases when volume decreases: shift to right —> “favor products” - Pressure decreases when volume increases: shift to left —> “favor reactants” - In an exothermic reaction: An increase in temperature causes the reaction to shift to the left because it is an addition of energy. A decrease in temperature causes the reaction to shift to the right because it is a release of energy. - In an endothermic reaction: An increase in temperature causes the reaction to shift to the right; a decrease in temperature causes the reaction to shift to the left. Chapter 16.1 The Concept of Equilibrium - Arrhenius Deﬁnition: - An acid releases H+ when dissociated in water - A base releases OH- when dissociated in water - Brønsted Deﬁniton: - Acid: a proton donor - must have a removable (acidic) proton - When a Brønsted acid donates a proton, the anion that remains is a conjugate base. - Base: a proton acceptor - Must have a pair of nonbonding electors - When a Brønsted base accepts a proton, the resulting cation is a conjugate acid. - The combination of a Brønsted acid and its conjugate (or the combination of a Brønsted base and its conjugate acid) is called a conjugate pair. Chapter 16.2 Molecular Structure and Acid Strength - The strength of an acid is affected by molecular structure. - Polar and weak bonds to the ionizable hydrogen least a stronger acid. - the larger the difference in electronegativity the ore polarized the bond is the easier it is to release the potion making it more acidic. - Resonance stabilization of the conjugate base favors the ionization process, resulting in a stronger acid. - Strong bonding means that the element holds on stronger to their proton which leads to weak acids. - Weak bondingmeans that the element easily releases protons which leads to strong acids. Chapter 16.3 The Acid-Base Properties of Water - Water is amphoteric, meaning it can act both as a Brønsted acid and a Brønsted base. - Pure water undergoes autoionizaiton (to a very small extent), resulting in concentrations of H and OH of 1.0 X 10 M at 25 C —> a neutral pH of 7 - Kw is the equilibrium constant for the autoionizaiton of water, also called the ion-product constant. -14 - At 25 degrees C, Kw = -1.0 X 10 Chapter 16.4 The pH and pOH Scales - The pOH scale is analogous to the pH scale, but pH measures acidity and pOH measures basicity - Sig Figs for Logs: The total number of signiﬁcant ﬁgures in the number before taking the log is equal to the number of signiﬁcant ﬁgures in the decimal place after taking the log [ex: - log(-1.0 X 10 ) —> 2 sig ﬁgs total = 14.00 —> 2 sig ﬁgs in decimal place] - Low pH = high [H+] - High pH = low [H+] - pH 7 = neutral - pH < 7 = acidic - pH > 7 = basic Chapter 16.5 Strong Acids and Bases - There are seven strong acids: HCl, HBr, HI, HNO3, HClO3, HClO4, and H2SO4 - Strong acids ionize completely in aqueous solution. - If the acid is a strong acid you can use the initial concentration in your calculations to ﬁnd pH or pOH. [HCl] = [H+] - The strong bases are the Group 1A and the heaviest Group 2A hydroxides: LiOh, NaOH, KOH, RbOH, CsOH, Ca(OH)2, Sr(OH)2, and Ba(OH)2. - Same as acids assume that they dissociate completely because they are strong bases. Therefore you can use the initial calculation to ﬁnd pOH or pH. [initial] = [OH-] Chapter 16.6 Weak Acids and Ionization Constants - A weak acid ionizes only partially. The acid ionization constant, Ka, is the equilibrium constant that indicates to what extent a weak acid ionizes. - Weak monoprotic acid, HA: - We solve for the pH of a solution of weak acid using the concentration of the acid, the Ka value, and an equilibrium table. - We can also determine the Ka of a weak acid if we know the initial concentration and the pH at equilibrium. - If % ionization < 5%, then the x in the denomination is insigniﬁcant and simpliﬁcation of the quadratic equation is allowed. Chapter 16.7 Weak Bases and Base Ionization Constants - A weak base ionizes only partially. The base ionization constant, Kb, is the equilibrium constant that indicates to what extent a weak base ionizes - The larger your Kb is the stronger your base is - We solve for the pH of a solution of weak base using the concentration of the base, the Kb, value and an equilibrium table. - We can also determine the Kb of a weak base if we know the concentration of the pH at equilibrium. Chapter 16.8 Weak Acids and Ionization Constants - A strong acid has a relatively weak conjugate base. - A weak acid has a relatively strong conjugate base. - A strong base has a relatively weak conjugate acid - A weak base has a relatively strong conjugate acide. Chapter 16.9 Diprotic and Polyprotic Acids - Diprotic and Polyprotic acids have more than one proton to donate. They undergo separate stepwise ionizations. Each ionization has a Ka value associated with it. - The Ka values for stepwise ionizations become progressively smaller. - In most cases, it is only necessary to consider the ﬁrst ionization of other species at equilibrium, it may be necessary to consider subsequent ionizations. Chapter 16.10 Acid-Base Properties of Salt Solutions - Salts dissolve in water to give neutral, acidic, or basic solutions depending on their constituent ions. Salt hydrolysis is the reaction of an ion with water to produce hydronium or hydroxide ions. - Cations that are strong conjugate acids (NH4 ) make a solution more acidic. - - Anions that are strong conjugate bases (F ) make a solution more basic - Anions that are conjugate bases of strong acids have no effect on pH - Small, highly charged metal ions hydrolyze to give acidic solutions. - In general, if the salt contains an ion and cation that both hydrolyze, the pH depends on the relative strengths of the weak acid (Ka) and base (Kb) - Kb > Ka, the solution is basic - Kb < Ka, the solution is acidic - Kb = Ka, the solution is neutral or heavily neutral Chapter 16.11 Acid Base Properties of Oxides and Hydroxides - Oxides of metals generally are basic; oxides of nonmetals generally are acidic - Metal hydroxides my be basic or amphoteric Chapter 16.12 Lewis Acid and Bases - Lewis theory provides more general deﬁnitions of acids and bases - A Lewis acid accepts a pair of electrons; a Lewis base donates a hydrogen atom - A Lewis base is an ion or a molecule with one or more lone pairs of electrons.