Pharm-D Clinical Program PDF

Pharm – D Clinical Program Pharmaceutical Analytical Chemistry I Code : PC 101 - C Presented By Ass.Prof. Ragab Ahmad Said  Lecture : 1 Chemical kinetics Rate of reaction Rate law zero order reaction First...

Pharm – D Clinical Program Pharmaceutical Analytical Chemistry I Code : PC 101 - C Presented By Ass.Prof. Ragab Ahmad Said  Lecture : 1 Chemical kinetics Rate of reaction Rate law zero order reaction First order reaction Second order reaction  Introduction Chemical reactions convert substances with well-define properties into other materials with different properties. Much of our study of chemical reactions concerns the formation of new substances from a given set of reactants. It is equally important to understand how rapidly chemical reactions occur. The rates of reactions span ranged from those that are complete within fractions of seconds, such as explosions, to those that take thousands or even millions of years, such as the formation of diamonds or other minerals in Earth's crust.  So, chemical kinetics is the area of chemistry that is concerned with the speeds or rates of reactions. It relates, for example, to how quickly a medicine is able to work, to whether the formation and depletion of ozone in the upper atmosphere are in balance, and to industrial challenges such as the development of catalysts to synthesize new materials. Our goal in this chapter is to understand how to determine the rates at which reactions occur and to consider the factors that control these rates. Factors That Affect Reaction Rates: Because reactions involve the breaking and forming of bonds, the speeds of reactions depend on the nature of the reactants themselves. Four factors allow us to change the rates at which particular reactions occur: 1- The physical state of the reactants. Reactants must come together to react. The more readily molecules collide with each other, the more rapidly they react. Reactions may classified into: - Homogeneous reactions: involving reactants in the same physical state. - Heterogeneous reactions: in which reactants are in different phases. Under heterogeneous conditions, a reaction is limited by the area of contact of the reactants. Thus, heterogeneous reactions that involve solids tend to proceed more rapidly if the surface area of the solid is increased. 2. The concentrations of the reactants. Most chemical reactions proceed faster if the concentration of one or more of the reactants is increased. As concentration increases, the frequency with which the reactant molecules collide increases, leading to increased rates. 3. The temperature at which the reaction occurs. The rates of chemical reactions increase as temperature is increased. Increasing temperature increases the kinetic energies of molecules. As molecules move more rapidly; they collide more frequently and also with higher energy; leading to increased reaction rates. 4. The presence of a catalyst. Catalysts are agents that increase reaction rates without being used up. They affect the kinds of collisions (the mechanism) that lead to reaction.  Reaction Rate The reaction rate, is the change in concentration of a reactant or a product with time (M/s). Any reaction can be represented by the general equation 𝑹𝒆𝒂𝒄𝒕𝒂𝒏𝒕𝒔 → 𝑷𝒓𝒐𝒅𝒖𝒄𝒕𝒔 From this equation, it was noted that during the course of a reaction, reactant molecules are consumed while product molecules are formed. As a result, we can follow the progress of a reaction by monitoring either the decrease in concentration of the reactants or the increase in concentration of the products. In general, it is more convenient to express the rate in terms of change in concentration with time. Thus, for the preceding reaction we can express the rate as: 𝜟𝑨 𝜟𝑩 𝐀 𝐁 𝒓𝒂𝒕𝒆 = − 𝒐𝒓 𝒓𝒂𝒕𝒆 = 𝜟𝒕 𝜟𝒕  in which Δ [ A] and Δ [B] are the changes in concentration (in molarity) over a period Δ t. Because the concentration of A decreases during the time interval, Δ[A] is a negative quantity. The rate of a reaction is a positive quantity, so a minus sign is needed in the rate expression to make the rate positive. On the other hand, the rate of product formation does not require a minus sign because 𝛥 [B] is a positive quantity (the concentration of B increases with time). The rate of reaction A B, represented as the decrease of A molecules with time and as the increase of B molecules with time.  For more complex reactions, we must be careful in writing the rate expression. Consider, for example, the reaction: 2A B Two moles of A disappear for each mole of B that forms. That is, the rate at which B forms is one half the rate at which A disappears. We write the rate as either 𝟏𝜟 𝑨 𝜟𝑩 𝒓𝒂𝒕𝒆 = − 𝒐𝒓 𝒓𝒂𝒕𝒆 = 𝟐 𝜟𝒕 𝜟𝒕 For the reaction a A + b B cC +dD 𝟏𝜟 𝑨 𝟏𝜟 𝑩 𝟏𝜟 𝑪 𝟏𝜟 𝑫 the rate is given by 𝒓𝒂𝒕𝒆 = − = − = = 𝒂 𝜟𝒕 𝒃 𝜟𝒕 𝒄 𝜟𝒕 𝒅 𝜟𝒕 where the expressions in brackets refer to the concentrations of the reactants and products at time t after the start of the reaction.  Concentration and Rate Laws The initial rate of a reaction depends on the initial concentrations. For example, we might study the rate of the reaction: by measuring the concentration of NH4+ or NO2- as a function of time or by measuring the volume of N2 collected as a function of time. Because the stoichiometric coefficients on NH4+, NO2- , and N2 are the same, all of these rates are the same. We express the way in which the rate depends on the reactant concentrations by the equation  For the general reaction: aA + bB cC +dD the rate law generally has the form 𝑹𝒂𝒕𝒆 = 𝒌 [𝑨]𝒎 [𝑩]𝒏 Notice that: only the concentrations of the reactants generally appear in the rate law. The constant k is called the rate constant. The magnitude of k changes with temperature and the exponents m and n are typically small whole numbers. The rate constant k, m and n must be determined experimentally. The exponents m and n are called reaction orders which enable us to appreciate better the dependence of rate on reactant concentrations. Suppose, for example, that, for a certain reaction, m = 1 and n = 2. The rate law for the reaction: 𝑹𝒂𝒕𝒆 = 𝒌 [𝑨] [𝑩]𝟐 This reaction is first order in A, second order in B, and third order overall (1+2 = 3). The sum of the powers to which all reactant concentrations appearing in the rate law are raised is called the overall reaction order.  Let us assume that initially [A] = 1.0 M and [B] = 1.0 M. The rate law tells us that if we double the concentration of A from 1.0 M to 2.0 M at constant [B], we also double the reaction rate: for [A] = 1.0 M rate1 = k (1.0 M) (1.0 M)2 = k(1.0 M)3 for [A] = 2.0 M rate2 = k (2.0M) ( 1.0M)2 = k (2.0 M)3 Hence, rate2 = 2 (rate1) On the other hand, if we double the concentration of B from 1.0 M to 2.0 M at constant [A], the reaction rate will increase by a factor of 4 because of the power 2 in the exponent: for [B] = 1.0 M rate1 = k (1.0 M) (1.0 M)2 = k(1.0 M)3 for [B] = 2.0 M rate2 = k (1.0M) ( 2.0M)2 = k (4.0 M)3 Hence, rate2 = 4 (rate1)  If, for a certain reaction, m = 0 and n = 1, then the rate law is rate = k [A]0 [B] = k [B] This reaction is zero order in A, first order in B, and first order overall. Thus, the rate of this reaction is independent of the concentration of A. Note be: Zero order does not mean that the rate is zero. It just means that the rate is independent of the concentration of A present.  Reaction Order The reaction rate can be expressed as mentioned before as: 𝑹𝒂𝒕𝒆 α [𝑨]𝒙 [𝑩]𝒚 𝑹𝒂𝒕𝒆 = 𝒌 [𝑨]𝒙 [𝑩]𝒚 This equation, known as the rate law, tells us that the rate of a reaction is not constant; its value at any time, t, is proportional to the concentrations of A and B raised to some powers. The proportionality constant, k, is called the rate constant which does not depend on the concentrations of the reactants. The rate constant is affected only by temperature as mentioned before. The order of a reaction may be zero, first, second – order reaction as follow:  1- Zero – order Reactions A Product Reactions whose order is zero are rare. For a zero-order reaction the rate law is given by rate = k [ A ]0 = k Thus, the rate of a zero-order reaction is a constant, independent of reactant concentration. [A ]t = - kt + [A]0 A plot of [A]t versus t gives a straight line with slope = -k and y intercept = [A]0. The half-life of a reaction, t1/2, is the time required for the concentration of a reactant to decrease to half of its initial concentration.  2- First-Order Reactions A first-order reaction is a reaction whose rate depends on the reactant concentration raised to the first power. A Product 𝚫 𝐀 In a first-order reaction of the type the rate is 𝒓𝒂𝒕𝒆 = − 𝚫𝐭 From the rate law, we also know that: rate = k [ A] 𝚫 𝐀 Thus 𝒓𝒂𝒕𝒆 = − =𝒌[𝑨] 𝚫𝐭 We can determine the units of the first-order rate constant k by transposing: 𝚫 𝐀 𝟏 𝒌=− 𝑨 𝚫𝐭 Because the unit for 𝛥[A] and [A] is M and that for 𝛥t is s, the unit for k is 𝑴 𝟏 = = 𝒔−𝟏 𝑴𝒔 𝒔  Note that: for a first-order reaction, doubling the concentration of the reactant doubles the rate. Figure: First-order reaction characteristics: (a) The exponential decrease of reactant concentration with time. (b) A plot of ln [A]t versus t. The slope of the line is equal to -k. Half-Life: By the definition of half-life, when t = t1/2, [A]t = [A]0 / 2, so, 1 0.693 t1/2= ln 2 = 𝑘 𝑘  3- Second-Order Reactions A second-order reaction is a reaction whose rate depends on the concentration of one reactant raised to the second power or on the concentrations of two different reactants, each raised to the first power. The simpler type involves only one kind of reactant molecule: 2A Product 𝛥[𝐴] For which rate = − 𝛥 𝑡 From the rate law rate = 𝑘 [𝐴]2 The units of k can be determined by writing 𝑟𝑎𝑡𝑒 𝑀/𝑠 𝑘 = = = 1/𝑀. 𝑠 [𝐴]2 𝑀2 Figure: A plot of 1/[A]t versus t for a second-order reaction. The slope of the line is equal to k.  Another type of second-order reaction is A + B Product The rate law is given by rate = k [A] [B] The reaction is first order in A and first order in B, so it has an overall reaction order of 2. Note that: for a second-order reaction, doubling the concentration of the reactant increase the rate by fourth. Half - life t1/2: The half-life of a second-order reaction by setting [A]t = [A]o / 2 𝟏 𝟏 = + 𝒌 𝒕𝟏 [𝑨]𝟎 /𝟐 𝑨𝟎 𝟐 𝟏 Solving for t1/2 𝒕𝟏 = 𝟐 𝒌 [ 𝑨 ]𝟎