Pharmaceutical Analytical Chemistry I Lecture Notes (PDF)

# Pharmaceutical Analytical Chemistry I ## (PC_101) ## Lecture No. (08) ### Assistant Prof. Ashraf Mohamed Taha ## 4. Measuring Reaction Rates - Our next step is to see how the rate of a reaction is obtained experimentally. We know that to determine the rate of a reaction we must monitor the conce...

# Pharmaceutical Analytical Chemistry I ## (PC_101) ## Lecture No. (08) ### Assistant Prof. Ashraf Mohamed Taha ## 4. Measuring Reaction Rates - Our next step is to see how the rate of a reaction is obtained experimentally. We know that to determine the rate of a reaction we must monitor the concentration of the reactant (or product) as a function of time. - For reactions in solution, the concentration of a species can often be measured by spectroscopic means. If ions are involved, the change in concentration can also be detected by an electrical conductance measurement. Reactions involving gases are most conveniently followed by pressure measurements. The most common way to study the kinetics of a reaction is through spectroscopy (Figure 2). - This loss of color and hence concentration can be monitored easily with a spectrometer which registers the amount of visible light absorbed by bromine (Figure 4). - Measuring the change (decrease) in bromine concentration at some initial time and then at some final time enables us to determine the average rate of the reaction during that interval according to Eq. 1: - average rate = Δ[Br₂] / Δτ = ([Br₂] final - [Br₂] initial) / (τ final - τ initial) - Using the data provided in Table 1 we can calculate the average rate over the first 50-s time interval as follows: - average rate = (0.0101 - 0.0120)M/ 50.0s = 3.80 × 10⁻⁵ M/s - If we had chosen the first 100 s as our time interval, the average rate would then be given by: - average rate = (0.00846 - 0.0120)M / 100.0s = 3.54 × 10⁻⁵ M/s - These calculations demonstrate that the average rate of the reaction depends on the time interval we choose. | Time (s) | [Br₂] (M) | Rate (M/s) | k = (rate/[Br₂]) (s⁻¹) | |:---:|:---:|:---:|:---:| | 0.0 | 0.0120 | 3.50 * 10⁻⁵ | 3.50 * 10⁻⁵ | | 50.0 | 0.0101 | 3.52 * 10⁻⁵ | 3.49 * 10⁻⁵ | | 100.0 | 0.00846 | 2.96 * 10⁻⁵ | 3.50 * 10⁻⁵ | | 150.0 | 0.00710 | 2.49 * 10⁻⁵ | 3.51 * 10⁻⁵ | | 200.0 | 0.00596 | 2.09 * 10⁻⁵ | 3.51 * 10⁻⁵ | | 250.0 | 0.00500 | 1.75 * 10⁻⁵ | 3.50 * 10⁻⁵ | | 300.0 | 0.00420 | 1.48 * 10⁻⁵ | 3.52 * 10⁻⁵ | | 350.0 | 0.00353 | 1.23 * 10⁻⁵ | 3.48 * 10⁻⁵ | | 400.0 | 0.00296 | 1.48 * 10⁻⁵ | 3.51 * 10⁻⁵ | *Table 1: Rates of the reaction between Molecular Bromine and Formic Acid at 25 °C* - **Average reaction rate and instantaneous rate** - By calculating the average reaction rate over shorter and shorter intervals, we can obtain the rate for a specific instant in time, which gives us the instantaneous rate of the reaction at that time. - Figure 5 shows the plot of [Br₂] versus time, based on the data shown in Table 1. Graphically, the instantaneous rate at 100 s after the start of the reaction, say, is given by the slope of the tangent to the curve at that instant. - The instantaneous rate at any other time can be determined in a similar manner. ## 4.1 Reaction of Molecular Bromine and Formic Acid (Solution state) - In aqueous solutions, molecular bromine reacts with formic acid (HCOOH) as follows: - Br₂(aq) + HCOOH(aq) → 2Br⁻(aq) + 2H⁺(aq) + CO₂(g) - Molecular bromine is reddish-brown in color. All the other species in the reaction are colorless. As the reaction progresses, the concentration of Br steadily decreases and its color fades (Figure 3). ## Relation between Concentration and the rate of the reactions - The rate of the bromine-formic acid reaction also depends on the concentration of formic acid. However, by adding a large excess of formic acid to the reaction mixture we can ensure that the concentration of formic acid remains virtually constant throughout the course of the reaction. - Under this condition the change in the amount of formic acid present in solution has no effect on the measured rate. - Let's consider the effect that the bromine concentration has on the rate of reaction. Look at the data in Table 1. Compare the concentration of Br₂ and the reaction rate at t = 50 s and t = 250 s. - Att = 50 s, the bromine concentration is 0.0101 M and the rate of reaction is 3.52 X 10⁻⁵ M/s. - Att = 250 s, the bromine concentration is 0.00500 M and the rate of reaction is 1.75 × 10⁻⁵ M/s. - The concentration at t = 50 s is double the concentration at t = 250 s (0.0101 M versus 0.00500 M), and the rate of reaction at t = 50 s is double the rate at t = 250 s (3.52 × 10⁻⁵ M/s versus 1.75 × 10⁻⁵ M/s). - We see that as the concentration of bromine is doubled, the rate of reaction also doubles. Thus, the rate is directly proportional to the Br₂ concentration (Equation 2). - rate ∝ [Br₂] - rate = k[Br₂] -- Eq. 2 - Where the term k is known as the rate constant, a constant of proportionality between the reaction rate and the concentration of reactant. - This direct proportionality between Br₂ concentration and rate is also supported by plotting the data. - Figure 6 is a plot of the rate versus Br₂ concentration. The fact that this graph is a straight line shows that the rate is directly proportional to the concentration. - The higher the concentration, the higher the rate. - Rearranging the last equation (Equation 2) gives Equation 3 - k = rate / [Br₂] -- Eq. 3 ## 4.2 Decomposition of Hydrogen Peroxide (Gas State) - If one of the products or reactants is a gas, we can use a manometer to find the reaction rate. Consider the decomposition of hydrogen peroxide at 20°C: - 2H₂O₂(aq) → 2H₂O(l) + O₂(g) - In this case, the rate of decomposition can be determined by monitoring the rate of oxygen evolution with a manometer (Figure 7). The oxygen pressure can be readily converted to concentration by using the ideal gas equation in Equation 4: - PV = nRT - P = (n/V)RT = [O₂]RT -- Eq. 4 - Where n/V gives the molarity of oxygen gas. Rearranging the Equation 4, we get the reaction rate, which is given by the rate of oxygen production, can now be written as (Equation 5) - rate = Δ[O₂] / Δτ = 1/RT * ΔP / Δτ -- Eq. 5 - Figure 8 shows the increase in oxygen pressure with time and the determination of an instantaneous rate at 400 min. - To express the rate in the normal units of M/s, we convert mmHg/min to atm/s, then multiply the slope of the tangent (ΔP/Δτ) by 1/RT, as shown in the above Equation 5. ## 5. Factors Affecting Reaction Rate ### I. Reactant concentrations: - Most chemical reactions proceed more quickly if the concentration of one or more reactants is increased. - As reactant concentration increases, the frequency with which the reactant molecules collide increases, leading to increased rates. ### II. Reaction temperature - Reaction rates generally increase as the temperature increases. The bacterial reactions that spoil milk, for instance, proceed more rapidly at room temperature than at the lower temperature of a refrigerator. - Increasing temperature increases the kinetic energies of molecules. As molecules move more rapidly, they collide more frequently and with higher energy, leading to increased reaction rates. ### III. Physical state of the reactants: - Reactants must come together to react. The more readily reactant molecules collide with one another, the more rapidly they react. Reactions may broadly be classified as homogeneous, involving either all gases or all liquids, or as heterogeneous, 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. - For example, a medicine in the form of a fine powder dissolves in the stomach and enters the blood more quickly than the same medicine in the form of a tablet. ### IV. The presence of a catalyst: - Catalysts are agents that increase reaction rates without themselves being used up. - They affect the kinds of collisions (and therefore alter the mechanism) that lead to reaction. Catalysts play many crucial roles in living organism.