Chem Big Idea 4 Answers

AP Chemistry Big Idea 4 Topics ● ● ● ● ● ● ● ● ● ● ● ● ● Reaction Rate Instantaneous Rate Factors that affect Rxn rate Rate Laws Reaction Order Integrated Rate Laws Reaction order graphs Activation Energy Catalyst Reaction Mechanism Elementary Step Intermediate Rate determining step Example review problems: 1. A(aq) + 2 B(aq) 🡪 3 C(aq) + D(aq) For the reaction above, carried out in solution of 30C, the following kinetic data were obtained: Experiment 1 2 3 4 5 6 Initial Conc. of Reactants (mole.liter-1) Ao Bo 0.240 0.480 0.240 0.120 0.360 0.240 0.120 0.120 0.240 0.0600 0.0140 1.35 Initial Rate of Reaction (mole.liter-1.hr-1) 8.00 2.00 9.00 0.500 1.00 ? (a) Write the rate-law expression for this reaction. (b) Calculate the value of the specific rate constant k at 30°C and specify its units. (c) Calculate the value of the initial rate of this reaction at 30°C for the initial concentrations shown in experiment 6. (d) Assume that the reaction goes to completion. Under the conditions specified for experiment 2, what would be the final molar concentration of C? Answer: (a) Rate = k [A]2[B] (b) = 289 L2mol-2hr-1 (c) Rate = k [A]2[B] = (289 L2mol-2hr-1)(0.0140 mol L-1)2(1.35 mol L-1) = 0.0766 mol L-1hr-1 (d) According to the equation: 2 mol B reacts with 1 mol A, therefore, B is the limiting reagent, while only 0.006 mole/L of A reacts. 1. For a hypothetical chemical reaction that has the stoichiometry 2 X + Y 🡪 Z, the following initial rate data were obtained. All measurements were made at the same temperature. Initial Rate of Formation of Z, (mol.L-1.sec-1) Initial [X]o, (mol.L-1) Initial [Y]o, (mol.L-1) 7.0*10-4 0.20 0.10 1.4*10-3 0.40 0.20 2.8*10-3 0.40 0.40 4.2*10-3 0.60 0.60 (a) Give the rate law for this reaction from the data above. (b) Calculate the specific rate constant for this reaction and specify its units. (c) How long must the reaction proceed to produce a concentration of Z equal to 0.20 molar, if the initial reaction concentrations are [X]o = 0.80 molar, [Y]o = 0.60 molar and [Z]0 = 0 molar? (d) Select from the mechanisms below the one most consistent with the observed data, and explain your choice. In these mechanisms M and N are reaction intermediates. (1) (2) (3) X+Y🡪M X + M 🡪Z X+X🡪M Y+M🡪Z Y🡪M M + X 🡪N N + X 🡪Z (slow) (fast) (fast) (slow) (slow) (fast) (fast) Answer: (a) Rate = k [X]o[Y] (b) k = rate/[Y] = (0.00070mol.L-1.sec-1)/(0.10 mol.L-1) = 0.0070 sec-1 (c) ln co/c = kt; ln 0.60/0.040 = (0.0070)t t = 58 sec. (d) Mechanism 3 is correct. The rate law shows that the slow reaction must involve one Y, consistent with mechanism 3. Mechanisms 1 and 2 would involve both [X] and [Y] in the rate law, not consistent with the rate law. 3. C2H4(g) + H2(g) 🡨🡪 C2H6(g) ΔH°= -137 kJ Account for the following observations regarding the exothermic reaction represented by the equation above. (a) An increase in the pressure of the reactants causes an increase in the reaction rate. (b) A small increase in temperature causes a large increase in the reaction rate. (c) The presence of metallic nickel causes an increase in reaction rate. (d) The presence of powdered nickel causes a larger increase in reaction rate than does the presence of a single piece of nickel of the same mass. Answer: (a) Effective concentrations are increased. So collision frequency is increased. (b) Slight increase in collision frequency occurs. More molecules have enough energy that many more collisions have the necessary activation energy. Raises reaction rate a great deal. (c) Catalytic nickel lowers the activation energy needed for a reaction. More often molecules have the needed energy when they collide. Reaction rate rises. (d) Greater surface area with powdered Ni. More catalytic sites means a greater rate. 4. Answer the following questions regarding the kinetics of chemical reactions. a) The diagram below at right shows the energy pathway for the reaction O3 + NO 🡨🡪 NO2 + O2. Clearly label the following directly on the diagram. i) The activation energy (Ea) for the forward reaction ii) The enthalpy change (ΔH) for the reaction b) Data for the chemical reaction 2A 🡪 B + C were collected by measuring the concentration of A at 10-minute intervals for 80 minutes. The following graphs were generated from analysis of the data. Use the information in the graphs above to answer the following. i) Write the rate-law expression for the reaction. Justify your answer. ii) Describe how to determine the value of the rate constant for the reaction. Answer (a) (b) (i) (ii) (iii) the rate at time, t, is the slope of the tangent to the curve at time t since the reaction is 1st order: ln[N2O3]t - ln[N2O3]o = -kt k= iv (c)i ii k would remain unchanged, it is temperature dependent, not concentration dependent. since the graph of ln[A] is a straight line, this indicates that it its 1st order with respect to A, ∴, rate = k [A] k = - slope of the straight line of the ln[A] vs. time graph 5. An environmental concern is the depletion of O3 in Earth's upper atmosphere, where O3 is normally in equilibrium with O2 and O. A proposed mechanism for the depletion of O3 in the upper atmosphere is shown below. Step I O3 + Cl 🡪 O2 + ClO Step II ClO + O 🡪 Cl + O2 (a) Write a balanced equation for the overall reaction represented by Step I and Step II above. (b) Clearly identify the catalyst in the mechanism above. Justify your answer. (c) Clearly identify the intermediate in the mechanism above. Justify your answer. (d) If the rate law for the overall reaction is found to be rate = k[O3] [Cl], determine the following. (i) The overall order of the reaction (ii) Appropriate units for the rate constant, k (iii) The rate-determining step of the reaction, along with justification for your answer Answer: (a) O3 + O 🡪 2 O2 (b) Cl; used in step I and regenerated in step II, the amount at the end is the same as the beginning (c) ClO; product of step I and used in step II, an intermediate is a material the is produced by a step and consumed later, it does not show as either a product or reactant in the overall equation. (d) (i) second order overall -1 -1 (ii) k unit is M time (iii) step 1. the rate law applies to the concentration of the materials in the slowest step, the rate determining step.