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a) three points Plot ln k or log k vs 1/T Eact = - R (slope) or - 2,303 R (slope) For partial credit, if the 2-point equation is given for the activation evergy, the student may receive a point. A student may also receive a point if it is stated that k is plotted vs 1/T or if ln K or log k is plotted vs T.
b) five points Plot ln PA or log PA vs time. Plot 1/PA vs time. If ln PA vs time is linear, the reaction is first order. If 1/PA vs time is linear, the reaction is second order. If first order, slope = - k1 or - k1 / 2.303. If second order, slope = k2.
1985
Average score = 3.52 a) three points
Points on ordinate take into account the initial amounts of the three substances, and PCl5 line rises while others fall. Lines curved at start and flat after equilibrium. Concentration changes should be consistant with the fact that all coefficients in the equation are unity.
b) two points - First order in both reactants, Inclusion of constant Rate = k [PCl3] [Cl2]
c) one point Reaction requires effective collisions between molecules of PCl3 and Cl2 As concentrations of these molecules increase, the number of effective collisions must increase and the rate of action increases.
d) two points The fraction of colliding molecules with the required activation evergy increases as the temperature rises.
b) 3 points Substitution of any one set of data from experiments 1-5 into the rate equation. For example, experiment #1: 8.00 mol L¯1 hr¯1 = k [0.240 mol / L]2 [0.480 mol / L] k = 289 L2 mol¯2 hr¯1
d) 4 points acknowledgement of a limiting reagent identification of B as the limiting reagent correct mole ratio [C] = (3C / 2B) x 0.120 mol / L of B
1984
Average score 4.81 a) three points; one point for correct form of law and two points for correct methodology without an
error; one point for correct methodology with an error Rate = k[Y]
b) two points
7.0 x 10¯4 mole / L sec = k (0.10 mole / L) k = 7.0 x 10¯3 sec¯1
c) two points
2.3 log co / c = k t 2.3 log 0.60 / 0.40 = (7.0 x 10¯3) (t) t = 58 s
d) two point
Page 8
AP* Kinetics Free Response Questions page 2
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.
1987
a) three points; one each for form of rate law, HgCl2 exponent, C2O42¯ exponent
Rate = k [HgCl2][C2O42¯]2
b) three points; two for correct substitution and arithmetic, one for units 0.52 x 10¯4 M/min = k [0.0836][0.202]2 k = 1.52 x 10¯2 M¯2 min¯1 (note: sometimes this unit is written as L2 mol¯2 min¯1)
c) one point + d[Cl¯] / dt = 0.52 x 10¯4 x (1 C2O4
2¯ / 2 Cl¯) =2.6 x 10¯5 M/min no credit for inverting ratio
d) two points 1.27 x 10¯4 M/min = (1.52 x 10¯2 M¯2 min¯1) (0.0316)[C2O4
1 point for correct order of the reaction with respect to H+
Note: Word explanations can also be used for part (a). The rate order can also be calculated from Experiment 4 and Experiment 1 or 2 or 3 after the orders of [Br−] and [BrO3
−] are determined. (b) Write the rate law for the overall reaction.
rate = k[Br−]1 [BrO3−]1 [H+]2
1 point for correct rate law based on exponents determined in part (a)
(c) Determine the value of the specific rate constant for the reaction at 298 K. Include the correct units.
rate = k[Br−]1 [BrO3
−]1 [H+]2
k = rate
[Br−]1[BrO3−]1[H+]2
Use data from any Experiment – using Experiment #1:
The first-order decomposition of a colored chemical species, X, into colorless products is monitored with a
spectrophotometer by measuring changes in absorbance over time. Species X has a molar absorptivity constant of 5.00 × 103 cm–1 M –1 and the path length of the cuvette containing the reaction mixture is 1.00 cm. The data from the experiment are given in the table below.
(c) Calculate the number of minutes it takes for the absorbance to drop from 0.600 to 0.075.
ln 0
[X][X]
t = −k t
ln 5
41.50 101.20 10
−
−××
= (−3.14 × 10−2 min−1) t
ln (0.125) = (−3.14 × 10−2 min−1) t
–2.08 = (−3.14 × 10−2 min−1) t t = 66.2 min
1 point for correct substitution
1 point for correct answer
Note: students may use half-lives to answer this question.
(d) Calculate the half-life of the reaction. Include units with your answer.
ln 0
[X][X]
t = − k t
ln 0
0
0.5 [X][X]
= (−3.14 × 10−2 min−1) t1/2
ln (0.5) = (−3.14 × 10−2 min−1) t1/2
−0.693 = (−3.14 × 10−2 min−1) t1/2
22.1 min = t1/2 OR
t1/2 = 0.693k
t1/2 = 2 1
0.6933.14 10 min− −×
= 22.1 min
1 point for correct magnitude
1 point for the correct units
(1 point for the half-life equation if no k is given)
(e) Experiments were performed to determine the value of the rate constant for this reaction at various temperatures. Data from these experiments were used to produce the graph below, where T is temperature. This graph can be used to determine the activation energy, Ea , of the reaction.
The decomposition of gas X to produce gases Y and Z is represented by the equation above. In a certain experiment, the reaction took place in a 5.00 L flask at 428 K. Data from this experiment were used to produce the information in the table below, which is plotted in the graphs that follow.