Question

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 5.00x103 cm–1M–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.

[X] (M)	Absorbance (A)	Time (min)
?	0.600	0.0
4.00 x 10-5	0.200	35.0
3.00 x 10-5	0.150	44.2
1.50 x 10-5	0.075	?

(a) Calculate the initial concentration of the unknown species. A = abc

(b) Calculate the rate constant for the first order reaction using the values given for concentration and time. Include units with your answers.

(c) Calculate the minutes it takes for the absorbance to drop from 0.600 to 0.075.

(d) Calculate the half-life of the reaction. Include units with your answer.

(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 Ea, the activation energy. (i) Label the vertical axis of the graph (ii) Explain how to calculate the activation energy from this graph.

Answer 1

d) half life, t_1/2 = 0.693 / k = 0.693 / (0.0314 min) = 22.07 min