The question
Name: ______________________ Date: ____________ Tracking a fading dye by absorbance (10 points)
Data table
Absorbance of a fading dye
A purple dye, D, reacts with hydroxide ions to form a colorless product:
D(aq) + OH⁻(aq) → DOH(aq)
A student mixes a dilute solution of D with a sodium hydroxide solution so that the starting concentrations are [D] = 1.00 × 10⁻⁵ M and [OH⁻] = 0.050 M. Because OH⁻ is present in a far larger amount than D, [OH⁻] stays essentially constant at 0.050 M during the run. The student places the mixture in a cuvette with a path length of 1.00 cm and measures the absorbance at 590 nm, where only D absorbs. The molar absorptivity of D at 590 nm is 9.00 × 10⁴ M⁻¹ cm⁻¹. The student also calculates ln(A) and 1/A for each reading.
| Time (s) | Absorbance, A | ln(A) | 1/A |
|---|---|---|---|
| 0 | 0.900 | −0.105 | 1.11 |
| 100 | 0.708 | −0.345 | 1.41 |
| 200 | 0.557 | −0.585 | 1.80 |
| 300 | 0.438 | −0.826 | 2.28 |
| 400 | 0.345 | −1.064 | 2.90 |
| 500 | 0.271 | −1.306 | 3.69 |
(a) Calculate the concentration of D in the cuvette at 200 s. [1 point]
(b) On the grid provided, plot ln(A) against time for the six readings and draw the best-fit line. [1 point]
(c) Determine the order of the reaction with respect to D. Justify your answer using the data. [2 points]
(d) Calculate the rate constant for the disappearance of D under these conditions. Include units. [2 points]
(e) Calculate the half-life of D under these conditions. [1 point]
(f) The student repeats the experiment with [OH⁻] = 0.100 M and the same starting [D]. The rate constant found from the ln(A) plot is 4.80 × 10⁻³ s⁻¹. (i) Write the rate law for the reaction. (ii) Calculate the value of the rate constant k in that rate law, with units. [2 points]
(g) Another student accidentally sets the spectrophotometer to 560 nm, where the molar absorptivity of D is lower, and repeats the first run. Every absorbance reading is smaller. Would that student's value of the rate constant from part (d) be greater than, less than or equal to the value found at 590 nm? Justify your answer. [1 point]