Crystal violet standard solutions were prepared and their absorbance at a certain wavelength was measured using a spectrophotometer. The path length was 1 cm. The data was plotted using Excel and a line was fit to the points (see below). A sample of unknown concentration was found to have an absorbance of 0.652 at the same wavelength. (a) What is the molar absorptivity of this compound at the certain wavelength? (b) What is the concentration of the unknown sample solution?

(a)  128459 L/mol·cm      

(b)  5.11 x 10⁻⁶ M

Explanation:

This question was incomplete, it is missing the Excel plot and the line fit, please see  attached image of the question.

Crystal violet standard solutions were prepared and their absorbance at a certain wavelength was measured using a spectrophotometer. The path length was 1 cm. The data was plotted using Excel and a line was fit to the points (see below). A sample of unknown concentration was found to have an absorbance of 0.652 at the same wavelength. (a) What is the molar absorptivity of this compound at the certain wavelength? (b) What is the concentration of the unknown sample solution?

(a) This problem we calls for the use of Beer´s law:

A = εcl

where A is the absorbance, ε is the molar absorptivity, c the concentration, and l the path of the cuvette used.

This equation when plotted A vs c will give a straight line since A is a function of c

Thus we can determine ε by using the calibration curve in the Excel plot

y  = 128459 x - 0.0042

the slope of this equation is the molar absorptivity since the length is one, so :

ε = 128459 L/mol·cm      

For part (b)

A = 0.652 = 128459 L/mol·cm x  c  x  1 cm  - 0.0042

⇒ 0.652 +0.0042 = 128459 c = 5.11 x 10⁻⁶ M

In absorbance spectrophotometry it is necessary to work with very dilute solutions to avoid deviations characteristic of high concentrations. One can always dilute the unknown and knowing exactly the dilution factor one can trace back the value for the a more concentrated solution.

1. the question asks the most appropriate, which seems to rule out "all of the above." your choice appears to be the correct one.

2. the protocol described is good for identifying correlation, but not cause and effect. for cause/effect, you need to devise a protocol that will assign the treatment (or not) to groups that have essentially the same "demographics" with respect to all the other variables. your choice regarding control group seems appropriate. random assignment of treatment (choice d) may be appropriate also. (i think you can argue that b and d are just different descriptions of the same method.)

3. d will randomize the birds, but may not guarantee there are 10 in each group. e will do both, so seems the better choice.

comment on question 2

based on the problem statement, it seems clear that confident, attentive drivers are more likely to use daytime running lights. so, the protocol might need to be devised in such a way that the lights would be turned on or off without the driver's knowledge. (an attentive driver will figure it out.) assigning a confident, attentive driver to a group required to drive without running lights might mess with his/her confidence and attentiveness. you don't want your experiment to do that. (nor do you want the experiment to subject a driver to greater risk of accident as a consequence of driving without running lights.) experiments involving human safety are always problematic.