You diluted your solution by a factor of 3. The spectrophotometer reads out a 0.

Question

You diluted your solution by a factor of 3. The spectrophotometer reads out a 0.5 absorbance. What is the absorbance of your original solution? Sometimes you have to dilute a sample more than once. This "serial dilution" usually occurs by a constant factor at each step. For example, a ten-fold serial dilution (i.e., diluting by a factor of 10 each time) will result in soJutions with concentrations of 1 M, 0.1 M, 0.01 M, and so on. To obtain the concentration of the original solution from 0.001 M, you would have to multiple by 100 (10 times 10) since two 1/10-dilution steps occurred. Your 1 mL sample had an absorbance of 2.5 according to the spectrophotometer. You dilute this solution by 1/2 Unfortunately, your sample had an absorbance of 1.3 and needs to be diluted again. You choose to dilute again by 1/2 and your new solution's absorbance is 0.8. How many times was this solution diluted? What is the absorbance of the original sample?

Explanation / Answer

Ans. Beer-Lambert’s Law, A = e C L             - equation 1,               where,

                                                A = Absorbance

                                                e = molar absorptivity at specified wavelength

                                                L = path length (in cm)

                                                C = Molar concentration of the solute

Given,

            I. Original solution os diluted by a factor 3. So, dilution factor = 1: 3, that means 1 volume of original solution is made upto 3 volume, the dilution factor being 1:3.

            II. Absorbance of diluted sample = 0.5

Now, note in above equation that absorbance is directly proportional to the concertation of solution.

So, Absorbance of original solution = Abs. of diluted sample / dilution factor

                                                = 0.5 / (1:3)

                                                = 1.5

Ans. 5. The solution is diluted twice as follows-

1st dilution: the solution is diluted by half, i.e. 1 volume is diluted upto two volumes so that half of the finally diluted solution consists of original solution. Let’s call this solution 1.

So, dilution factor = 1: 2

2nd dilution- Solution 1 is diluted by half to make solution 2.

So, current dilution factor (solution 1 to solution 2) = 1:2

Now,

Total dilution factor = [1st dilution] x [2nd dilution]

                                    = ( ½) x ( ½)

                                    = ¼

Therefore, the solution was total diluted 4 times, i.e. the concentration of solution 2 is one-fourth of the original solution.

Absorbance of original sample = 2.5 as given in text

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