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The following questions concern the relative concentration uncertainty in
Chapter 13, Problem 13-27(choose chapter or problem)
The following questions concern the relative concentration uncertainty in spectrophotometry.(a) If the relative concentration uncertainty is given by Equation 13-13, use calculusto show that the minimum uncertainty occurs at 36.8% T. What is theabsorbance that minimizes the concentration uncertainty? Assume that Sr isindependent of concentration.(b) Under shot-noise-limited conditions, the relative concentration uncertaintyis given by Equation 13-14. Another form of the equation for the shot-noiselimitedcase is 12s, -kT-l"c In Twhere k is a constant. Use calculus and derive the transmittance and absorbancethat minimize the concentration uncertainty.(c) Describe how you could experimentally determine whether a spectrophotometerwas operating under Case I, Case II, or Case III conditions.
Questions & Answers
QUESTION:
The following questions concern the relative concentration uncertainty in spectrophotometry.(a) If the relative concentration uncertainty is given by Equation 13-13, use calculusto show that the minimum uncertainty occurs at 36.8% T. What is theabsorbance that minimizes the concentration uncertainty? Assume that Sr isindependent of concentration.(b) Under shot-noise-limited conditions, the relative concentration uncertaintyis given by Equation 13-14. Another form of the equation for the shot-noiselimitedcase is 12s, -kT-l"c In Twhere k is a constant. Use calculus and derive the transmittance and absorbancethat minimize the concentration uncertainty.(c) Describe how you could experimentally determine whether a spectrophotometerwas operating under Case I, Case II, or Case III conditions.
ANSWER:Step 1 of 5
The term absorbance highlights light's amount being absorbed by a particular solution while transmittance is the phenomenon of light passing from the solution without getting absorbed.
Beer's law overlooks these phenomena.
(a)
Given Data:
*The transmittance is 36.8 %.
The formula employed to determine the relative uncertainty in concentration is:
The above equation is differentiated,
The minimum value of the relative concentration uncertainty will be achieved when the following situation is agreed upon.
The probability of the situation occurs when,
The above equation is rearranged and the value 
Thus,
Solving the equation,
Thereby, it can be concluded that the relative concentration uncertainty’s least value can occur at 36.8 % of T.