Into a 50.00mL volumetric flasks were pipetted 10.mL aliquots of a natural water
ID: 600634 • Letter: I
Question
Into a 50.00mL volumetric flasks were pipetted 10.mL aliquots of a natural water sample. Exactly 0.00, 5.00, 10.00, 15.00 and 20.00mL of standard addition solution containing 11.1 pp of Fe were added to each, followed by an excess of thiocyanate ion to give the read complex Fe(SCN).After dilution to volume, the instrument response was measured with a colorimeter for
each of the five solutions. The responses were found to be .240, .437, .621, .809, and 1.009
a)what is the concentration of Fe in the water sample?
b)what is the standard deviation of the concentration of Fe?
Explanation / Answer
Each of the 50 mL flasks contains the same unknown amout of Fe^+3. Flasks 2,3,4 and 5 contain an additional lnow amount of Fe^+3. You will obtain 5 equals in 2 unknowns. Absorbance = a constant x (unknown amt of Fe+3 + known amount of Fe^+3) Least squares analysis allows you to select the value of the constant and the unknown amt of Fe^+3 that minimizes the sum of the squares of the deviation. The water sample should be about 6.8 ppm Fe^+3 (my SWAG). You can write 5 equations in 2 unknowns (where c = a constant and x = the Fe^+3 ppm in the water sample). In #1- #5 you diluted 10 mL of the water sample to 50 mL, so the ppm of the Fe^+3 in the solution is 0.2x. In #2 you diluted 5.00 mL of 11.1 ppm Fe^+3 to 50 mL so known contribution to the total Fe^+3 concentration is 0.1 * 11.1 ppm = 1.11 ppm. #1: 0.240 = c(0.00 + 0.2x) #2: 0.437 = c(1.11 + 0.2x) #3: 0.621 = c(2.22 + 0.2x) #4: 0.809 = c(3.33 + 0.2x) #5: 1.009 = c(4.44 + 0.2x) To do a least squares analysis with 2 unknowns (c and x) you can rewrite the equations in this form (where d represents the deviation of the function- sum of the deviation^2 = sum of (absorbance - c known Fe^+3 - c unknown Fe^3)^2 Take the partial derivative of function with respect to each of the variables (c and unknown Fe^3 conc) in turn and set each drivative to zero. This yields two equations that can be solved simultaneously. The water should be about 6.9 ppm Fe^+3 (a SWAG).
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