Atomic emission spectroscopy and the method of standard addition are used to det

Question

Atomic emission spectroscopy and the method of standard addition are used to determine the Na^+ concentration and its uncertainty in an unknown sample. Increasing amounts of a 1.75 mu g/mL standard Na^+ solution are added to a series of volumetric flasks containing 10.00 mL of the unknown solution. The volumetric flasks are then diluted to a final volume of 200.0 mL. Atomic emission spectroscopy is then used to measure the emission intensity of each solution. Based on the data in the table above, determine the original concentration of Na^+ as well as its uncertainty in the unknown sample. Report the uncertainty with three significant figures.

Explanation / Answer

Concentration of standard in solution,

with 0 ml std, concentration of standard = 0 ug/ml

with 5 ml std, concentration of standard = 1.75 x 5/200 = 0.04375 ug/ml

with 10 ml std, concentration of standard = 1.75 x 10/200 = 0.08750 ug/ml

with 15 ml stad, concentration of standard = 1.75 x 15/200 = 0.13125 ug/ml

with 20 ml stad, concentration of standard = 1.75 x 20/200 = 0.1750 ug/ml

So, with x be the concentration of Na+ in the unknown solution

From 1 and 2,

x/(x + 0.04375) = 348/491

concentration of Na+ (x) = 0.1065 ug/ml

From 1 and 3,

x/(x + 0.0875) = 348/639

concentration of Na+ (x) = 0.1046 ug/ml

From 1 and 4,

x/(x + 0.13125) = 348/804

concentration of Na+ (x) = 0.1002 ug/ml

From 1 and 5,

x/(x + 0.1750) = 348/945

concentration of Na+ (x) = 0.1020 ug/ml

So, average of all is concentration of Na+ in unknown = 0.1033 ug/ml

variance = sum(x-mean)/4 = 5.8075 x 10^-6

sq.rt.(variance) = 2.410 x 10^-3

Uncertainty = 0.002410 ug/ml

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