Passage
A group of students were given water from two reservoirs and asked to determine water hardness using flame atomic absorbance (AA) spectroscopy. Water hardness can be found by relating the concentration of calcium and magnesium ions to the concentration of carbonate species in the sample using Equation 1.[CO₃^2-] = 2.5[Ca²⁺] + 4.1[Mg²⁺]Equation 1To correlate the concentration of the metal ions to absorbance, the students made standard solutions of MgO (MW = 40.31 g/mol) and CaO (MW = 56.08 g/mol) by diluting small portions of 0.01 M MgO and 0.01 M CaO stock solutions with 2% HNO₃ into 100 mL volumetric flasks. The calibration curves generated from the standard solutions are shown in Figures 1 and 2.
Figure 1 Calibration curve from the absorption of the Ca²⁺ solution standards
Figure 2 Calibration curve from the absorption of the Mg²⁺ solution standardsLanthanum(III) chloride (MM = 245.25) can be used to eliminate chemical interference in a sample by competitively binding to PO₄³⁻, releasing calcium to be atomized in the flame for detection.The students prepared unknown Samples 1 and 2 by mixing 25 mL reservoir water, 16 mL of 2% HNO₃, and 9 mL of 0.1 M LaCl₃ for a total sample volume of 50 mL each. The samples were each tested three times using flame AA spectroscopy, yielding the results reported in Table 1.Table 1 AA Spectroscopy Results for Reservoir Water Samples

-The passage states that the standard solutions were prepared for analysis by diluting small portions of the stock solutions. How does the concentration of the MgO standard solution with the lowest nonzero absorbance compare to the concentration of the MgO stock solution?

Question

Passage
A group of students were given water from two reservoirs and asked to determine water hardness using flame atomic absorbance (AA) spectroscopy. Water hardness can be found by relating the concentration of calcium and magnesium ions to the concentration of carbonate species in the sample using Equation 1.[CO₃^2-] = 2.5[Ca²⁺] + 4.1[Mg²⁺]Equation 1To correlate the concentration of the metal ions to absorbance, the students made standard solutions of MgO (MW = 40.31 g/mol) and CaO (MW = 56.08 g/mol) by diluting small portions of 0.01 M MgO and 0.01 M CaO stock solutions with 2% HNO₃ into 100 mL volumetric flasks. The calibration curves generated from the standard solutions are shown in Figures 1 and 2.

Figure 1 Calibration curve from the absorption of the Ca²⁺ solution standards

Figure 2 Calibration curve from the absorption of the Mg²⁺ solution standardsLanthanum(III) chloride (MM = 245.25) can be used to eliminate chemical interference in a sample by competitively binding to PO₄³⁻, releasing calcium to be atomized in the flame for detection.The students prepared unknown Samples 1 and 2 by mixing 25 mL reservoir water, 16 mL of 2% HNO₃, and 9 mL of 0.1 M LaCl₃ for a total sample volume of 50 mL each. The samples were each tested three times using flame AA spectroscopy, yielding the results reported in Table 1.Table 1 AA Spectroscopy Results for Reservoir Water Samples

-The passage states that the standard solutions were prepared for analysis by diluting small portions of the stock solutions. How does the concentration of the MgO standard solution with the lowest nonzero absorbance compare to the concentration of the MgO stock solution?

Quizplus · Accepted Answer

11ecba2d_11d0_48cb_a3bf_b11920bbfc10_MD0008_00 To make standard solutions of a particular solute, a certain volume, or aliquot, of stock solution is added to a flask and diluted with solvent to achieve the desired solute concentration. The amount of solute in the original aliquot of stock solution and the amount of solute in the diluted standard solution are the same; the only difference is the concentration. A ratio of the concentrations can be used to determine how much larger or smaller the concentration of one solution is compared to the other. The standard solution with the lowest nonzero absorbance value is the solution with the lowest concentration. According to the calibration curve, this would be the 0.0001 M solution of Mg²⁺. The factor by which the concentration of the standard solution is smaller than the concentration of the stock solution is determined by the concentration ratio: Concentration ratio = [stock solution] / [standard solution]Concentration ratio = (1 × 10⁻² M) / (1 × 10⁻⁴ M) = 1 × 10² M The dilution factor can also be determined by the ratio of the volume of the diluted solution and the volume of original solution used. (Choice A) The incorrect factor of 1 × 10⁻⁶ can be obtained by multiplying the concentrations (adding the exponents: −4 + −2 = −6) rather than dividing (subtracting the exponents). (Choice B) The incorrect factor of 1 × 10¹ can be obtained by correctly setting up the molar ratio but incorrectly determining the standard concentration to be 1 × 10⁻³ M rather than 1 × 10⁻⁴ M. (Choice D) The incorrect factor of 1 × 10³ can be obtained by correctly setting up the molar ratio but incorrectly determining the standard concentration to be 1 × 10⁻⁵ M rather than 1 × 10⁻⁴ M. Educational objective: A standard solution can be made by diluting a particular amount of a stock solution. Because the number of solute particles stays the same, the ratio of concentrations can be calculated to determine how much smaller the concentration of the standard solution is compared to the stock solution.