Answer to Question #113557 in Inorganic Chemistry for jen

Question #113557
suppose a 100mL solution was prepared using 2.2g of copper ore, but in order to fit on your Beer's Law plot, you had to take a 10mL portion and dilute it to 500mL. The resulting solution had an absorbance value of 0.42. Determine the initial molarity of the 100mL solution and the percent copper in the sample
1
Expert's answer
2020-05-03T15:23:41-0400

To solve this problem, we need a calibration curve of the absorption versus concentration of the copper salt at a given light frequency (Beer's law plot). If you have one, it's best to use the data from it.


According to the Lambert's Beer law:

A = Cl,

A - absorbance

l - the path length

ϵ - the molar absorptivity


Herefrom, С = A / ϵl


ϵl also call slope of the Beer's law plot, this value is a constant for each solution, you have to take it from your plot. Let's accept slope of the Beer's law plot = 432 L/mol.


Cresulting solution = 0.42/432 = 0.000972 mol/L


As our solution is diluted, we calculate the concentration of the original solution:


Cinitial solution = Сresulting solution*Vresulting solution/Vinitial solution = 0.000972*500/10 = 0.0486 mol/L

(Do not forget that we diluted 10 ml of the initial solution!)


Now we can find the mass of copper in the original solution:


m(Cu) = Cinitial solution*Vinitial solution*M(Cu) = 0.0486*0.1*64.55 = 0.309 g


Percent copper in the sample is:

(Cu) = 100%* m(Cu)/m(copper ore) = 100% * 0.309/2.2 = 14..04%.


Answer: initial molarity of the 100mL solution is 0.0486 mol/L and percent copper in the sample is 14.04%.


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