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

Expert's answer

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 = C"\\epsilon"l,

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.

C_{resulting solution} = 0.42/432 = 0.000972 mol/L

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

C_{initial solution} = С_{resulting solution}*V_{resulting solution}/V_{initial 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) = C_{initial solution}*V_{initial solution}*M(Cu) = 0.0486*0.1*64.55 = 0.309 g

Percent copper in the sample is:

"\\omega" (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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