Question

How to determine the concetnration and mass of the copper in a penny?

Mass of the penny: 2.5g

0.2mL Concentration (wavelength = 626nm): Absorbance: 0.04

0.4mL Concentration (wavelength = 626nm): Absorbance: 0.1

0.6mL Concentration (wavelength = 626nm): Absorbance: 0.15

0.8mL Concentration (wavelength = 626nm): Absorbance: 0.18

penny standard solution (wavelength = 626nm): Absorbance: 0.12

(the stock solution contains 10mg/mL Cu2+)

The Absorbance vs. Concentration graph

the line of best fit : y=0.0523x + 0.0239

Using these values and the equation, calculate the concentration of copper and find the mass of the copper in a penny.

Answer 1

Ans. Given, Stock [Cu²⁺] is in terms of mg/ mL.

So, it’s assumed that the final concentration of all standard aliquots is also in terms of “mg / mL”.

So, the graph is plotted as “mg Cu²⁺ / mL” on X-axis vs respective absorbance on Y-axis.

# Given, best-fit line is y = 0.0523x + 0.0239.

In the graph, Y-axis indicates absorbance and X-axis depicts concentration. The linear regression equation in in form of “ y = mx + x”                    , where-

            y = Y-axis value, depicts absorbance

            x = X-axis value, depicts concertation with respect to its absorbance

            m = slope ; (y/x) ration.

That is, according to the trendline (linear regression) equation y = 0.0523x + 0.0239 obtained from the graph, 1 absorbance unit (1 Y = Y) is equal to 0.0523 units on X-axis (concentration) plus 0.0239.

# Given, abs of unknown = 0.12   

Putting the value y = 0.12 in trendline equation-

            0.12 = 0.0523x + 0.0239

            Or, x = (0.12 – 0.0239) / 0.0523

            Hence, x = 1.837

Hence, [Cu²⁺] in unknown aliquot = 1.837 mg/ mL

# Determine mass of Cu in penny:

We have, [Cu²⁺] in unknown aliquot = 1.837 mg/ mL

To calculate the mass of Cu in penny, following information are required-

I. Volume of original solution which the coin was dissolved

II. Dilution of original penny solution, if any.

III. Volume of standard penny solution made upto by using a small volume of original penny solution, if applicable.

IV. Volume of unknown aliquot made upto.

All these information would be required to calculate the total mass of Cu in the copper.

# Note: You can calculate the total mass of Cu from the data “[Cu²⁺] in unknown aliquot = 1.837 mg/ mL” and multiplying this value with overall dilution factors.

For example, if the total dilution factor (from penny to unknown aliquot) was 1/1000, the total amount of Cu in penny would be 1.837 mg / (1 / 1000) = 1837.0 mg.

Also, you can gradually use C1V1 = C2V2 for each dilution step, beginning from unknown aliquot towards original penny solution to get the total mass of Cu in penny.