A student wanted to determine the amount of copper in a sample of copper ore. The student

dissolved a 2.500 ± 0.001 g piece of copper ore in about 75 mL of nitric acid; then, a
complexing agent was added. The student transferred this solution to a volumetric flask and
used de-ionized water to fill to a final volume of 100.00 ± 0.08 mL. From that volumetric
flask, the student transferred 15.0 mL of solution into a 250.00 ± 0.08 mL volumetric flask
and diluted to the mark with de-ionized water. This final solution (from the 250.00 mL
volumetric flask) showed an absorbance of 0.545 ± 0.004 at 610 nm in the spectrometer.
The student used a series of aqueous copper solutions of known concentration to generate a
calibration curve at 610 nm and obtained a best-fit line of y = (3,256)x + 0.007.
What is the % copper by mass in the ore sample from above with the correct significant figures?

I've worked this below.

To determine the percentage of copper by mass in the ore sample, we need to follow a series of steps:

Step 1: Calculate the concentration of copper in the final solution from the absorbance value.

The calibration curve equation is given as y = (3,256)x + 0.007, where "y" is the absorbance and "x" is the concentration of copper. Since the absorbance value for the final solution is 0.545 ± 0.004, we can substitute this value into the equation and solve for "x."

0.545 ± 0.004 = (3,256)x + 0.007

Solving for "x" gives us:

x = (0.545 ± 0.004 - 0.007) / (3,256)

x = 0.000168 ± 0.000002 (concentration of copper in mol/L)

Step 2: Convert the concentration of copper to its mass in the final solution.

To convert the concentration in mol/L to mass, we need to use the molar mass of copper, which is 63.546 g/mol.

Mass of copper in the final solution = concentration of copper (mol/L) * volume of final solution (L) * molar mass of copper (g/mol)

The volume of the final solution is 250.00 ± 0.08 mL, which is 0.25000 ± 0.00008 L. Substituting the values, we have:

Mass of copper in the final solution = (0.000168 ± 0.000002) * (0.25000 ± 0.00008) * 63.546

Mass of copper in the final solution = 0.00211668 ± 0.00000258 g

Step 3: Calculate the mass percentage of copper in the ore sample.

The mass of the ore sample dissolved was 2.500 ± 0.001 g. To determine the percentage of copper, we divide the mass of copper in the final solution by the mass of the ore sample and multiply by 100.

Percentage of copper = (Mass of copper in the final solution / Mass of the ore sample) * 100

Percentage of copper = (0.00211668 ± 0.00000258 g) / (2.500 ± 0.001 g) * 100

Percentage of copper = 0.0846672 ± 0.0001032 %

Therefore, the percentage of copper by mass in the ore sample, with the correct significant figures, is approximately 0.085 ± 0.0001%.