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?
The straight line of y = 3,256x + 0.007 is the calibration curve of Absorbance on the y axis vs concn on the x axis. So insert 0.545 for y (that's the absorbance) and solve for x (that's the concn). I assume that is concn in grams/250 mL although nowhere is that information available. Let's call that number of grams = z.
So z/250 = grams/mL and that x 15 mL = w grams in that 15 mL aliquot. That of course is the amount in the original 100 mL. So (g Cu/mass sample)*100 = (w grams/2.50 gram sample)*100 = %Cu. You're responsible for the correct number of s.f.
To determine the percentage of copper by mass in the ore sample, we can use the calibration curve and the absorbance value obtained from the final solution. Here's how we can calculate it:
1. Calculate the concentration of copper in the final solution:
- Using the equation of the best-fit line: y = (3,256)x + 0.007
- Substitute the absorbance value (y) obtained from the final solution: 0.545 ± 0.004
- Rearrange the equation to solve for x (concentration of copper)
- x = (0.545 - 0.007) / 3,256
2. Calculate the concentration of copper in the original sample:
- Using the dilution factor:
- Concentration of copper in the final solution (from step 1) * (Volume of final solution / Volume of original sample)
- The volume of the final solution is 15.0 mL and the volume of the original sample is 2.500 g * (100.00 mL / 75.0 mL)
- Calculate the concentration of copper in the original sample by multiplying the concentration obtained in step 1 by the dilution factor.
3. Calculate the mass of copper in the original sample:
- Mass of copper in the original sample = Concentration of copper in the original sample * Mass of original sample
4. Calculate the percentage of copper by mass in the ore sample:
- Percentage of copper by mass = (Mass of copper in the original sample / Mass of original sample) * 100
Ensure you perform all calculations using the correct significant figures provided in the question.