For this question, you must do all of your calculations and your answer with proper sig figs. During an experiment, you use 1.68 g of copper to start your reaction. After you carry through all the different steps, you recover 1.90 g of copper. What is the percent error of the recovered copper? Enter your answer with the correct number of significant figures and the correct sign (but do not enter units).
The Correct Answer and Explanation is:
To calculate the percent error, we use the formula:Percent Error=∣Experimental Value−Accepted Value∣∣Accepted Value∣×100\text{Percent Error} = \frac{\left| \text{Experimental Value} – \text{Accepted Value} \right|}{\left| \text{Accepted Value} \right|} \times 100Percent Error=∣Accepted Value∣∣Experimental Value−Accepted Value∣×100
In this case:
- The experimental value is the mass of copper recovered, which is 1.90 g.
- The accepted value is the initial amount of copper used, which is 1.68 g.
Now, let’s plug these values into the formula:Percent Error=∣1.90−1.68∣∣1.68∣×100\text{Percent Error} = \frac{\left| 1.90 – 1.68 \right|}{\left| 1.68 \right|} \times 100Percent Error=∣1.68∣∣1.90−1.68∣×100Percent Error=0.221.68×100\text{Percent Error} = \frac{0.22}{1.68} \times 100Percent Error=1.680.22×100Percent Error=0.13095×100=13.1\text{Percent Error} = 0.13095 \times 100 = 13.1Percent Error=0.13095×100=13.1
So, the percent error is 13.1%.
Explanation:
- Significant Figures: In the problem, both values (1.68 g and 1.90 g) have 3 significant figures. When performing arithmetic with measured quantities, the result should be expressed with the correct number of significant figures. Here, the difference (0.22) has 2 significant figures, so the final answer should be rounded to 3 significant figures to match the precision of the given data.
- Absolute Error: The absolute difference between the experimental and accepted values is 0.22 g. This is the discrepancy between the amount of copper used and the amount recovered.
- Result: The final percent error is reported as 13.1%, rounded to 3 significant figures.
This calculation shows the discrepancy between the expected and actual recovery of copper, indicating that the recovered amount was slightly higher than initially used, but the error is not excessively large.
