The accepted (true) density of aluminum is 2.70g/cm3 (chem.libretexts.org). If a student, after performing an experiment, found the value to be 2.45g/cm3, calculate the percent error for this value. Ο 9.3% 9.26% Ο 25%
The Correct Answer and Explanation is :
To calculate the percent error, the formula used is:
[
\text{Percent Error} = \left( \frac{\left| \text{Experimental Value} – \text{Accepted Value} \right|}{\text{Accepted Value}} \right) \times 100
]
Given:
- Experimental Value = 2.45 g/cm³
- Accepted Value = 2.70 g/cm³
Substitute the values into the formula:
[
\text{Percent Error} = \left( \frac{\left| 2.45 – 2.70 \right|}{2.70} \right) \times 100
]
First, calculate the absolute difference between the experimental and accepted values:
[
\left| 2.45 – 2.70 \right| = 0.25
]
Now divide this by the accepted value (2.70 g/cm³):
[
\frac{0.25}{2.70} \approx 0.0926
]
Finally, multiply by 100 to convert the decimal into a percentage:
[
0.0926 \times 100 = 9.26\%
]
Thus, the percent error is 9.26%.
Explanation:
Percent error is used to measure the accuracy of an experimental value compared to a known or accepted value. It quantifies the discrepancy between the two values as a percentage of the accepted value. A lower percent error indicates a more accurate result, while a higher percent error suggests a larger difference between the experimental and accepted values.
In this case, the experimental value of aluminum’s density (2.45 g/cm³) is slightly lower than the accepted value (2.70 g/cm³). The calculated percent error of 9.26% indicates that the student’s result deviated by about 9.26% from the true value. This level of error might suggest experimental inconsistencies such as measurement inaccuracies, impurities in the aluminum sample, or errors in the apparatus used.