The molar mass of butane (C4H10) should be 58 g/mol (as calculated from periodic table). If a student measured the molar mass of butane to be 65, what is the % error of the measurement? Use no decimal place, such as “5”, or “13”.
The Correct Answer and Explanation is:
To find the percentage error, we use the following formula: Percentage Error=(∣Measured Value−Actual Value∣Actual Value)×100\text{Percentage Error} = \left( \frac{|\text{Measured Value} – \text{Actual Value}|}{\text{Actual Value}} \right) \times 100
In this problem:
- Measured Value = 65 g/mol
- Actual Value = 58 g/mol (the correct molar mass of butane)
Now substitute into the formula: Percentage Error=(∣65−58∣58)×100=(758)×100≈12.07\text{Percentage Error} = \left( \frac{|65 – 58|}{58} \right) \times 100 = \left( \frac{7}{58} \right) \times 100 \approx 12.07
Rounded to no decimal place, the percentage error is: 12\boxed{12}
Explanation (Approximately 300 Words):
Percentage error is a common way to express the accuracy of a measurement by comparing the measured value to the actual or accepted value. It helps identify how far off a result is from the truth, which is useful in experimental and laboratory settings.
In this case, we are comparing the measured molar mass of butane, 65 g/mol, to the actual molar mass, which is 58 g/mol. The actual value is determined using atomic masses from the periodic table:
- Carbon (C) has an atomic mass of about 12.01 g/mol.
- Hydrogen (H) has an atomic mass of about 1.008 g/mol.
- Butane (C₄H₁₀) has:
4×12.01+10×1.008=48.04+10.08=58.12 g/mol4 \times 12.01 + 10 \times 1.008 = 48.04 + 10.08 = 58.12 \, \text{g/mol},
which is commonly rounded to 58 g/mol.
The student’s value of 65 g/mol is higher than the actual value. The absolute difference is 7 g/mol. To express how significant this difference is relative to the actual value, we divide by 58 and multiply by 100. This gives a percentage error of about 12.07%.
By rounding to the nearest whole number (as instructed), we get a final answer of 12%.
Percentage error helps evaluate the reliability and precision of experimental procedures. A smaller percentage indicates a more accurate measurement, while larger errors suggest the need to improve methods, calibration, or technique.