Chapter 3.1, Problem 15LC

Interpretation Introduction

Interpretation : The error and the percent error are to be calculated.

Concept Introduction : Error is the measurement of the difference between the experimental value and the accepted value. The absolute value of the error divided by the accepted value, multiplied by 100%, is the percent error of measurement.

The formula to calculate error is:

  $\text{error = experimental}\text{value}-\text{accepted}\text{value}$

The formula to calculate the percent error is:

  $\text{percent error = }\frac{\left|\text{error}\right|}{\text{accepted}\text{value}}\text{×100\%}$

Answer to Problem 15LC

The error for the boiling point of octane is $-{1.6}^{\circ }\text{C}$ .

The percent error for the boiling point of octane is $1.27\%$ .

Explanation of Solution

The formula to calculate error is,

  $\text{error = experimental}\text{value}-\text{accepted}\text{value}$

The experimental value is ${124.1}^{\circ }\text{C}$ .

The accepted value is ${125.7}^{\circ }\text{C}$ .

To calculate the error, substitute the values in the above equation.

  $\begin{array}{c}\text{error = experimental}\text{value}-\text{accepted}\text{value}\\ \text{=}{124.1}^{\circ }\text{C}-{125.7}^{\circ }\text{C}\\ \text{=}-\text{1}{\text{.6}}^{\circ }\text{C}\end{array}$

The value of error is $-\text{1}{\text{.6}}^{\circ }\text{C}$ .

The magnitude of error is $\text{1}{\text{.6}}^{\circ }\text{C}$ .

The formula to calculate the percent error is,

  $\text{percent error = }\frac{\left|\text{error}\right|}{\text{accepted}\text{value}}\text{×100\%}$

To calculate the percent error, substitute the values in the above equation.

  $\begin{array}{c}\text{percent error = }\frac{\left|\text{error}\right|}{\text{accepted}\text{value}}\text{×100\%}\\ \text{=}\frac{\left|{1.6}^{\circ }\cancel{\text{C}}\right|}{{125.7}^{\circ }\cancel{\text{C}}}\times 100\%\\ =1.27\%\end{array}$

Conclusion

The error for the boiling point of octane is ${1.6}^{\circ }\text{C}$ .

The percent error for the boiling point of octane is $1.27\%$ .