Chapter 1, Problem 62RGQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# You set out to determine the density of lead in the laboratory. Using a top loading balance to determine the mass and the water displacement method (Study Question 41) to determine the volume of a variety of pieces of lead, you calculate the following densities: 11.6 g/cm3, 11.8 g/cm3, 11.5 g/cm3, and 12.0 g/cm3. You consult a reference book and find that the accepted value for the density of lead is 11.3 g/cm3. Calculate your average value, percent error, and standard deviation of your results.

Interpretation Introduction

Interpretation: The average, percent error and standard deviation has to be calculated.

Concept introduction:

Precision: Is a measurement indicates how well several determination of the same quantity agree.

Accuracy: Is the agreement of a measurement with the accepted value of the quantity.

Percent error: The difference between measured result and the accepted value.

Percenterror=ErrorinmeasurementAcceptedvalue×100%

Error in measurement = Experimentally determined value - Accepted value.

Explanation

Average density Value:

â€‚Â AverageÂ densityÂ :Â 11.6+Â 11.8Â +Â 11.5Â Â +Â 12.04Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =Â 11.725Â g/cm3.

Hence, the average density value is obtained as shown above. Hence, the average value is 11.725Â g/cm3.

Percent error:

â€‚Â Errorâ€‰inâ€‰measurementÂ =â€‰11.725Â g/cm3Â -Â 11.3Â g/cm3Percentâ€‰errorâ€‰â€‰=â€‰â€‰11.725Â g/cm3Â -Â 11.3Â g/cm311.3Â g/cm3Ã—â€‰100%Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =Â 3.7%

From the above calculation, the percent error is obtained as shown above.

Standard deviation:

â€‚Â SDÂ =Î£|x-Î¼|2Nwhere,â€‰xâ€‰isÂ valuesÂ inÂ theÂ dataÂ set,Â Â Â Â Â Â Â Â Â Â Â Î¼â€‰isâ€‰averageÂ ofÂ theÂ dataÂ setÂ (meanÂ value),Â Â Â Â Â Â Â Â Â Â Â Â NÂ isÂ no.ofÂ dataÂ points.GivenÂ :Â FindÂ meanÂ valueÂ (Î¼):Î¼Â =Â 11

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