Experiment to determine relationship between inches and centimeters and density of metal cylinder

This experiment involves making measurements and calculations to determine the relationship between inches and centimeters and the density of a solid metal cylinder. The first objective involves using two scales to measure the same length. The second objective involves making measurements to allow us to calculate the density of the metal sample.

To find the density of any material we need to find the mass and volume of a sample.There are several strategies for making sufficient measurements to obtain the information required. The methods chosen for this course rely on a direct measurement of mass and the use of displacement to measure volume.  Performing the experiment will help you become familiar with the use of common lab measuring devices, review the density concept, and practice observing the significant figure conventions to round off calculation results.

When a result based on measurements can be compared to an accepted value, we can express the percent error in the measurement as:

The solid tested will be a pure metal element having an accepted, known density.  You will be asked to find the percent error of the value for the density of the metal sample that you obtain from your measurements.

No special hazards are involved in this exercise.  Nevertheless, the use of safety goggles is required due to the presence of other potentially hazardous materials in the lab area.

Record the values of all measurements in the data section of the report pages.  The procedure of part A provides the data for the length unit relationship.  Parts B and C provide the data needed to determine the density of a metal sample.  Follow any special instructions given in class.

Obtain a meter stick from the equipment cart.  Pull your lab equipment drawer open and use the meter stick to measure across the top width of the drawer face.  The metric side of the stick is marked in centimeters with ten millimeter (0.1 cm) marks in between each centimeter mark.  If the “zero” end of the meter stick is worn or damaged, you may wish to line up a convenient mark (e.g., 10 cm) with one end of the drawer, read the length at the other end of the drawer, and subtract the initial mark value.  In the data section of the lab report pages, record the width of the drawer face in centimeters to the nearest tenth of a centimeter.

Next, turn over the meter stick to use the inch scale.  The scale is marked at one-eighth inch intervals between inches.  Imagine dividing all marks in half so that you can estimate length to the nearest one-sixteenth of an inch.  Measure the top width of the drawer face again recording inches and fractions to the nearest sixteenth inch.  This data will be used to find an experimental conversion factor between inches and centimeters.

Additional Topics

Choose a metal cylinder from the box on the equipment cart.  Each metal sample should be stamped with the symbol of the metal element it is made of.  Record this symbol in the data section.  Measure the mass on the electronic balance. Record the accepted density from the periodic table in the lab.

Follow instructions given in class as to which volumetric cylinder to use for this part (usually 25 mL cylinders available at the equipment cart).  Add tap water to the cylinder until it is about half full.  Set the cylinder on the benchtop and read the markings level with the lowest point in the middle of the curved water level.  This curved water surface is called the meniscus.  Depending on the size of the cylinder you use, estimate and record the volume reading to the nearest 0.1 mL.

Tilt the cylinder and gently slide the metal sample down the inside of the glass until it reaches the bottom.  Do this slowly to avoid breaking the glass or splashing out any of the water.  The metal should be completely submerged in the water.  If not, repeat the procedure from the beginning using more water.  Take another reading of the volume level and record the value.  The difference between the two readings is the volume of water raised or displaced to make room for the metal.  Therefore, it equals the metal sample’s volume.

Following procedures B and C provides you with the two items of data necessary to calculate the density of your metal sample.  Make this calculation and then compare to the accepted value by finding your percent error.

Work the before-lab questions before your lab day.  Your instructor may collect or check that these questions have been done.  In the lab, be sure that all data is recorded by each member of a lab team so that each will have the necessary information to complete the calculations.  After performing the experiment, complete the calculation sections by providing the results indicated.

Show work for each result in the space available or attach additional pages.  Include all unit labels.  Be careful to follow the significant figure conventions as you round off results to the appropriate decimal place.  All pages with the REPORT heading are to be turned in to complete the exercise.

1. Using your textbook or other resources, write the accepted (now considered the defining) relationship between the inch and the centimeter.  That is, record how many centimeters are equal to one inch.

2. A student used the procedure for parts B and C of the exercise and obtained the following data: a mass of metal cylinder, 44.020 g; an initial volume of water in the graduated cylinder, 11.6 mL; volume level after adding a metal sample to water, 17.8 mL.  Use this data and show your work to determine the values listed below.  Show units and round results to appropriate significant digits.

Volume of water displaced by the solid sample ________________

Volume of the metal sample ________________

Density of metal sample ________________

3. Practice using the significant figure conventions.  Record the result of each calculation with correct units and the proper number of significant digits.

554 g - 0.23 g

5 m x 125 m x 2.00 m

5 m ÷ 11.0 s