You are provided with a sample of either zinc or tin – we aren’t telling you which! The goal of this simple experiment is to identify which sample you have by determining its density. Uncertainties will be important!

You will measure the mass and the volume of your sample and calculate the density. Since the densities of zinc and tin are nearly equal, it will be necessary to deal with uncertainties correctly in order to distinguish the materials. For each measurement you make, estimate and record its uncertainty. Propagate theses uncertainties to give an overall uncertainty in the calculated value of density.

Use a triple beam laboratory balance to measure the mass of the metal sample. What is the resolution (precision) of the balance? Your lab partner should repeat this measurement independently.

Question 1: What is the mass and its uncertainty of the sample using the triple beam balance?

Repeat the mass measurements using an electronic balance. Calibrate the scale first.

How do I calibrate the scale?

From the manufacturer's instructions: (Link to calibration video)

• Hold the 'Z' key and then hold the on/off button.
• Release both keys, wait for the scale to display 'Cal' and then a series of numbers
• Press 'Z' again
• After the display reads '200.00', place a 200g mass in the center of the scale and press 'Z' again
• Your scale is now calibrated!

Question 2: Which is the more precise mass measurement?

Question 3: What is your best measure of the mass of the sample?

Question 4: Give an estimate of the uncertainty in your mass measurement. Show your work!

Use a caliper to measure the relevant dimensions of the sample. What is the resolution (precision) of the caliper? Estimate any uncertainty in these measurements due to the irregular shape which is difficult to measure with the caliper.

Question 5: What is the volume of the sample using Method 1? What is its uncertainty?

Half-fill the 50 ml beaker with tap water. Immerse the sample completely in the water and measure the change in water level. Measure the inside diameter of the beaker. Calculate the volume of the sample.

Question 6: What is the volume (with its uncertainty) measured using Method 2?

Remove the sample from the water. Place the half-full beaker of water on the electronic balance. Tare (zero) the balance. Suspend the sample completely under water, but not touching the bottom or sides of the beaker. Measure the mass of the displaced water.

Next, use a lab balance and a two-liter volumetric flask to obtain the density of KPTC tap water. Estimate uncertainties in the water’s density.

Question 7: What is the volume (and its uncertainty) of the sample obtained from Method 3?

For each of the volume measurement methods you used, along with the mass of the sample, calculate the density of the sample. Propagate your individual uncertainties to calculate the final uncertainty of the sample density.

Question 8: Is the sample tin or zinc? Comment on your level of confidence, based on your uncertainties. Literature values for the element densities are given in Table 1.

Table 1: Literature values for the densities of tin and zinc.

Identify possible sources of systematic uncertainties which may have influenced your experiment.