Question

a. identifying an unknown metal
transfer the densities calculated from page 11 to the appropriate places below:

density of the unknown metal using volume by calculation: 6.0 cm³

density of the unknown metal using volume by displacement: 6.2 cm³

a. compare the density of your unknown metal to the densities of common substances below:

substance	density (in g/cm³)	substance	density (in g/cm³)
lead	11.4	stainless steel	7.74
silver	10.5	titanium	4.51
zinc	7.14	aluminum	2.70
brass	8.69	ice (0°c)	0.917
copper	8.96	water (at 4°c)	1.00

b. identify your metal by comparing its density with the densities provided above: zinc or titanium
c. explain if the appearance of the metal fits the identity as determined by density.

d. use the following.
percent error = \\(\frac{|\text{experiment density of metal - true density for metal from table}|}{\text{true density for metal from table}}\times100\\%\\)
and show the calculation for the percent error for each density below: (note: because percent error is the absolute value of the difference of the two values divided by the true value, percent error is always positive.)

percent error for density using volume by calculation: 33%

percent error for density using volume by displacement: 15%

e. which method (volume by calculation or volume by displacement) resulted in a higher percent error and a less accurate density? is this what you would expect? explain possible sources of experimental error.

• if the metal is titanium, volume by calculation resulted in a higher percent error. if the metal is zinc, volume by displacement resulted in a higher percent error.
• possible sources of error include measurement errors, air bubbles, sample

Explanation:

Step1: Identify the unknown metal

Given the calculated densities of the unknown metal using volume - by - calculation ($6.0\ g/cm^{3}$) and volume - by - displacement ($6.2\ g/cm^{3}$), comparing with the densities in the table, it is close to the density of titanium ($4.51\ g/cm^{3}$) and zinc ($7.14\ g/cm^{3}$). Let's assume it's titanium for the following error calculations.

Step2: Calculate percent error for volume - by - calculation

The formula for percent error is $\text{Percent Error}=\frac{\vert\text{Experiment Density of Metal}-\text{True Density for Metal from Table}\vert}{\text{True Density for Metal from Table}}\times 100\%$. For volume - by - calculation with a density of $6.0\ g/cm^{3}$ and true density of titanium $4.51\ g/cm^{3}$, we have $\text{Percent Error}=\frac{\vert6.0 - 4.51\vert}{4.51}\times 100\%=\frac{1.49}{4.51}\times 100\%\approx 33\%$.

Step3: Calculate percent error for volume - by - displacement

For volume - by - displacement with a density of $6.2\ g/cm^{3}$ and true density of titanium $4.51\ g/cm^{3}$, we have $\text{Percent Error}=\frac{\vert6.2 - 4.51\vert}{4.51}\times 100\%=\frac{1.69}{4.51}\times 100\%\approx 37.5\%$ (rounded to one decimal place).

Step4: Answer part e

The volume - by - displacement method resulted in a higher percent error. Possible sources of experimental error for volume - by - displacement include air bubbles trapped around the metal sample which can cause an over - estimation of the volume of water displaced, leading to a less accurate density. For volume - by - calculation, errors can come from inaccurate measurements of the dimensions used to calculate the volume. Whether this is expected depends on the experimental setup and measurement techniques. If the object has an irregular shape, volume - by - displacement might be more error - prone due to air - bubble issues.

Answer:

a. The unknown metal's density is close to titanium ($4.51\ g/cm^{3}$) and zinc ($7.14\ g/cm^{3}$).
b. Assuming it's titanium based on density comparison.
c. Without a description of the metal's appearance, we can't fully answer. But if it's titanium, it is a silver - gray metal.
d. Percent error for volume - by - calculation: approximately $33\%$, percent error for volume - by - displacement: approximately $37.5\%$.
e. Volume - by - displacement method resulted in a higher percent error. Possible sources of error for volume - by - displacement are air bubbles around the sample; for volume - by - calculation, errors can be from inaccurate dimension measurements.