To determine the identity of the unknown metal, we need to perform the following steps:
1. Calculate the density of the unknown metal:
The formula for density ([tex]\( \rho \)[/tex]) is:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
Given:
[tex]\[
\text{mass} = 192.04 \text{ grams}
\][/tex]
[tex]\[
\text{volume} = 21.3 \text{ mL}
\][/tex]
Substituting the given values into the formula, we get:
[tex]\[
\rho = \frac{192.04 \text{ g}}{21.3 \text{ mL}} \approx 9.015962441314553 \text{ g/mL}
\][/tex]
2. Compare the calculated density with the densities of the given metals:
The densities of the given metals are:
- Aluminum: [tex]\(2.7 \text{ g/mL}\)[/tex]
- Gold: [tex]\(19.3 \text{ g/mL}\)[/tex]
- Lead: [tex]\(11.4 \text{ g/mL}\)[/tex]
- Copper: [tex]\(9.0 \text{ g/mL}\)[/tex]
3. Determine the metal with the closest density to the calculated value:
We observe the calculated density ([tex]\( \approx 9.016 \text{ g/mL} \)[/tex]) and compare it with the provided densities of the metals:
- Aluminum: [tex]\(2.7 \text{ g/mL}\)[/tex] (much lower)
- Gold: [tex]\(19.3 \text{ g/mL}\)[/tex] (much higher)
- Lead: [tex]\(11.4 \text{ g/mL}\)[/tex] (higher)
- Copper: [tex]\(9.0 \text{ g/mL}\)[/tex] (very close)
4. Conclusion:
Among the given options, the density of copper ([tex]\(9.0 \text{ g/mL}\)[/tex]) is the closest to our calculated density ([tex]\( \approx 9.016 \text{ g/mL}\)[/tex]). Therefore, the unknown metal is most likely copper.
Thus, the identity of the unknown metal is copper.
The answer is:
[tex]\[ \boxed{\text{copper}} \][/tex]
