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(2 pts) An irregularly shaped unknown metal has a mass of 192.04 grams. You perform a water displacement experiment and find the volume of the metal to be 21.3 mL. What is the unknown metal?

a. aluminum [tex]\((2.7 \, g/mL)\)[/tex]

b. gold [tex]\((19.3 \, g/mL)\)[/tex]

c. lead [tex]\((11.4 \, g/mL)\)[/tex]

d. copper [tex]\((9.0 \, g/mL)\)[/tex]

Calculate the density:

[tex]\[
\text{Density} = \frac{192.04 \, g}{21.3 \, mL}
\][/tex]



Answer :

GinnyAnswer
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]

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