Answered

Select the correct answer.

Marcus measured the masses and volumes of samples of four different substances and calculated their densities. The table shows Marcus's measured and calculated values.

| Substance | Mass (g) | Volume (cm³) | Density (g/cm³) |
|-----------|-----------|---------------|------------------|
| Aluminum | 5.7 | 2.1 | 2.7 |
| Copper | 14.4 | 1.6 | 9.0 |
| Iron | 9.5 | 1.2 | 7.9 |
| Titanium | 8.6 | 1.8 | 4.8 |

Next, Marcus obtained another sample, made of one of the four substances he had already measured. The table shows Marcus's measured values for this unknown sample.

| Substance | Mass (g) | Volume (cm³) |
|-----------|-----------|--------------|
| ? | 9.5 | 2.1 |

What is the unknown sample made of?

A. Aluminum



Answer :

To determine what substance the unknown sample is made of, we need to calculate its density and then compare it to the densities of the substances in the given table.

1. Calculate the density of the unknown sample:

The mass of the unknown sample is given as [tex]\(9.5\)[/tex] grams, and its volume is [tex]\(2.1\)[/tex] cubic centimeters. The density [tex]\(\rho\)[/tex] is calculated using the formula:
[tex]\[ \rho = \frac{\text{mass}}{\text{volume}} \][/tex]

Plugging in the given values:
[tex]\[ \rho = \frac{9.5 \, \text{g}}{2.1 \, \text{cm}^3} \approx 4.523809523809524 \, \text{g/cm}^3 \][/tex]

2. Compare the calculated density with the densities of the known substances:

According to the table:
- Aluminum has a density of [tex]\(2.7 \, \text{g/cm}^3\)[/tex]
- Copper has a density of [tex]\(9.0 \, \text{g/cm}^3\)[/tex]
- Iron has a density of [tex]\(7.9 \, \text{g/cm}^3\)[/tex]
- Titanium has a density of [tex]\(4.8 \, \text{g/cm}^3\)[/tex]

3. Identify the closest match:

The calculated density of the unknown sample is approximately [tex]\(4.523809523809524 \, \text{g/cm}^3\)[/tex]. Comparing this with the densities of the known substances, it is clear that the calculated density is closest to the density of titanium, which has a density of [tex]\(4.8 \, \text{g/cm}^3\)[/tex].

Therefore, the unknown sample is most likely made of titanium.

The correct answer is:
D. titanium