To identify the most likely substance given the data, let's follow these steps:
1. Given Data:
- Mass of the substance: [tex]\( 46.9 \)[/tex] grams
- Volume of the substance: [tex]\( 3.5 \)[/tex] cm[tex]\(^3\)[/tex]
- Temperature: [tex]\( 23^\circ \)[/tex]C (room temperature)
2. Calculate the Density of the Unknown Substance:
[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{46.9 \, \text{grams}}{3.5 \, \text{cm}^3} = 13.4 \, \text{g/cm}^3
\][/tex]
3. Compare with Given Densities for Different Substances:
- Density of molybdenum: [tex]\( 10.28 \, \text{g/cm}^3 \)[/tex]
- Density of mercury: [tex]\( 13.53 \, \text{g/cm}^3 \)[/tex]
- Density of hafnium: [tex]\( 13.31 \, \text{g/cm}^3 \)[/tex]
- Density of lead: [tex]\( 11.34 \, \text{g/cm}^3 \)[/tex]
4. Find the Closest Density:
- The calculated density of the unknown substance is [tex]\( 13.4 \, \text{g/cm}^3 \)[/tex].
- Comparing this with the given densities:
- The density of molybdenum: [tex]\( 10.28 \, \text{g/cm}^3 \)[/tex] is quite different from 13.4 g/cm[tex]\(^3\)[/tex].
- The density of mercury: [tex]\( 13.53 \, \text{g/cm}^3 \)[/tex] is close but not as close as hafnium.
- The density of hafnium: [tex]\( 13.31 \, \text{g/cm}^3 \)[/tex] is very close to 13.4 g/cm[tex]\(^3\)[/tex].
- The density of lead: [tex]\( 11.34 \, \text{g/cm}^3 \)[/tex] is also quite different from 13.4 g/cm[tex]\(^3\)[/tex].
Therefore, the closest match in terms of density is hafnium.
5. Room Temperature Consideration:
- While mercury has a density close to [tex]\( 13.4 \, \text{g/cm}^3 \)[/tex], it is liquid at [tex]\( 23^\circ \)[/tex]C because its melting point is [tex]\(-39^\circ \)[/tex]C.
- Hafnium, having a melting point of [tex]\( 2,233^\circ \)[/tex]C, remains solid at [tex]\( 23^\circ \)[/tex]C.
Therefore, taking into consideration both the density and the state of the substance at room temperature, the most likely identity of the substance is:
C. hafnium
