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Sagot :
To determine the type of metal of the unknown sample, we need to calculate its density and compare it to the densities of the known metals listed.
1. Density Calculation for the Unknown Sample:
- Mass of the unknown sample: [tex]\(33.5 \, \text{g}\)[/tex]
- Volume of the unknown sample: [tex]\(3.2 \, \text{cm}^3\)[/tex]
[tex]\[ \text{Density of the unknown sample} = \frac{\text{mass}}{\text{volume}} = \frac{33.5}{3.2} \approx 10.46875 \, \text{g/cm}^3 \][/tex]
2. Density Calculation for Each Known Metal:
- Aluminum:
[tex]\[ \text{Density of aluminum} = \frac{14.6 \, \text{g}}{5.4 \, \text{cm}^3} \approx 2.70 \, \text{g/cm}^3 \][/tex]
- Iron:
[tex]\[ \text{Density of iron} = \frac{33.1 \, \text{g}}{4.2 \, \text{cm}^3} \approx 7.88 \, \text{g/cm}^3 \][/tex]
- Lead:
[tex]\[ \text{Density of lead} = \frac{35.2 \, \text{g}}{3.1 \, \text{cm}^3} \approx 11.35 \, \text{g/cm}^3 \][/tex]
- Magnesium:
[tex]\[ \text{Density of magnesium} = \frac{10.6 \, \text{g}}{6.1 \, \text{cm}^3} \approx 1.74 \, \text{g/cm}^3 \][/tex]
- Silver:
[tex]\[ \text{Density of silver} = \frac{47.2 \, \text{g}}{4.5 \, \text{cm}^3} \approx 10.49 \, \text{g/cm}^3 \][/tex]
3. Comparison of Densities:
- Aluminum: [tex]\(2.70 \, \text{g/cm}^3\)[/tex]
- Iron: [tex]\(7.88 \, \text{g/cm}^3\)[/tex]
- Lead: [tex]\(11.35 \, \text{g/cm}^3\)[/tex]
- Magnesium: [tex]\(1.74 \, \text{g/cm}^3\)[/tex]
- Silver: [tex]\(10.49 \, \text{g/cm}^3\)[/tex]
4. Analyzing the Densities:
- The calculated density of the unknown sample is approximately [tex]\(10.47 \, \text{g/cm}^3\)[/tex].
- Among the given metals:
- Aluminum: 2.70
- Iron: 7.87
- Lead: 11.34
- Magnesium: 1.74
- The calculated density of the unknown sample (10.46875) is closest to the density of silver (10.488888888888889).
Based on this comparison, the unknown sample is most likely to be silver.
Therefore, the correct answer is not listed among the choices provided, as silver is not an option. However, given the numerical data:
The closest match for the unknown sample, considering provided options and calculations, resembles that of silver, which would be indicated as the answer if it was listed.
1. Density Calculation for the Unknown Sample:
- Mass of the unknown sample: [tex]\(33.5 \, \text{g}\)[/tex]
- Volume of the unknown sample: [tex]\(3.2 \, \text{cm}^3\)[/tex]
[tex]\[ \text{Density of the unknown sample} = \frac{\text{mass}}{\text{volume}} = \frac{33.5}{3.2} \approx 10.46875 \, \text{g/cm}^3 \][/tex]
2. Density Calculation for Each Known Metal:
- Aluminum:
[tex]\[ \text{Density of aluminum} = \frac{14.6 \, \text{g}}{5.4 \, \text{cm}^3} \approx 2.70 \, \text{g/cm}^3 \][/tex]
- Iron:
[tex]\[ \text{Density of iron} = \frac{33.1 \, \text{g}}{4.2 \, \text{cm}^3} \approx 7.88 \, \text{g/cm}^3 \][/tex]
- Lead:
[tex]\[ \text{Density of lead} = \frac{35.2 \, \text{g}}{3.1 \, \text{cm}^3} \approx 11.35 \, \text{g/cm}^3 \][/tex]
- Magnesium:
[tex]\[ \text{Density of magnesium} = \frac{10.6 \, \text{g}}{6.1 \, \text{cm}^3} \approx 1.74 \, \text{g/cm}^3 \][/tex]
- Silver:
[tex]\[ \text{Density of silver} = \frac{47.2 \, \text{g}}{4.5 \, \text{cm}^3} \approx 10.49 \, \text{g/cm}^3 \][/tex]
3. Comparison of Densities:
- Aluminum: [tex]\(2.70 \, \text{g/cm}^3\)[/tex]
- Iron: [tex]\(7.88 \, \text{g/cm}^3\)[/tex]
- Lead: [tex]\(11.35 \, \text{g/cm}^3\)[/tex]
- Magnesium: [tex]\(1.74 \, \text{g/cm}^3\)[/tex]
- Silver: [tex]\(10.49 \, \text{g/cm}^3\)[/tex]
4. Analyzing the Densities:
- The calculated density of the unknown sample is approximately [tex]\(10.47 \, \text{g/cm}^3\)[/tex].
- Among the given metals:
- Aluminum: 2.70
- Iron: 7.87
- Lead: 11.34
- Magnesium: 1.74
- The calculated density of the unknown sample (10.46875) is closest to the density of silver (10.488888888888889).
Based on this comparison, the unknown sample is most likely to be silver.
Therefore, the correct answer is not listed among the choices provided, as silver is not an option. However, given the numerical data:
The closest match for the unknown sample, considering provided options and calculations, resembles that of silver, which would be indicated as the answer if it was listed.
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