Sure, let's solve this problem step-by-step.
1. Convert Volume to Cubic Centimeters:
- The volume given is 0.600 liters.
- To convert liters to cubic centimeters, use the conversion factor [tex]\(1 \text{ liter} = 1000 \text{ cm}^3\)[/tex].
[tex]\[
0.600 \text{ liters} \times 1000 \text{ cm}^3/\text{liter} = 600.0 \text{ cm}^3
\][/tex]
2. Calculate the Density:
- Density ([tex]\(\rho\)[/tex]) is calculated using the formula:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
- Given:
- Mass = 661 grams
- Volume = 600.0 cm³
[tex]\[
\rho = \frac{661 \text{ g}}{600.0 \text{ cm}^3} \approx 1.102 \text{ g/cm}^3
\][/tex]
- Rounding to 3 significant digits:
[tex]\[
\rho \approx 1.10 \text{ g/cm}^3
\][/tex]
3. Identify the Unknown Liquid:
- We need to compare the calculated density with the densities of known liquids:
| Liquid | Density (g/cm³) |
|--------------------|-----------------|
| Tetrahydrofuran | 0.889 |
| Diethylamine | 0.706 |
| Pentane | 0.626 |
| Dimethyl sulfoxide | 1.100 |
- The calculated density (1.10 g/cm³) is closest to the density of Dimethyl sulfoxide.
Conclusion:
- The density of the liquid is 1.10 g/cm³ (rounded to 3 significant digits).
- It is possible to identify the liquid as Dimethyl sulfoxide based on the given options.
